





Network Working Group                                        S. Shalunov
Request for Comments: 4656                                 B. Teitelbaum
Category: Standards Track                                        A. Karp
                                                                J. Boote
                                                            M. Zekauskas
                                                               Internet2
                                                          September 2006


             A One-way Active Measurement Protocol (OWAMP)

Status of This Memo

   This document specifies an Internet standards track protocol for the
   Internet community, and requests discussion and suggestions for
   improvements.  Please refer to the current edition of the "Internet
   Official Protocol Standards" (STD 1) for the standardization state
   and status of this protocol.  Distribution of this memo is unlimited.

Copyright Notice

   Copyright (C) The Internet Society (2006).

Abstract

   The One-Way Active Measurement Protocol (OWAMP) measures
   unidirectional characteristics such as one-way delay and one-way
   loss.  High-precision measurement of these one-way IP performance
   metrics became possible with wider availability of good time sources
   (such as GPS and CDMA).  OWAMP enables the interoperability of these
   measurements.

Table of Contents

   1. Introduction ....................................................2
      1.1. Relationship of Test and Control Protocols .................3
      1.2. Logical Model ..............................................4
   2. Protocol Overview ...............................................5
   3. OWAMP-Control ...................................................6
      3.1. Connection Setup ...........................................6
      3.2. Integrity Protection (HMAC) ...............................11
      3.3. Values of the Accept Field ................................11
      3.4. OWAMP-Control Commands ....................................12
      3.5. Creating Test Sessions ....................................13
      3.6. Send Schedules ............................................18
      3.7. Starting Test Sessions ....................................19
      3.8. Stop-Sessions .............................................20
      3.9. Fetch-Session .............................................24



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   4. OWAMP-Test .....................................................27
      4.1. Sender Behavior ...........................................28
           4.1.1. Packet Timings .....................................28
           4.1.2. OWAMP-Test Packet Format and Content ...............29
      4.2. Receiver Behavior .........................................33
   5. Computing Exponentially Distributed Pseudo-Random Numbers ......35
      5.1. High-Level Description of the Algorithm ...................35
      5.2. Data Types, Representation, and Arithmetic ................36
      5.3. Uniform Random Quantities .................................37
   6. Security Considerations ........................................38
      6.1. Introduction ..............................................38
      6.2. Preventing Third-Party Denial of Service ..................38
      6.3. Covert Information Channels ...............................39
      6.4. Requirement to Include AES in Implementations .............39
      6.5. Resource Use Limitations ..................................39
      6.6. Use of Cryptographic Primitives in OWAMP ..................40
      6.7. Cryptographic Primitive Replacement .......................42
      6.8. Long-term Manually Managed Keys ...........................43
      6.9. (Not) Using Time as Salt ..................................44
      6.10. The Use of AES-CBC and HMAC ..............................44
   7. Acknowledgements ...............................................45
   8. IANA Considerations ............................................45
   9. Internationalization Considerations ............................46
   10. References ....................................................46
      10.1. Normative References .....................................46
      10.2. Informative References ...................................47
   Appendix A: Sample C Code for Exponential Deviates ................49
   Appendix B: Test Vectors for Exponential Deviates .................54

1.  Introduction

   The IETF IP Performance Metrics (IPPM) working group has defined
   metrics for one-way packet delay [RFC2679] and loss [RFC2680] across
   Internet paths.  Although there are now several measurement platforms
   that implement collection of these metrics [SURVEYOR] [SURVEYOR-INET]
   [RIPE] [BRIX], there is not currently a standard that would permit
   initiation of test streams or exchange of packets to collect
   singleton metrics in an interoperable manner.

   With the increasingly wide availability of affordable global
   positioning systems (GPS) and CDMA-based time sources, hosts
   increasingly have available to them very accurate time sources,
   either directly or through their proximity to Network Time Protocol
   (NTP) primary (stratum 1) time servers.  By standardizing a technique
   for collecting IPPM one-way active measurements, we hope to create an
   environment where IPPM metrics may be collected across a far broader
   mesh of Internet paths than is currently possible.  One particularly
   compelling vision is of widespread deployment of open OWAMP servers



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   that would make measurement of one-way delay as commonplace as
   measurement of round-trip time using an ICMP-based tool like ping.

   Additional design goals of OWAMP include: being hard to detect and
   manipulate, security, logical separation of control and test
   functionality, and support for small test packets.  (Being hard to
   detect makes interference with measurements more difficult for
   intermediaries in the middle of the network.)

   OWAMP test traffic is hard to detect because it is simply a stream of
   UDP packets from and to negotiated port numbers, with potentially
   nothing static in the packets (size is negotiated, as well).  OWAMP
   also supports an encrypted mode that further obscures the traffic and
   makes it impossible to alter timestamps undetectably.

   Security features include optional authentication and/or encryption
   of control and test messages.  These features may be useful to
   prevent unauthorized access to results or man-in-the-middle attacks
   that attempt to provide special treatment to OWAMP test streams or
   that attempt to modify sender-generated timestamps to falsify test
   results.

   In this document, the key words "MUST", "REQUIRED", "SHOULD",
   "RECOMMENDED", and "MAY" are to be interpreted as described in
   [RFC2119].

1.1.  Relationship of Test and Control Protocols

   OWAMP actually consists of two inter-related protocols: OWAMP-Control
   and OWAMP-Test.  OWAMP-Control is used to initiate, start, and stop
   test sessions and to fetch their results, whereas OWAMP-Test is used
   to exchange test packets between two measurement nodes.

   Although OWAMP-Test may be used in conjunction with a control
   protocol other than OWAMP-Control, the authors have deliberately
   chosen to include both protocols in the same RFC to encourage the
   implementation and deployment of OWAMP-Control as a common
   denominator control protocol for one-way active measurements.  Having
   a complete and open one-way active measurement solution that is
   simple to implement and deploy is crucial to ensuring a future in
   which inter-domain one-way active measurement could become as
   commonplace as ping.  We neither anticipate nor recommend that
   OWAMP-Control form the foundation of a general-purpose extensible
   measurement and monitoring control protocol.

   OWAMP-Control is designed to support the negotiation of one-way
   active measurement sessions and results retrieval in a
   straightforward manner.  At session initiation, there is a



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   negotiation of sender and receiver addresses and port numbers,
   session start time, session length, test packet size, the mean
   Poisson sampling interval for the test stream, and some attributes of
   the very general [RFC 2330] notion of packet type, including packet
   size and per-hop behavior (PHB) [RFC2474], which could be used to
   support the measurement of one-way network characteristics across
   differentiated services networks.  Additionally, OWAMP-Control
   supports per-session encryption and authentication for both test and
   control traffic, measurement servers that can act as proxies for test
   stream endpoints, and the exchange of a seed value for the pseudo-
   random Poisson process that describes the test stream generated by
   the sender.

   We believe that OWAMP-Control can effectively support one-way active
   measurement in a variety of environments, from publicly accessible
   measurement beacons running on arbitrary hosts to network monitoring
   deployments within private corporate networks.  If integration with
   Simple Network Management Protocol (SNMP) or proprietary network
   management protocols is required, gateways may be created.

1.2.  Logical Model

   Several roles are logically separated to allow for broad flexibility
   in use.  Specifically, we define the following:

   Session-Sender      The sending endpoint of an OWAMP-Test session;

   Session-Receiver    The receiving endpoint of an OWAMP-Test session;

   Server              An end system that manages one or more OWAMP-Test
                       sessions, is capable of configuring per-session
                       state in session endpoints, and is capable of
                       returning the results of a test session;

   Control-Client      An end system that initiates requests for
                       OWAMP-Test sessions, triggers the start of a set
                       of sessions, and may trigger their termination;
                       and

   Fetch-Client        An end system that initiates requests to fetch
                       the results of completed OWAMP-Test sessions.










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   One possible scenario of relationships between these roles is shown
   below.

       +----------------+               +------------------+
       | Session-Sender |--OWAMP-Test-->| Session-Receiver |
       +----------------+               +------------------+
         ^                                     ^
         |                                     |
         |                                     |
         |                                     |
         |  +----------------+<----------------+
         |  |     Server     |<-------+
         |  +----------------+        |
         |    ^                       |
         |    |                       |
         | OWAMP-Control         OWAMP-Control
         |    |                       |
         v    v                       v
       +----------------+     +-----------------+
       | Control-Client |     |   Fetch-Client  |
       +----------------+     +-----------------+

   (Unlabeled links in the figure are unspecified by this document and
   may be proprietary protocols.)

   Different logical roles can be played by the same host.  For example,
   in the figure above, there could actually be only two hosts: one
   playing the roles of Control-Client, Fetch-Client, and Session-
   Sender, and the other playing the roles of Server and Session-
   Receiver.  This is shown below.

       +-----------------+                   +------------------+
       | Control-Client  |<--OWAMP-Control-->| Server           |
       | Fetch-Client    |                   |                  |
       | Session-Sender  |---OWAMP-Test----->| Session-Receiver |
       +-----------------+                   +------------------+

   Finally, because many Internet paths include segments that transport
   IP over ATM, delay and loss measurements can include the effects of
   ATM segmentation and reassembly (SAR).  Consequently, OWAMP has been
   designed to allow for small test packets that would fit inside the
   payload of a single ATM cell (this is only achieved in
   unauthenticated mode).








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2.  Protocol Overview

   As described above, OWAMP consists of two inter-related protocols:
   OWAMP-Control and OWAMP-Test.  The former is layered over TCP and is
   used to initiate and control measurement sessions and to fetch their
   results.  The latter protocol is layered over UDP and is used to send
   singleton measurement packets along the Internet path under test.

   The initiator of the measurement session establishes a TCP connection
   to a well-known port, 861, on the target point and this connection
   remains open for the duration of the OWAMP-Test sessions.  An OWAMP
   server SHOULD listen to this well-known port.

   OWAMP-Control messages are transmitted only before OWAMP-Test
   sessions are actually started and after they are completed (with the
   possible exception of an early Stop-Sessions message).

   The OWAMP-Control and OWAMP-Test protocols support three modes of
   operation: unauthenticated, authenticated, and encrypted.  The
   authenticated or encrypted modes require that endpoints possess a
   shared secret.

   All multi-octet quantities defined in this document are represented
   as unsigned integers in network byte order unless specified
   otherwise.

3.  OWAMP-Control

   The type of each OWAMP-Control message can be found after reading the
   first 16 octets.  The length of each OWAMP-Control message can be
   computed upon reading its fixed-size part.  No message is shorter
   than 16 octets.

   An implementation SHOULD expunge unused state to prevent denial-of-
   service attacks, or unbounded memory usage, on the server.  For
   example, if the full control message is not received within some
   number of minutes after it is expected, the TCP connection associated
   with the OWAMP-Control session SHOULD be dropped.  In absence of
   other considerations, 30 minutes seems like a reasonable upper bound.

3.1.  Connection Setup

   Before either a Control-Client or a Fetch-Client can issue commands
   to a Server, it has to establish a connection to the server.

   First, a client opens a TCP connection to the server on a well-known
   port 861.  The server responds with a server greeting:




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      0                   1                   2                   3
      0 1 2 3 4 5 6 7 8 9 0 1 2 3 4 5 6 7 8 9 0 1 2 3 4 5 6 7 8 9 0 1
     +-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+
     |                                                               |
     |                      Unused (12 octets)                       |
     |                                                               |
     |+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-++-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+
     |                            Modes                              |
     +-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+
     |                                                               |
     |                     Challenge (16 octets)                     |
     |                                                               |
     |                                                               |
     +-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+
     |                                                               |
     |                        Salt (16 octets)                       |
     |                                                               |
     |                                                               |
     +-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+
     |                        Count (4 octets)                       |
     +-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+
     |                                                               |
     |                        MBZ (12 octets)                        |
     |                                                               |
     +-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+

   The following Mode values are meaningful: 1 for unauthenticated, 2
   for authenticated, and 4 for encrypted.  The value of the Modes field
   sent by the server is the bit-wise OR of the mode values that it is
   willing to support during this session.  Thus, the last three bits of
   the Modes 32-bit value are used.  The first 29 bits MUST be zero.  A
   client MUST ignore the values in the first 29 bits of the Modes
   value.  (This way, the bits are available for future protocol
   extensions.  This is the only intended extension mechanism.)

   Challenge is a random sequence of octets generated by the server; it
   is used subsequently by the client to prove possession of a shared
   secret in a manner prescribed below.

   Salt and Count are parameters used in deriving a key from a shared
   secret as described below.

   Salt MUST be generated pseudo-randomly (independently of anything
   else in this document).

   Count MUST be a power of 2.  Count MUST be at least 1024.  Count
   SHOULD be increased as more computing power becomes common.




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   If the Modes value is zero, the server does not wish to communicate
   with the client and MAY close the connection immediately.  The client
   SHOULD close the connection if it receives a greeting with Modes
   equal to zero.  The client MAY close the connection if the client's
   desired mode is unavailable.

   Otherwise, the client MUST respond with the following Set-Up-Response
   message:

      0                   1                   2                   3
      0 1 2 3 4 5 6 7 8 9 0 1 2 3 4 5 6 7 8 9 0 1 2 3 4 5 6 7 8 9 0 1
     +-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+
     |                             Mode                              |
     +-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+
     |                                                               |
     .                                                               .
     .                       KeyID (80 octets)                       .
     .                                                               .
     |                                                               |
     +-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+
     |                                                               |
     .                                                               .
     .                       Token (64 octets)                       .
     .                                                               .
     |                                                               |
     +-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+
     |                                                               |
     .                                                               .
     .                     Client-IV (16 octets)                     .
     .                                                               .
     |                                                               |
     +-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+

   Here Mode is the mode that the client chooses to use during this
   OWAMP-Control session.  It will also be used for all OWAMP-Test
   sessions started under control of this OWAMP-Control session.  In
   Mode, one or zero bits MUST be set within last three bits.  If it is
   one bit that is set within the last three bits, this bit MUST
   indicate a mode that the server agreed to use (i.e., the same bit
   MUST have been set by the server in the server greeting).  The first
   29 bits of Mode MUST be zero.  A server MUST ignore the values of the
   first 29 bits.  If zero Mode bits are set by the client, the client
   indicates that it will not continue with the session; in this case,
   the client and the server SHOULD close the TCP connection associated
   with the OWAMP-Control session.






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   In unauthenticated mode, KeyID, Token, and Client-IV are unused.
   Otherwise, KeyID is a UTF-8 string, up to 80 octets in length (if the
   string is shorter, it is padded with zero octets), that tells the
   server which shared secret the client wishes to use to authenticate
   or encrypt, while Token is the concatenation of a 16-octet challenge,
   a 16-octet AES Session-key used for encryption, and a 32-octet HMAC-
   SHA1 Session-key used for authentication.  The token itself is
   encrypted using the AES (Advanced Encryption Standard) [AES] in
   Cipher Block Chaining (CBC). Encryption MUST be performed using an
   Initialization Vector (IV) of zero and a key derived from the shared
   secret associated with KeyID.  (Both the server and the client use
   the same mappings from KeyIDs to shared secrets.  The server, being
   prepared to conduct sessions with more than one client, uses KeyIDs
   to choose the appropriate secret key; a client would typically have
   different secret keys for different servers.  The situation is
   analogous to that with passwords.)

   The shared secret is a passphrase; it MUST not contain newlines.  The
   secret key is derived from the passphrase using a password-based key
   derivation function PBKDF2 (PKCS #5) [RFC2898].  The PBKDF2 function
   requires several parameters: the PRF is HMAC-SHA1 [RFC2104]; the salt
   and count are as transmitted by the server.

   AES Session-key, HMAC Session-key and Client-IV are generated
   randomly by the client.  AES Session-key and HMAC Session-key MUST be
   generated with sufficient entropy not to reduce the security of the
   underlying cipher [RFC4086].  Client-IV merely needs to be unique
   (i.e., it MUST never be repeated for different sessions using the
   same secret key; a simple way to achieve that without the use of
   cumbersome state is to generate the Client-IV values using a
   cryptographically secure pseudo-random number source:  if this is
   done, the first repetition is unlikely to occur before 2^64 sessions
   with the same secret key are conducted).


















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   The server MUST respond with the following Server-Start message:

      0                   1                   2                   3
      0 1 2 3 4 5 6 7 8 9 0 1 2 3 4 5 6 7 8 9 0 1 2 3 4 5 6 7 8 9 0 1
     +-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+
     |                                                               |
     |                         MBZ (15 octets)                       |
     |                                                               |
     |                                               +-+-+-+-+-+-+-+-+
     |                                               |   Accept      |
     +-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+
     |                                                               |
     |                     Server-IV (16 octets)                     |
     |                                                               |
     |                                                               |
     +-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+
     |                     Start-Time (Timestamp)                    |
     |                                                               |
     +-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+
     |                         MBZ (8 octets)                        |
     |                                                               |
     +-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+

   The MBZ parts MUST be zero.  The client MUST ignore their value.  MBZ
   (MUST be zero) fields here and after have the same semantics: the
   party that sends the message MUST set the field so that all bits are
   equal to zero; the party that interprets the message MUST ignore the
   value.  (This way, the field could be used for future extensions.)

   Server-IV is generated randomly by the server.  In unauthenticated
   mode, Server-IV is unused.

   The Accept field indicates the server's willingness to continue
   communication.  A zero value in the Accept field means that the
   server accepts the authentication and is willing to conduct further
   transactions.  Non-zero values indicate that the server does not
   accept the authentication or, for some other reason, is not willing
   to conduct further transactions in this OWAMP-Control session.  The
   full list of available Accept values is described in Section 3.3,
   "Values of the Accept Field".

   If a negative (non-zero) response is sent, the server MAY (and the
   client SHOULD) close the connection after this message.

   Start-Time is a timestamp representing the time when the current
   instantiation of the server started operating.  (For example, in a
   multi-user general purpose operating system, it could be the time
   when the server process was started.)  If Accept is non-zero, Start-



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   Time SHOULD be set so that all of its bits are zeros.  In
   authenticated and encrypted modes, Start-Time is encrypted as
   described in Section 3.4, "OWAMP-Control Commands", unless Accept is
   non-zero.  (Authenticated and encrypted mode cannot be entered unless
   the control connection can be initialized.)

   Timestamp format is described in Section 4.1.2.  The same
   instantiation of the server SHOULD report the same exact Start-Time
   value to each client in each session.

   The previous transactions constitute connection setup.

3.2.  Integrity Protection (HMAC)

   Authentication of each message (also referred to as a command in this
   document) in OWAMP-Control is accomplished by adding an HMAC to it.
   The HMAC that OWAMP uses is HMAC-SHA1 truncated to 128 bits.  Thus,
   all HMAC fields are 16 octets.  An HMAC needs a key.  The HMAC
   Session-key is communicated along with the AES Session-key during
   OWAMP-Control connection setup.  The HMAC Session-key SHOULD be
   derived independently of the AES Session-key (an implementation, of
   course, MAY use the same mechanism to generate the random bits for
   both keys).  Each HMAC sent covers everything sent in a given
   direction between the previous HMAC (but not including it) and up to
   the beginning of the new HMAC.  This way, once encryption is set up,
   each bit of the OWAMP-Control connection is authenticated by an HMAC
   exactly once.

   When encrypting, authentication happens before encryption, so HMAC
   blocks are encrypted along with the rest of the stream.  When
   decrypting, the order, of course, is reversed: first one decrypts,
   then one checks the HMAC, then one proceeds to use the data.

   The HMAC MUST be checked as early as possible to avoid using and
   propagating corrupt data.

   In open mode, the HMAC fields are unused and have the same semantics
   as MBZ fields.

3.3.  Values of the Accept Field

   Accept values are used throughout the OWAMP-Control protocol to
   communicate the server response to client requests.  The full set of
   valid Accept field values are as follows:

     0    OK.

     1    Failure, reason unspecified (catch-all).



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     2    Internal error.

     3    Some aspect of request is not supported.

     4    Cannot perform request due to permanent resource limitations.

     5    Cannot perform request due to temporary resource limitations.

   All other values are reserved.  The sender of the message MAY use the
   value of 1 for all non-zero Accept values.  A message sender SHOULD
   use the correct Accept value if it is going to use other values.  The
   message receiver MUST interpret all values of Accept other than these
   reserved values as 1.  This way, other values are available for
   future extensions.

3.4.  OWAMP-Control Commands

   In authenticated or encrypted mode (which are identical as far as
   OWAMP-Control is concerned, and only differ in OWAMP-Test), all
   further communications are encrypted with the AES Session-key (using
   CBC mode) and authenticated with HMAC Session-key.  The client
   encrypts everything it sends through the just-established OWAMP-
   Control connection using stream encryption with Client-IV as the IV.
   Correspondingly, the server encrypts its side of the connection using
   Server-IV as the IV.

   The IVs themselves are transmitted in cleartext.  Encryption starts
   with the block immediately following the block containing the IV.
   The two streams (one going from the client to the server and one
   going back) are encrypted independently, each with its own IV, but
   using the same key (the AES Session-key).

   The following commands are available for the client: Request-Session,
   Start-Sessions, Stop-Sessions, and Fetch-Session.  The command Stop-
   Sessions is available to both the client and the server.  (The server
   can also send other messages in response to commands it receives.)

   After the client sends the Start-Sessions command and until it both
   sends and receives (in an unspecified order) the Stop-Sessions
   command, it is said to be conducting active measurements.  Similarly,
   the server is said to be conducting active measurements after it
   receives the Start-Sessions command and until it both sends and
   receives (in an unspecified order) the Stop-Sessions command.

   While conducting active measurements, the only command available is
   Stop-Sessions.

   These commands are described in detail below.



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3.5.  Creating Test Sessions

   Individual one-way active measurement sessions are established using
   a simple request/response protocol.  An OWAMP client MAY issue zero
   or more Request-Session messages to an OWAMP server, which MUST
   respond to each with an Accept-Session message.  An Accept-Session
   message MAY refuse a request.












































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   The format of Request-Session message is as follows:

      0                   1                   2                   3
      0 1 2 3 4 5 6 7 8 9 0 1 2 3 4 5 6 7 8 9 0 1 2 3 4 5 6 7 8 9 0 1
     +-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+
     |      1        |  MBZ  | IPVN  |  Conf-Sender  | Conf-Receiver |
     +-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+
     |                  Number of Schedule Slots                     |
     +-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+
     |                      Number of Packets                        |
     +-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+
     |          Sender Port          |         Receiver Port         |
     +-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+
     |                        Sender Address                         |
     +-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+
     |                                                               |
     |           Sender Address (cont.) or MBZ (12 octets)           |
     |                                                               |
     +-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+
     |                        Receiver Address                       |
     +-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+
     |                                                               |
     |           Receiver Address (cont.) or MBZ (12 octets)         |
     |                                                               |
     +-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+
     |                                                               |
     |                        SID (16 octets)                        |
     |                                                               |
     |                                                               |
     +-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+
     |                         Padding Length                        |
     +-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+
     |                           Start Time                          |
     |                                                               |
     +-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+
     |                       Timeout, (8 octets)                     |
     |                                                               |
     +-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+
     |                       Type-P Descriptor                       |
     +-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+
     |                         MBZ (8 octets)                        |
     |                                                               |
     +-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+
     |                                                               |
     |                       HMAC (16 octets)                        |
     |                                                               |
     |                                                               |
     +-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+



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   This is immediately followed by one or more schedule slot
   descriptions (the number of schedule slots is specified in the
   "Number of Schedule Slots" field above):

      0                   1                   2                   3
      0 1 2 3 4 5 6 7 8 9 0 1 2 3 4 5 6 7 8 9 0 1 2 3 4 5 6 7 8 9 0 1
     +-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+
     |    Slot Type  |                                               |
     +-+-+-+-+-+-+-+-+         MBZ (7 octets)                        |
     |                                                               |
     +-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+
     |                 Slot Parameter (Timestamp)                    |
     |                                                               |
     +-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+

   These are immediately followed by HMAC:

      0                   1                   2                   3
      0 1 2 3 4 5 6 7 8 9 0 1 2 3 4 5 6 7 8 9 0 1 2 3 4 5 6 7 8 9 0 1
     +-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+
     |                                                               |
     |                       HMAC (16 octets)                        |
     |                                                               |
     |                                                               |
     +-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+

   All these messages constitute one logical message: the Request-
   Session command.

   Above, the first octet (1) indicates that this is the Request-Session
   command.

   IPVN is the IP version numbers for Sender and Receiver.  When the IP
   version number is 4, 12 octets follow the 4-octet IPv4 address stored
   in Sender Address and Receiver Address.  These octets MUST be set to
   zero by the client and MUST be ignored by the server.  Currently
   meaningful IPVN values are 4 and 6.

   Conf-Sender and Conf-Receiver MUST be set to 0 or 1 by the client.
   The server MUST interpret any non-zero value as 1.  If the value is
   1, the server is being asked to configure the corresponding agent
   (sender or receiver).  In this case, the corresponding Port value
   SHOULD be disregarded by the server.  At least one of Conf-Sender and
   Conf-Receiver MUST be 1.  (Both can be set, in which case the server
   is being asked to perform a session between two hosts it can
   configure.)





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   Number of Schedule Slots, as mentioned before, specifies the number
   of slot records that go between the two blocks of HMAC.  It is used
   by the sender to determine when to send test packets (see next
   section).

   Number of Packets is the number of active measurement packets to be
   sent during this OWAMP-Test session (note that either the server or
   the client can abort the session early).

   If Conf-Sender is not set, Sender Port is the UDP port from which
   OWAMP-Test packets will be sent.  If Conf-Receiver is not set,
   Receiver Port is the UDP port OWAMP-Test to which packets are
   requested to be sent.

   The Sender Address and Receiver Address fields contain, respectively,
   the sender and receiver addresses of the end points of the Internet
   path over which an OWAMP test session is requested.

   SID is the session identifier.  It can be used in later sessions as
   an argument for the Fetch-Session command.  It is meaningful only if
   Conf-Receiver is 0.  This way, the SID is always generated by the
   receiving side.  See the end of the section for information on how
   the SID is generated.

   Padding length is the number of octets to be appended to the normal
   OWAMP-Test packet (see more on padding in discussion of OWAMP-Test).

   Start Time is the time when the session is to be started (but not
   before Start-Sessions command is issued).  This timestamp is in the
   same format as OWAMP-Test timestamps.

   Timeout (or a loss threshold) is an interval of time (expressed as a
   timestamp).  A packet belonging to the test session that is being set
   up by the current Request-Session command will be considered lost if
   it is not received during Timeout seconds after it is sent.

   Type-P Descriptor covers only a subset of (very large) Type-P space.
   If the first two bits of the Type-P Descriptor are 00, then the
   subsequent six bits specify the requested Differentiated Services
   Codepoint (DSCP) value of sent OWAMP-Test packets, as defined in
   [RFC2474].  If the first two bits of Type-P descriptor are 01, then
   the subsequent 16 bits specify the requested PHB Identification Code
   (PHB ID), as defined in [RFC2836].

   Therefore, the value of all zeros specifies the default best-effort
   service.





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   If Conf-Sender is set, the Type-P Descriptor is to be used to
   configure the sender to send packets according to its value.  If
   Conf-Sender is not set, the Type-P Descriptor is a declaration of how
   the sender will be configured.

   If Conf-Sender is set and the server does not recognize the Type-P
   Descriptor, or it cannot or does not wish to set the corresponding
   attributes on OWAMP-Test packets, it SHOULD reject the session
   request.  If Conf-Sender is not set, the server SHOULD accept or
   reject the session, paying no attention to the value of the Type-P
   Descriptor.

   To each Request-Session message, an OWAMP server MUST respond with an
   Accept-Session message:

      0                   1                   2                   3
      0 1 2 3 4 5 6 7 8 9 0 1 2 3 4 5 6 7 8 9 0 1 2 3 4 5 6 7 8 9 0 1
     +-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+
     |    Accept     |  MBZ          |            Port               |
     +-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-|
     |                                                               |
     |                        SID (16 octets)                        |
     |                                                               |
     |                                                               |
     +-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+
     |                                                               |
     |                        MBZ (12 octets)                        |
     |                                                               |
     +-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+
     |                                                               |
     |                       HMAC (16 octets)                        |
     |                                                               |
     |                                                               |
     +-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+

   In this message, zero in the Accept field means that the server is
   willing to conduct the session.  A non-zero value indicates rejection
   of the request.  The full list of available Accept values is
   described in Section 3.3, "Values of the Accept Field".

   If the server rejects a Request-Session message, it SHOULD not close
   the TCP connection.  The client MAY close it if it receives a
   negative response to the Request-Session message.

   The meaning of Port in the response depends on the values of Conf-
   Sender and Conf-Receiver in the query that solicited the response.
   If both were set, the Port field is unused.  If only Conf-Sender was
   set, Port is the port from which to expect OWAMP-Test packets.  If



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   only Conf-Receiver was set, Port is the port to which OWAMP-Test
   packets are sent.

   If only Conf-Sender was set, the SID field in the response is unused.
   Otherwise, SID is a unique server-generated session identifier.  It
   can be used later as handle to fetch the results of a session.

   SIDs SHOULD be constructed by concatenation of the 4-octet IPv4 IP
   number belonging to the generating machine, an 8-octet timestamp, and
   a 4-octet random value.  To reduce the probability of collisions, if
   the generating machine has any IPv4 addresses (with the exception of
   loopback), one of them SHOULD be used for SID generation, even if all
   communication is IPv6-based.  If it has no IPv4 addresses at all, the
   last four octets of an IPv6 address MAY be used instead.  Note that
   SID is always chosen by the receiver.  If truly random values are not
   available, it is important that the SID be made unpredictable, as
   knowledge of the SID might be used for access control.

3.6.  Send Schedules

   The sender and the receiver both need to know the same send schedule.
   This way, when packets are lost, the receiver knows when they were
   supposed to be sent.  It is desirable to compress common schedules
   and still to be able to use an arbitrary one for the test sessions.
   In many cases, the schedule will consist of repeated sequences of
   packets: this way, the sequence performs some test, and the test is
   repeated a number of times to gather statistics.

   To implement this, we have a schedule with a given number of slots.
   Each slot has a type and a parameter.  Two types are supported:
   exponentially distributed pseudo-random quantity (denoted by a code
   of 0) and a fixed quantity (denoted by a code of 1).  The parameter
   is expressed as a timestamp and specifies a time interval.  For a
   type 0 slot (exponentially distributed pseudo-random quantity), this
   interval is the mean value (or 1/lambda if the distribution density
   function is expressed as lambda*exp(-lambda*x) for positive values of
   x).  For a type 1 (fixed quantity) slot, the parameter is the delay
   itself.  The sender starts with the beginning of the schedule and
   executes the instructions in the slots: for a slot of type 0, wait an
   exponentially distributed time with a mean of the specified parameter
   and then send a test packet (and proceed to the next slot); for a
   slot of type 1, wait the specified time and send a test packet (and
   proceed to the next slot).  The schedule is circular: when there are
   no more slots, the sender returns to the first slot.

   The sender and the receiver need to be able to reproducibly execute
   the entire schedule (so, if a packet is lost, the receiver can still
   attach a send timestamp to it).  Slots of type 1 are trivial to



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   reproducibly execute.  To reproducibly execute slots of type 0, we
   need to be able to generate pseudo-random exponentially distributed
   quantities in a reproducible manner.  The way this is accomplished is
   discussed later in Section 5, "Computing Exponentially Distributed
   Pseudo-Random Numbers".

   Using this mechanism, one can easily specify common testing
   scenarios.  The following are some examples:

   +  Poisson stream: a single slot of type 0.

   +  Periodic stream: a single slot of type 1.

   +  Poisson stream of back-to-back packet pairs: two slots, type 0
      with a non-zero parameter and type 1 with a zero parameter.

   Further, a completely arbitrary schedule can be specified (albeit
   inefficiently) by making the number of test packets equal to the
   number of schedule slots.  In this case, the complete schedule is
   transmitted in advance of an OWAMP-Test session.

3.7.  Starting Test Sessions

   Having requested one or more test sessions and received affirmative
   Accept-Session responses, an OWAMP client MAY start the execution of
   the requested test sessions by sending a Start-Sessions message to
   the server.

   The format of this message is as follows:

      0                   1                   2                   3
      0 1 2 3 4 5 6 7 8 9 0 1 2 3 4 5 6 7 8 9 0 1 2 3 4 5 6 7 8 9 0 1
     +-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+
     |      2        |                                               |
     +-+-+-+-+-+-+-+-+                                               |
     |                        MBZ (15 octets)                        |
     |                                                               |
     |                                                               |
     +-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+
     |                                                               |
     |                       HMAC (16 octets)                        |
     |                                                               |
     |                                                               |
     +-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+

   The server MUST respond with an Start-Ack message (which SHOULD be
   sent as quickly as possible).  Start-Ack messages have the following
   format:



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      0                   1                   2                   3
      0 1 2 3 4 5 6 7 8 9 0 1 2 3 4 5 6 7 8 9 0 1 2 3 4 5 6 7 8 9 0 1
     +-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+
     |     Accept    |                                               |
     +-+-+-+-+-+-+-+-+                                               |
     |                        MBZ (15 octets)                        |
     |                                                               |
     |                                                               |
     +-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+
     |                                                               |
     |                       HMAC (16 octets)                        |
     |                                                               |
     |                                                               |
     +-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+

   If Accept is non-zero, the Start-Sessions request was rejected; zero
   means that the command was accepted.  The full list of available
   Accept values is described in Section 3.3, "Values of the Accept
   Field".  The server MAY, and the client SHOULD, close the connection
   in the case of a rejection.

   The server SHOULD start all OWAMP-Test streams immediately after it
   sends the response or immediately after their specified start times,
   whichever is later.  If the client represents a Sender, the client
   SHOULD start its OWAMP-Test streams immediately after it sees the
   Start-Ack response from the Server (if the Start-Sessions command was
   accepted) or immediately after their specified start times, whichever
   is later.  See more on OWAMP-Test sender behavior in a separate
   section below.

3.8.  Stop-Sessions

   The Stop-Sessions message may be issued by either the Control-Client
   or the Server.  The format of this command is as follows:

      0                   1                   2                   3
      0 1 2 3 4 5 6 7 8 9 0 1 2 3 4 5 6 7 8 9 0 1 2 3 4 5 6 7 8 9 0 1
     +-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+
     |      3        |    Accept     |              MBZ              |
     +-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+
     |                      Number of Sessions                       |
     +-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+
     |                        MBZ (8 octets)                         |
     |                                                               |
     +-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+

   This is immediately followed by zero or more session description
   records (the number of session description records is specified in



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   the "Number of Sessions" field above).  The session description
   record is used to indicate which packets were actually sent by the
   sender process (rather than skipped).  The header of the session
   description record is as follows:

      0                   1                   2                   3
      0 1 2 3 4 5 6 7 8 9 0 1 2 3 4 5 6 7 8 9 0 1 2 3 4 5 6 7 8 9 0 1
     +-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-|
     |                                                               |
     |                        SID (16 octets)                        |
     |                                                               |
     |                                                               |
     +-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+
     |                           Next Seqno                          |
     +-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+
     |                     Number of Skip Ranges                     |
     +-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+

   This is immediately followed by zero or more Skip Range descriptions
   as specified by the "Number of Skip Ranges" field above.  Skip Ranges
   are simply two sequence numbers that, together, indicate a range of
   packets that were not sent:

      0                   1                   2                   3
      0 1 2 3 4 5 6 7 8 9 0 1 2 3 4 5 6 7 8 9 0 1 2 3 4 5 6 7 8 9 0 1
     +-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-|
     |                      First Seqno Skipped                      |
     +-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+
     |                       Last Seqno Skipped                      |
     +-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+

   Skip Ranges MUST be in order.  The last (possibly full, possibly
   incomplete) block (16 octets) of data MUST be padded with zeros, if
   necessary.  This ensures that the next session description record
   starts on a block boundary.

   Finally, a single block (16 octets) of HMAC is concatenated on the
   end to complete the Stop-Sessions message.

     +-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+
     |                                                               |
     |                       HMAC (16 octets)                        |
     |                                                               |
     |                                                               |
     +-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+

   All these records comprise one logical message: the Stop-Sessions
   command.



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   Above, the first octet (3) indicates that this is the Stop-Sessions
   command.

   Non-zero Accept values indicate a failure of some sort.  Zero values
   indicate normal (but possibly premature) completion.  The full list
   of available Accept values is described in Section 3.3, "Values of
   the Accept Field".

   If Accept had a non-zero value (from either party), results of all
   OWAMP-Test sessions spawned by this OWAMP-Control session SHOULD be
   considered invalid, even if a Fetch-Session with SID from this
   session works for a different OWAMP-Control session.  If Accept was
   not transmitted at all (for whatever reason, including the TCP
   connection used for OWAMP-Control breaking), the results of all
   OWAMP-Test sessions spawned by this OWAMP-control session MAY be
   considered invalid.

   Number of Sessions indicates the number of session description
   records that immediately follow the Stop-Sessions header.

   Number of Sessions MUST contain the number of send sessions started
   by the local side of the control connection that have not been
   previously terminated by a Stop-Sessions command (i.e., the Control-
   Client MUST account for each accepted Request-Session where Conf-
   Receiver was set; the Control-Server MUST account for each accepted
   Request-Session where Conf-Sender was set).  If the Stop-Sessions
   message does not account for exactly the send sessions controlled by
   that side, then it is to be considered invalid and the connection
   SHOULD be closed and any results obtained considered invalid.

   Each session description record represents one OWAMP-Test session.

   SID is the session identifier (SID) used to indicate which send
   session is being described.

   Next Seqno indicates the next sequence number that would have been
   sent from this send session.  For completed sessions, this will equal
   NumPackets from the Request-Session.

   Number of Skip Ranges indicates the number of holes that actually
   occurred in the sending process.  This is a range of packets that
   were never actually sent by the sending process.  For example, if a
   send session is started too late for the first 10 packets to be sent
   and this is the only hole in the schedule, then "Number of Skip
   Ranges" would be 1.  The single Skip Range description will have
   First Seqno Skipped equal to 0 and Last Seqno Skipped equal to 9.
   This is described further in the "Sender Behavior" section.




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   If the OWAMP-Control connection breaks when the Stop-Sessions command
   is sent, the receiver MAY not completely invalidate the session
   results.  It MUST discard all record of packets that follow (in other
   words, that have greater sequence number than) the last packet that
   was actually received before any lost packet records.  This will help
   differentiate between packet losses that occurred in the network and
   packets the sending process may have never sent.

   If a receiver of an OWAMP-Test session learns, through an OWAMP-
   Control Stop-Sessions message, that the OWAMP-Test sender's last
   sequence number is lower than any sequence number actually received,
   the results of the complete OWAMP-Test session MUST be invalidated.

   A receiver of an OWAMP-Test session, upon receipt of an OWAMP-Control
   Stop-Sessions command, MUST discard any packet records -- including
   lost packet records -- with a (computed) send time that falls between
   the current time minus Timeout and the current time.  This ensures
   statistical consistency for the measurement of loss and duplicates in
   the event that the Timeout is greater than the time it takes for the
   Stop-Sessions command to take place.

   To effect complete sessions, each side of the control connection
   SHOULD wait until all sessions are complete before sending the Stop-
   Sessions message.  The completed time of each session is determined
   as Timeout after the scheduled time for the last sequence number.
   Endpoints MAY add a small increment to the computed completed time
   for send endpoints to ensure that the Stop-Sessions message reaches
   the receiver endpoint after Timeout.

   To effect a premature stop of sessions, the party that initiates this
   command MUST stop its OWAMP-Test send streams to send the Session
   Packets Sent values before sending this command.  That party SHOULD
   wait until receiving the response Stop-Sessions message before
   stopping the receiver streams so that it can use the values from the
   received Stop-Sessions message to validate the data.
















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3.9.  Fetch-Session

   The format of this client command is as follows:

      0                   1                   2                   3
      0 1 2 3 4 5 6 7 8 9 0 1 2 3 4 5 6 7 8 9 0 1 2 3 4 5 6 7 8 9 0 1
     +-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+
     |      4        |                                               |
     +-+-+-+-+-+-+-+-+                                               |
     |                        MBZ (7 octets)                         |
     +-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+
     |                         Begin Seq                             |
     +-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+
     |                          End Seq                              |
     +-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+
     |                                                               |
     |                        SID (16 octets)                        |
     |                                                               |
     |                                                               |
     +-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+
     |                                                               |
     |                       HMAC (16 octets)                        |
     |                                                               |
     |                                                               |
     +-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+

   Begin Seq is the sequence number of the first requested packet.  End
   Seq is the sequence number of the last requested packet.  If Begin
   Seq is all zeros and End Seq is all ones, complete session is said to
   be requested.

   If a complete session is requested and the session is still in
   progress or has terminated in any way other than normally, the
   request to fetch session results MUST be denied.  If an incomplete
   session is requested, all packets received so far that fall into the
   requested range SHOULD be returned.  Note that, since no commands can
   be issued between Start-Sessions and Stop-Sessions, incomplete
   requests can only happen on a different OWAMP-Control connection
   (from the same or different host as Control-Client).












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   The server MUST respond with a Fetch-Ack message.  The format of this
   server response is as follows:

      0                   1                   2                   3
      0 1 2 3 4 5 6 7 8 9 0 1 2 3 4 5 6 7 8 9 0 1 2 3 4 5 6 7 8 9 0 1
     +-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+
     |     Accept    | Finished      |          MBZ (2 octets)       |
     +-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+
     |                           Next Seqno                          |
     +-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+
     |                    Number of Skip Ranges                      |
     +-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+
     |                       Number of Records                       |
     +-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+
     |                                                               |
     |                       HMAC (16 octets)                        |
     |                                                               |
     |                                                               |
     +-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+

   Again, non-zero in the Accept field means a rejection of command.
   The server MUST specify zero for all remaining fields if Accept is
   non-zero.  The client MUST ignore all remaining fields (except for
   the HMAC) if Accept is non-zero.  The full list of available Accept
   values is described in Section 3.3, "Values of the Accept Field".

   Finished is non-zero if the OWAMP-Test session has terminated.

   Next Seqno indicates the next sequence number that would have been
   sent from this send session.  For completed sessions, this will equal
   NumPackets from the Request-Session.  This information is only
   available if the session has terminated.  If Finished is zero, then
   Next Seqno MUST be set to zero by the server.

   Number of Skip Ranges indicates the number of holes that actually
   occurred in the sending process.  This information is only available
   if the session has terminated.  If Finished is zero, then Skip Ranges
   MUST be set to zero by the server.

   Number of Records is the number of packet records that fall within
   the requested range.  This number might be less than the Number of
   Packets in the reproduction of the Request-Session command because of
   a session that ended prematurely, or it might be greater because of
   duplicates.

   If Accept was non-zero, this concludes the response to the Fetch-
   Session message.  If Accept was 0, the server then MUST immediately
   send the OWAMP-Test session data in question.



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   The OWAMP-Test session data consists of the following (concatenated):

   +  A reproduction of the Request-Session command that was used to
      start the session; it is modified so that actual sender and
      receiver port numbers that were used by the OWAMP-Test session
      always appear in the reproduction.

   +  Zero or more (as specified) Skip Range descriptions.  The last
      (possibly full, possibly incomplete) block (16 octets) of Skip
      Range descriptions is padded with zeros, if necessary.

   +  16 octets of HMAC.

   +  Zero or more (as specified) packet records.  The last (possibly
      full, possibly incomplete) block (16 octets) of data is padded
      with zeros, if necessary.

   +  16 octets of HMAC.

   Skip Range descriptions are simply two sequence numbers that,
   together, indicate a range of packets that were not sent:

      0                   1                   2                   3
      0 1 2 3 4 5 6 7 8 9 0 1 2 3 4 5 6 7 8 9 0 1 2 3 4 5 6 7 8 9 0 1
     +-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-|
     |                      First Seqno Skipped                      |
     +-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+
     |                       Last Seqno Skipped                      |
     +-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+

   Skip Range descriptions should be sent out in order, as sorted by
   First Seqno.  If any Skip Ranges overlap or are out of order, the
   session data is to be considered invalid and the connection SHOULD be
   closed and any results obtained considered invalid.

   Each packet record is 25 octets and includes 4 octets of sequence
   number, 8 octets of send timestamp, 2 octets of send timestamp error
   estimate, 8 octets of receive timestamp, 2 octets of receive
   timestamp error estimate, and 1 octet of Time To Live (TTL), or Hop
   Limit in IPv6:











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        0                   1                   2                   3
        0 1 2 3 4 5 6 7 8 9 0 1 2 3 4 5 6 7 8 9 0 1 2 3 4 5 6 7 8 9 0 1
       +-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+
     00|                          Seq Number                           |
       +-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+
     04|      Send Error Estimate      |    Receive Error Estimate     |
       +-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+
     08|                         Send Timestamp                        |
     12|                                                               |
       +-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+
     16|                       Receive Timestamp                       |
     20|                                                               |
       +-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+
     24|    TTL        |
       +-+-+-+-+-+-+-+-+

   Packet records are sent out in the same order the actual packets were
   received.  Therefore, the data is in arrival order.

   Note that lost packets (if any losses were detected during the
   OWAMP-Test session) MUST appear in the sequence of packets.  They can
   appear either at the point when the loss was detected or at any later
   point.  Lost packet records are distinguished as follows:

   +  A send timestamp filled with the presumed send time (as computed
      by the send schedule).

   +  A send error estimate filled with Multiplier=1, Scale=64, and S=0
      (see the OWAMP-Test description for definition of these quantities
      and explanation of timestamp format and error estimate format).

   +  A normal receive error estimate as determined by the error of the
      clock being used to declare the packet lost.  (It is declared lost
      if it is not received by the Timeout after the presumed send time,
      as determined by the receiver's clock.)

   +  A receive timestamp consisting of all zero bits.

   +  A TTL value of 255.

4.  OWAMP-Test

   This section describes OWAMP-Test protocol.  It runs over UDP, using
   sender and receiver IP and port numbers negotiated during the
   Request-Session exchange.






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   As with OWAMP-Control, OWAMP-Test has three modes: unauthenticated,
   authenticated, and encrypted.  All OWAMP-Test sessions that are
   spawned by an OWAMP-Control session inherit its mode.

   OWAMP-Control client, OWAMP-Control server, OWAMP-Test sender, and
   OWAMP-Test receiver can potentially all be different machines.  (In a
   typical case, we expect that there will be only two machines.)

4.1.  Sender Behavior

4.1.1.  Packet Timings

   Send schedules based on slots, described previously, in conjunction
   with scheduled session start time, enable the sender and the receiver
   to compute the same exact packet sending schedule independently of
   each other.  These sending schedules are independent for different
   OWAMP-Test sessions, even if they are governed by the same OWAMP-
   Control session.

   Consider any OWAMP-Test session.  Once Start-Sessions exchange is
   complete, the sender is ready to start sending packets.  Under normal
   OWAMP use circumstances, the time to send the first packet is in the
   near future (perhaps a fraction of a second away).  The sender SHOULD
   send packets as close as possible to their scheduled time, with the
   following exception: if the scheduled time to send is in the past,
   and is separated from the present by more than Timeout time, the
   sender MUST NOT send the packet.  (Indeed, such a packet would be
   considered lost by the receiver anyway.)  The sender MUST keep track
   of which packets it does not send.  It will use this to tell the
   receiver what packets were not sent by setting Skip Ranges in the
   Stop-Sessions message from the sender to the receiver upon completion
   of the test.  The Skip Ranges are also sent to a Fetch-Client as part
   of the session data results.  These holes in the sending schedule can
   happen if a time in the past was specified in the Request-Session
   command, or if the Start-Sessions exchange took unexpectedly long, or
   if the sender could not start serving the OWAMP-Test session on time
   due to internal scheduling problems of the OS.  Packets that are in
   the past but are separated from the present by less than Timeout
   value SHOULD be sent as quickly as possible.  With normal test rates
   and timeout values, the number of packets in such a burst is limited.
   Nevertheless, hosts SHOULD NOT intentionally schedule sessions so
   that such bursts of packets occur.

   Regardless of any scheduling delays, each packet that is actually
   sent MUST have the best possible approximation of its real time of
   departure as its timestamp (in the packet).





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4.1.2.  OWAMP-Test Packet Format and Content

   The sender sends the receiver a stream of packets with the schedule
   specified in the Request-Session command.  The sender SHOULD set the
   TTL in IPv4 (or Hop Limit in IPv6) in the UDP packet to 255.  The
   format of the body of a UDP packet in the stream depends on the mode
   being used.

   For unauthenticated mode:

      0                   1                   2                   3
      0 1 2 3 4 5 6 7 8 9 0 1 2 3 4 5 6 7 8 9 0 1 2 3 4 5 6 7 8 9 0 1
     +-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+
     |                        Sequence Number                        |
     +-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+
     |                          Timestamp                            |
     |                                                               |
     +-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+
     |        Error Estimate         |                               |
     +-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+                               |
     |                                                               |
     .                                                               .
     .                         Packet Padding                        .
     .                                                               .
     |                                                               |
     +-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+

























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   For authenticated and encrypted modes:

      0                   1                   2                   3
      0 1 2 3 4 5 6 7 8 9 0 1 2 3 4 5 6 7 8 9 0 1 2 3 4 5 6 7 8 9 0 1
     +-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+
     |                        Sequence Number                        |
     +-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+
     |                                                               |
     |                        MBZ (12 octets)                        |
     |                                                               |
     +-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+
     |                          Timestamp                            |
     |                                                               |
     +-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+
     |        Error Estimate         |                               |
     +-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+                               |
     |                         MBZ (6 octets)                        |
     +-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+
     |                                                               |
     |                       HMAC (16 octets)                        |
     |                                                               |
     |                                                               |
     +-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+
     |                                                               |
     .                                                               .
     .                        Packet Padding                         .
     .                                                               .
     |                                                               |
     +-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+

   The format of the timestamp is the same as in [RFC1305] and is as
   follows: the first 32 bits represent the unsigned integer number of
   seconds elapsed since 0h on 1 January 1900; the next 32 bits
   represent the fractional part of a second that has elapsed since
   then.

   So, Timestamp is represented as follows:

      0                   1                   2                   3
      0 1 2 3 4 5 6 7 8 9 0 1 2 3 4 5 6 7 8 9 0 1 2 3 4 5 6 7 8 9 0 1
     +-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+
     |                   Integer part of seconds                     |
     +-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+
     |                 Fractional part of seconds                    |
     +-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+






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   The Error Estimate specifies the estimate of the error and
   synchronization.  It has the following format:

         0                   1
         0 1 2 3 4 5 6 7 8 9 0 1 2 3 4 5
        +-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+
        |S|Z|   Scale   |   Multiplier  |
        +-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+

   The first bit, S, SHOULD be set if the party generating the timestamp
   has a clock that is synchronized to UTC using an external source
   (e.g., the bit should be set if GPS hardware is used and it indicates
   that it has acquired current position and time or if NTP is used and
   it indicates that it has synchronized to an external source, which
   includes stratum 0 source, etc.).  If there is no notion of external
   synchronization for the time source, the bit SHOULD NOT be set.  The
   next bit has the same semantics as MBZ fields elsewhere: it MUST be
   set to zero by the sender and ignored by everyone else.  The next six
   bits, Scale, form an unsigned integer; Multiplier is an unsigned
   integer as well.  They are interpreted as follows: the error estimate
   is equal to Multiplier*2^(-32)*2^Scale (in seconds).  (Notation
   clarification: 2^Scale is two to the power of Scale.)  Multiplier
   MUST NOT be set to zero.  If Multiplier is zero, the packet SHOULD be
   considered corrupt and discarded.

   Sequence numbers start with zero and are incremented by one for each
   subsequent packet.

   The minimum data segment length is, therefore, 14 octets in
   unauthenticated mode, and 48 octets in both authenticated mode and
   encrypted modes.

   The OWAMP-Test packet layout is the same in authenticated and
   encrypted modes.  The encryption and authentication operations are,
   however, different.  The difference is that in encrypted mode both
   the sequence number and the timestamp are protected to provide
   maximum data confidentiality and integrity protection, whereas in
   authenticated mode the sequence number is protected while the
   timestamp is sent in clear text.  Sending the timestamp in clear text
   in authenticated mode allows one to reduce the time between when a
   timestamp is obtained by a sender and when the packet is shipped out.
   In encrypted mode, the sender has to fetch the timestamp, encrypt it,
   and send it; in authenticated mode, the middle step is removed,
   potentially improving accuracy (the sequence number can be encrypted
   and authenticated before the timestamp is fetched).

   In authenticated mode, the first block (16 octets) of each packet is
   encrypted using AES Electronic Cookbook (ECB) mode.



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   Similarly to each OWAMP-Control session, each OWAMP-Test session has
   two keys: an AES Session-key and an HMAC Session-key.  However, there
   is a difference in how the keys are obtained: in the case of OWAMP-
   Control, the keys are generated by the client and communicated (as
   part of the Token) during connection setup as part of Set-Up-Response
   message; in the case of OWAMP-Test, described here, the keys are
   derived from the OWAMP-Control keys and the SID.

   The OWAMP-Test AES Session-key is obtained as follows: the OWAMP-
   Control AES Session-key (the same AES Session-key as is used for the
   corresponding OWAMP-Control session, where it is used in a different
   chaining mode) is encrypted, using AES, with the 16-octet session
   identifier (SID) as the key; this is a single-block ECB encryption;
   its result is the OWAMP-Test AES Session-key to use in encrypting
   (and decrypting) the packets of the particular OWAMP-Test session.
   Note that all of OWAMP-Test AES Session-key, OWAMP-Control AES
   Session-key, and the SID are comprised of 16 octets.

   The OWAMP-Test HMAC Session-key is obtained as follows: the OWAMP-
   Control HMAC Session-key (the same HMAC Session-key as is used for
   the corresponding OWAMP-Control session) is encrypted, using AES,
   with the 16-octet session identifier (SID) as the key; this is a
   two-block CBC encryption, always performed with IV=0; its result is
   the OWAMP-Test HMAC Session-key to use in authenticating the packets
   of the particular OWAMP-Test session.  Note that all of OWAMP-Test
   HMAC Session-key and OWAMP-Control HMAC Session-key are comprised of
   32 octets, while the SID is 16 octets.

   ECB mode used for encrypting the first block of OWAMP-Test packets in
   authenticated mode does not involve any actual chaining; this way,
   lost, duplicated, or reordered packets do not cause problems with
   deciphering any packet in an OWAMP-Test session.

   In encrypted mode, the first two blocks (32 octets) are encrypted
   using AES CBC mode.  The AES Session-key to use is obtained in the
   same way as the key for authenticated mode.  Each OWAMP-Test packet
   is encrypted as a separate stream, with just one chaining operation;
   chaining does not span multiple packets so that lost, duplicated, or
   reordered packets do not cause problems.  The initialization vector
   for the CBC encryption is a value with all bits equal to zero.

   Implementation note: Naturally, the key schedule for each OWAMP-Test
   session MAY be set up only once per session, not once per packet.








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   HMAC in OWAMP-Test only covers the part of the packet that is also
   encrypted.  So, in authenticated mode, HMAC covers the first block
   (16 octets); in encrypted mode, HMAC covers two first blocks (32
   octets).  In OWAMP-Test HMAC is not encrypted (note that this is
   different from OWAMP-Control, where encryption in stream mode is
   used, so everything including the HMAC blocks ends up being
   encrypted).

   In unauthenticated mode, no encryption or authentication is applied.

   Packet Padding in OWAMP-Test SHOULD be pseudo-random (it MUST be
   generated independently of any other pseudo-random numbers mentioned
   in this document).  However, implementations MUST provide a
   configuration parameter, an option, or a different means of making
   Packet Padding consist of all zeros.

   The time elapsed between packets is computed according to the slot
   schedule as mentioned in Request-Session command description.  At
   that point, we skipped over the issue of computing exponentially
   distributed pseudo-random numbers in a reproducible fashion.  It is
   discussed later in a separate section.

4.2.  Receiver Behavior

   The receiver knows when the sender will send packets.  The following
   parameter is defined: Timeout (from Request-Session).  Packets that
   are delayed by more than Timeout are considered lost (or "as good as
   lost").  Note that there is never an actual assurance of loss by the
   network: a "lost" packet might still be delivered at any time.  The
   original specification for IPv4 required that packets be delivered
   within TTL seconds or never (with TTL having a maximum value of 255).
   To the best of the authors' knowledge, this requirement was never
   actually implemented (and, of course, only a complete and universal
   implementation would ensure that packets do not travel for longer
   than TTL seconds).  In fact, in IPv6, the name of this field has
   actually been changed to Hop Limit.  Further, IPv4 specification
   makes no claims about the time it takes the packet to traverse the
   last link of the path.

   The choice of a reasonable value of Timeout is a problem faced by a
   user of OWAMP protocol, not by an implementor.  A value such as two
   minutes is very safe.  Note that certain applications (such as
   interactive "one-way ping" might wish to obtain the data faster than
   that.

   As packets are received,

   +  timestamp the received packet;



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   +  in authenticated or encrypted mode, decrypt and authenticate as
      necessary (packets for which authentication fails MUST be
      discarded); and

   +  store the packet sequence number, send time, receive time, and the
      TTL for IPv4 (or Hop Limit for IPv6) from the packet IP header for
      the results to be transferred.

   Packets not received within the Timeout are considered lost.  They
   are recorded with their true sequence number, presumed send time,
   receive time value with all bits being zero, and a TTL (or Hop Limit)
   of 255.

   Implementations SHOULD fetch the TTL/Hop Limit value from the IP
   header of the packet.  If an implementation does not fetch the actual
   TTL value (the only good reason not to do so is an inability to
   access the TTL field of arriving packets), it MUST record the TTL
   value as 255.

   Packets that are actually received are recorded in the order of
   arrival.  Lost packet records serve as indications of the send times
   of lost packets.  They SHOULD be placed either at the point where the
   receiver learns about the loss or at any later point; in particular,
   one MAY place all the records that correspond to lost packets at the
   very end.

   Packets that have send time in the future MUST be recorded normally,
   without changing their send timestamp, unless they have to be
   discarded.  (Send timestamps in the future would normally indicate
   clocks that differ by more than the delay.  Some data -- such as
   jitter -- can be extracted even without knowledge of time difference.
   For other kinds of data, the adjustment is best handled by the data
   consumer on the basis of the complete information in a measurement
   session, as well as, possibly, external data.)

   Packets with a sequence number that was already observed (duplicate
   packets) MUST be recorded normally.  (Duplicate packets are sometimes
   introduced by IP networks.  The protocol has to be able to measure
   duplication.)

   If any of the following is true, the packet MUST be discarded:

   +  Send timestamp is more than Timeout in the past or in the future.

   +  Send timestamp differs by more than Timeout from the time when the
      packet should have been sent according to its sequence number.

   +  In authenticated or encrypted mode, HMAC verification fails.



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5.  Computing Exponentially Distributed Pseudo-Random Numbers

   Here we describe the way exponential random quantities used in the
   protocol are generated.  While there is a fair number of algorithms
   for generating exponential random variables, most of them rely on
   having logarithmic function as a primitive, resulting in potentially
   different values, depending on the particular implementation of the
   math library.  We use algorithm 3.4.1.S from [KNUTH], which is free
   of the above-mentioned problem, and which guarantees the same output
   on any implementation.  The algorithm belongs to the ziggurat family
   developed in the 1970s by G. Marsaglia, M. Sibuya, and J. H. Ahrens
   [ZIGG].  It replaces the use of logarithmic function by clever bit
   manipulation, still producing the exponential variates on output.

5.1.  High-Level Description of the Algorithm

   For ease of exposition, the algorithm is first described with all
   arithmetic operations being interpreted in their natural sense.
   Later, exact details on data types, arithmetic, and generation of the
   uniform random variates used by the algorithm are given.  It is an
   almost verbatim quotation from [KNUTH], p.133.

   Algorithm S: Given a real positive number "mu", produce an
   exponential random variate with mean "mu".

   First, the constants

   Q[k] = (ln2)/(1!) + (ln2)^2/(2!) + ... + (ln2)^k/(k!),  1 <= k <= 11

   are computed in advance.  The exact values which MUST be used by all
   implementations are given in the next section.  This is necessary to
   ensure that exactly the same pseudo-random sequences are produced by
   all implementations.

   S1. [Get U and shift.] Generate a 32-bit uniform random binary
   fraction

             U = (.b0 b1 b2 ... b31)    [note the binary point]

   Locate the first zero bit b_j and shift off the leading (j+1) bits,
   setting U <- (.b_{j+1} ... b31)

   Note: In the rare case that the zero has not been found, it is
   prescribed that the algorithm return (mu*32*ln2).

   S2. [Immediate acceptance?] If U < ln2, set X <- mu*(j*ln2 + U) and
   terminate the algorithm. (Note that Q[1] = ln2.)




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   S3. [Minimize.] Find the least k >= 2 such that U < Q[k]. Generate k
   new uniform random binary fractions U1,...,Uk and set V <-
   min(U1,...,Uk).

   S4. [Deliver the answer.] Set X <- mu*(j + V)*ln2.

5.2.  Data Types, Representation, and Arithmetic

   The high-level algorithm operates on real numbers, typically
   represented as floating point numbers.  This specification prescribes
   that unsigned 64-bit integers be used instead.

   u_int64_t integers are interpreted as real numbers by placing the
   decimal point after the first 32 bits.  In other words, conceptually,
   the interpretation is given by the following map:

          u_int64_t u;

          u  |--> (double)u / (2**32)

   The algorithm produces a sequence of such u_int64_t integers that,
   for any given value of SID, is guaranteed to be the same on any
   implementation.

   We specify that the u_int64_t representations of the first 11 values
   of the Q array in the high-level algorithm MUST be as follows:

   #1      0xB17217F8,
   #2      0xEEF193F7,
   #3      0xFD271862,
   #4      0xFF9D6DD0,
   #5      0xFFF4CFD0,
   #6      0xFFFEE819,
   #7      0xFFFFE7FF,
   #8      0xFFFFFE2B,
   #9      0xFFFFFFE0,
   #10     0xFFFFFFFE,
   #11     0xFFFFFFFF

   For example, Q[1] = ln2 is indeed approximated by 0xB17217F8/(2**32)
   = 0.693147180601954; for j > 11, Q[j] is 0xFFFFFFFF.

   Small integer j in the high-level algorithm is represented as
   u_int64_t value j * (2**32).

   Operation of addition is done as usual on u_int64_t numbers; however,
   the operation of multiplication in the high-level algorithm should be
   replaced by



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      (u, v) |---> (u * v) >> 32.

   Implementations MUST compute the product (u * v) exactly.  For
   example, a fragment of unsigned 128-bit arithmetic can be implemented
   for this purpose (see the sample implementation in Appendix A).

5.3.  Uniform Random Quantities

   The procedure for obtaining a sequence of 32-bit random numbers (such
   as U in algorithm S) relies on using AES encryption in counter mode.
   To describe the exact working of the algorithm, we introduce two
   primitives from Rijndael.  Their prototypes and specification are
   given below, and they are assumed to be provided by the supporting
   Rijndael implementation, such as [RIJN].

   +  A function that initializes a Rijndael key with bytes from seed
      (the SID will be used as the seed):

      void KeyInit(unsigned char seed[16]);

   +  A function that encrypts the 16-octet block inblock with the
      specified key, returning a 16-octet encrypted block.  Here,
      keyInstance is an opaque type used to represent Rijndael keys:

      void BlockEncrypt(keyInstance key, unsigned char inblock[16]);

   Algorithm Unif: given a 16-octet quantity seed, produce a sequence of
   unsigned 32-bit pseudo-random uniformly distributed integers.  In
   OWAMP, the SID (session ID) from Control protocol plays the role of
   seed.

   U1. [Initialize Rijndael key] key <- KeyInit(seed) [Initialize an
   unsigned 16-octet (network byte order) counter] c <- 0

   U2. [Need more random bytes?]  Set i <- c mod 4.  If (i == 0) set s
   <- BlockEncrypt(key, c)

   U3. [Increment the counter as unsigned 16-octet quantity] c <- c + 1

   U4. [Do output] Output the i_th quartet of octets from s starting
   from high-order octets, converted to native byte order and
   represented as OWPNum64 value (as in 3.b).

   U5. [Loop] Go to step U2.







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6.  Security Considerations

6.1.  Introduction

   The goal of authenticated mode is to let one passphrase-protect the
   service provided by a particular OWAMP-Control server.  One can
   imagine a variety of circumstances where this could be useful.
   Authenticated mode is designed to prohibit theft of service.

   An additional design objective of the authenticated mode was to make
   it impossible for an attacker who cannot read traffic between OWAMP-
   Test sender and receiver to tamper with test results in a fashion
   that affects the measurements, but not other traffic.

   The goal of encrypted mode is quite different: to make it hard for a
   party in the middle of the network to make results look "better" than
   they should be.  This is especially true if one of client and server
   does not coincide with either sender or receiver.

   Encryption of OWAMP-Control using AES CBC mode with blocks of HMAC
   after each message aims to achieve two goals: (i) to provide secrecy
   of exchange, and (ii) to provide authentication of each message.

6.2.  Preventing Third-Party Denial of Service

   OWAMP-Test sessions directed at an unsuspecting party could be used
   for denial of service (DoS) attacks.  In unauthenticated mode,
   servers SHOULD limit receivers to hosts they control or to the OWAMP-
   Control client.

   Unless otherwise configured, the default behavior of servers MUST be
   to decline requests where the Receiver Address field is not equal to
   the address that the control connection was initiated from or an
   address of the server (or an address of a host it controls).  Given
   the TCP handshake procedure and sequence numbers in the control
   connection, this ensures that the hosts that make such requests are
   actually those hosts themselves, or at least on the path towards
   them.  If either this test or the handshake procedure were omitted,
   it would become possible for attackers anywhere in the Internet to
   request that large amounts of test packets be directed against victim
   nodes somewhere else.

   In any case, OWAMP-Test packets with a given source address MUST only
   be sent from the node that has been assigned that address (i.e.,
   address spoofing is not permitted).






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6.3.  Covert Information Channels

   OWAMP-Test sessions could be used as covert channels of information.
   Environments that are worried about covert channels should take this
   into consideration.

6.4.  Requirement to Include AES in Implementations

   Notice that AES, in counter mode, is used for pseudo-random number
   generation, so implementation of AES MUST be included even in a
   server that only supports unauthenticated mode.

6.5.  Resource Use Limitations

   An OWAMP server can consume resources of various kinds.  The two most
   important kinds of resources are network capacity and memory (primary
   or secondary) for storing test results.

   Any implementation of OWAMP server MUST include technical mechanisms
   to limit the use of network capacity and memory.  Mechanisms for
   managing the resources consumed by unauthenticated users and users
   authenticated with a KeyID and passphrase SHOULD be separate.  The
   default configuration of an implementation MUST enable these
   mechanisms and set the resource use limits to conservatively low
   values.

   One way to design the resource limitation mechanisms is as follows:
   assign each session to a user class.  User classes are partially
   ordered with "includes" relation, with one class ("all users") that
   is always present and that includes any other class.  The assignment
   of a session to a user class can be based on the presence of
   authentication of the session, the KeyID, IP address range, time of
   day, and, perhaps, other factors.  Each user class would have a limit
   for usage of network capacity (specified in units of bit/second) and
   memory for storing test results (specified in units of octets).
   Along with the limits for resource use, current use would be tracked
   by the server.  When a session is requested by a user in a specific
   user class, the resources needed for this session are computed: the
   average network capacity use (based on the sending schedule) and the
   maximum memory use (based on the number of packets and number of
   octets each packet would need to be stored internally -- note that
   outgoing sessions would not require any memory use).  These resource
   use numbers are added to the current resource use numbers for the
   given user class; if such addition would take the resource use
   outside of the limits for the given user class, the session is
   rejected.  When resources are reclaimed, corresponding measures are
   subtracted from the current use.  Network capacity is reclaimed as
   soon as the session ends.  Memory is reclaimed when the data is



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   deleted.  For unauthenticated sessions, memory consumed by an OWAMP-
   Test session SHOULD be reclaimed after the OWAMP-Control connection
   that initiated the session is closed (gracefully or otherwise).  For
   authenticated sessions, the administrator who configures the service
   should be able to decide the exact policy, but useful policy
   mechanisms that MAY be implemented are the ability to automatically
   reclaim memory when the data is retrieved and the ability to reclaim
   memory after a certain configurable (based on user class) period of
   time passes after the OWAMP-Test session terminates.

6.6.  Use of Cryptographic Primitives in OWAMP

   At an early stage in designing the protocol, we considered using
   Transport Layer Security (TLS) [RFC2246, RFC3546] and IPsec [RFC2401]
   as cryptographic security mechanisms for OWAMP; later, we also
   considered DTLS.  The disadvantages of those are as follows (not an
   exhaustive list):

   Regarding TLS:

   +  TLS could be used to secure TCP-based OWAMP-Control, but it would
      be difficult to use it to secure UDP-based OWAMP-Test: OWAMP-Test
      packets, if lost, are not resent, so packets have to be
      (optionally) encrypted and authenticated while retaining
      individual usability.  Stream-based TLS cannot be easily used for
      this.

   +  Dealing with streams, TLS does not authenticate individual
      messages (even in OWAMP-Control).  The easiest way out would be to
      add some known-format padding to each message and to verify that
      the format of the padding is intact before using the message.  The
      solution would thus lose some of its appeal ("just use TLS").  It
      would also be much more difficult to evaluate the security of this
      scheme with the various modes and options of TLS; it would almost
      certainly not be secure with all.  The capacity of an attacker to
      replace parts of messages (namely, the end) with random garbage
      could have serious security implications and would need to be
      analyzed carefully.  Suppose, for example, that a parameter that
      is used in some form to control the rate were replaced by random
      garbage; chances are that the result (an unsigned integer) would
      be quite large.

   +  Dependent on the mode of use, one can end up with a requirement
      for certificates for all users and a PKI.  Even if one is to
      accept that PKI is desirable, there just isn't a usable one today.






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   +  TLS requires a fairly large implementation.  OpenSSL, for example,
      is larger than our implementation of OWAMP as a whole.  This can
      matter for embedded implementations.

   Regarding DTLS:

   +  Duplication and, similarly, reordering are network phenomena that
      OWAMP needs to be able to measure; yet anti-replay measures and
      reordering protection of DTLS would prevent the duplicated and
      reordered packets from reaching the relevant part of the OWAMP
      code.  One could, of course, modify DTLS so that these protections
      are weakened or even specify examining the messages in a carefully
      crafted sequence somewhere in between DTLS checks; but then, of
      course, the advantage of using an existing protocol would not be
      realized.

   +  In authenticated mode, the timestamp is in the clear and is not
      protected cryptographically in any way, while the rest of the
      message has the same protection as in encrypted mode.  This mode
      allows one to trade off cryptographic protection against accuracy
      of timestamps.  For example, the APAN hardware implementation of
      OWAMP [APAN] is capable of supporting authenticated mode.  The
      accuracy of these measurements is in the sub-microsecond range.
      The errors in OWAMP measurements of Abilene [Abilene] (done using
      a software implementation, in its encrypted mode) exceed 10us.
      Users in different environments have different concerns, and some
      might very well care about every last microsecond of accuracy.  At
      the same time, users in these same environments might care about
      access control to the service.  Authenticated mode permits them to
      control access to the server yet to use unprotected timestamps,
      perhaps generated by a hardware device.

   Regarding IPsec:

   +  What we now call authenticated mode would not be possible (in
      IPsec you can't authenticate part of a packet).

   +  The deployment paths of IPsec and OWAMP could be separate if OWAMP
      does not depend on IPsec.  After nine years of IPsec, only 0.05%
      of traffic on an advanced backbone network, such as Abilene, uses
      IPsec (for comparison purposes with encryption above layer 4, SSH
      use is at 2-4% and HTTPS use is at 0.2-0.6%).  It is desirable to
      be able to deploy OWAMP on as large a number of different
      platforms as possible.







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   +  The deployment problems of a protocol dependent on IPsec would be
      especially acute in the case of lightweight embedded devices.
      Ethernet switches, DSL "modems", and other such devices mostly do
      not support IPsec.

   +  The API for manipulating IPsec from an application is currently
      poorly understood.  Writing a program that needs to encrypt some
      packets, to authenticate some packets, and to leave some open --
      for the same destination -- would become more of an exercise in
      IPsec than in IP measurement.

   For the enumerated reasons, we decided to use a simple cryptographic
   protocol (based on a block cipher in CBC mode) that is different from
   TLS and IPsec.

6.7.  Cryptographic Primitive Replacement

   It might become necessary in the future to replace AES, or the way it
   is used in OWAMP, with a new cryptographic primitive, or to make
   other security-related changes to the protocol.  OWAMP provides a
   well-defined point of extensibility: the Modes word in the server
   greeting and the Mode response in the Set-Up-Response message.  For
   example, if a simple replacement of AES with a different block cipher
   with a 128-bit block is needed, this could be accomplished as
   follows: take two bits from the reserved (MBZ) part of the Modes word
   of the server greeting; use one of these bits to indicate encrypted
   mode with the new cipher and another one to indicate authenticated
   mode with the new cipher.  (Bit consumption could, in fact, be
   reduced from two to one, if the client is allowed to return a mode
   selection with more than a single bit set: one could designate a
   single bit to mean that the new cipher is supported (in the case of
   the server) or selected (in the case of the client) and continue to
   use already allocated bits for authenticated and encrypted modes;
   this optimization is unimportant conceptually, but it could be useful
   in practice to make the best use of bits.)  Then, if the new cipher
   is negotiated, all subsequent operations simply use it instead of
   AES.  Note that the normal transition sequence would be used in such
   a case: implementations would probably first start supporting and
   preferring the new cipher, and then drop support for the old cipher
   (presumably no longer considered secure).











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   If the need arises to make more extensive changes (perhaps to replace
   AES with a 256-bit-block cipher), this would be more difficult and
   would require changing the layout of the messages.  However, the
   change can still be conducted within the framework of OWAMP
   extensibility using the Modes/Mode words.  The semantics of the new
   bits (or single bit, if the optimization described above is used)
   would include the change to message layout as well as the change in
   the cryptographic primitive.

   Each of the bits in the Modes word can be used for an independent
   extension.  The extensions signaled by various bits are orthogonal;
   for example, one bit might be allocated to change from AES-128 to
   some other cipher, another bit might be allocated to add a protocol
   feature (such as, e.g., support for measuring over multicast), yet
   another might be allocated to change a key derivation function, etc.
   The progression of versions is not a linear order, but rather a
   partial order.  An implementation can implement any subset of these
   features (of course, features can be made mandatory to implement,
   e.g., new more secure ciphers if they are needed).

   Should a cipher with a different key size (say, a 256-bit key) become
   needed, a new key derivation function for OWAMP-Test keys would also
   be needed.  The semantics of change in the cipher SHOULD then in the
   future be tied to the semantics of change in the key derivation
   function (KDF).  One KDF that might be considered for the purpose
   might be a pseudo-random function (PRF) with appropriately sized
   output, such as 256 bits (perhaps HMAC-SHA256, if it is then still
   considered a secure PRF), which could then be used to derive the
   OWAMP-Test session keys from the OWAMP-Control session key by using
   the OWAMP-Control session key as the HMAC key and the SID as HMAC
   message.

   Note that the replacement scheme outlined above is trivially
   susceptible to downgrade attacks: a malicious party in the middle can
   flip modes bits as the mode is negotiated so that the oldest and
   weakest mode supported by the two parties is used.  If this is deemed
   problematic at the time of cryptographic primitive replacement, the
   scheme might be augmented with a measure to prevent such an attack
   (by perhaps exchanging the modes again once a secure communications
   channel is established, comparing the two sets of mode words, and
   dropping the connection should they not match).

6.8.  Long-term Manually Managed Keys

   OWAMP-Control uses long-term keys with manual management.  These keys
   are used to automatically negotiate session keys for each OWAMP-
   Control session running in authenticated or encrypted mode.  The
   number of these keys managed by a server scales linearly with (and,



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   in fact, is equal to) the number of administratively different users
   (perhaps particular humans, roles, or robots representing sites) that
   need to connect to this server.  Similarly, the number of different
   manual keys managed by each client is the number of different servers
   that the client needs to connect to.  This use of manual long-term
   keys is compliant with [BCP107].

6.9.  (Not) Using Time as Salt

   A natural idea is to use the current time as salt when deriving
   session keys.  Unfortunately, this appears to be too limiting.

   Although OWAMP is often run on hosts with well-synchronized clocks,
   it is also possible to run it on hosts with clocks completely
   untrained.  The delays obtained thus are, of course, not directly
   usable; however, some metrics, such as unidirectional loss,
   reordering, measures of congestion such as the median delay minus
   minimum, and many others are usable directly and immediately (and
   improve upon the information that would have been provided by a
   round-trip measurement).  Further, even delay information can be
   useful with appropriate post-processing.  Indeed, one can even argue
   that running the clocks free and post-processing the results of a
   mesh of measurements will result in better accuracy, as more
   information is available a posteriori and correlation of data from
   different hosts is possible in post-processing, but not with online
   clock training.

   Given this, time is not used as salt in key derivation.

6.10.  The Use of AES-CBC and HMAC

   OWAMP relies on AES-CBC for confidentiality and on HMAC-SHA1
   truncated to 128 bits for message authentication.  Random IV choice
   is important for prevention of a codebook attack on the first block
   (it should also be noted that, with its 128-bit block size, AES is
   more resistant to codebook attacks than are ciphers with shorter
   blocks; we use random IV anyway).

   HMAC MUST verify.  It is crucial to check for this before using the
   message; otherwise, existential forgery becomes possible.  The
   complete message for which HMAC verification fails MUST be discarded
   (both for short messages consisting of a few blocks and potentially
   for long messages, such as a response to the Fetch-Session command).
   If such a message is part of OWAMP-Control, the connection MUST be
   dropped.

   Since OWAMP messages can have different numbers of blocks, the
   existential forgery attack described in example 9.62 of [MENEZES]



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   becomes a concern.  To prevent it (and to simplify implementation),
   the length of any message becomes known after decrypting its first
   block.

   A special case is the first (fixed-length) message sent by the
   client.  There, the token is a concatenation of the 128-bit challenge
   (transmitted by the server in the clear), a 128-bit AES Session-key
   (generated randomly by the client, encrypted with AES-CBC with IV=0),
   and a 256-bit HMAC-SHA1 Session-key used for authentication.  Since
   IV=0, the challenge (a single cipher block) is simply encrypted with
   the secret key.  Therefore, we rely on resistance of AES to chosen
   plaintext attacks (as the challenge could be substituted by an
   attacker).  It should be noted that the number of blocks of chosen
   plaintext an attacker can have encrypted with the secret key is
   limited by the number of sessions the client wants to initiate.  An
   attacker who knows the encryption of a server's challenge can produce
   an existential forgery of the session key and thus disrupt the
   session; however, any attacker can disrupt a session by corrupting
   the protocol messages in an arbitrary fashion.  Therefore, no new
   threat is created here; nevertheless, we require that the server
   never issues the same challenge twice.  (If challenges are generated
   randomly, a repetition would occur, on average, after 2^64 sessions;
   we deem this satisfactory as this is enough even for an implausibly
   busy server that participates in 1,000,000 sessions per second to go
   without repetitions for more than 500 centuries.)  With respect to
   the second part of the token, an attacker can produce an existential
   forgery of the session key by modifying the second half of the
   client's token while leaving the first part intact.  This forgery,
   however, would be immediately discovered by the client when the HMAC
   on the server's next message (acceptance or rejection of the
   connection) does not verify.

7.  Acknowledgements

   We would like to thank Guy Almes, Mark Allman, Jari Arkko, Hamid
   Asgari, Steven Van den Berghe, Eric Boyd, Robert Cole, Joan
   Cucchiara, Stephen Donnelly, Susan Evett, Sam Hartman, Kaynam
   Hedayat, Petri Helenius, Scott Hollenbeck, Russ Housley, Kitamura
   Yasuichi, Daniel H. T. R. Lawson, Will E. Leland, Bruce A. Mah,
   Allison Mankin, Al Morton, Attila Pasztor, Randy Presuhn, Matthew
   Roughan, Andy Scherrer, Henk Uijterwaal, and Sam Weiler for their
   comments, suggestions, reviews, helpful discussion and proof-reading.

8.  IANA Considerations

   IANA has allocated a well-known TCP port number (861) for the OWAMP-
   Control part of the OWAMP protocol.




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9.  Internationalization Considerations

   The protocol does not carry any information in a natural language,
   with the possible exception of the KeyID in OWAMP-Control, which is
   encoded in UTF-8.

10.  References

10.1.  Normative References

   [AES]           Advanced Encryption Standard (AES),
                   http://csrc.nist.gov/encryption/aes/

   [BCP107]        Bellovin, S. and R. Housley, "Guidelines for
                   Cryptographic Key Management", BCP 107, RFC 4107,
                   June 2005.

   [RFC2104]       Krawczyk, H., Bellare, M., and R. Canetti, "HMAC:
                   Keyed-Hashing for Message Authentication", RFC 2104,
                   February 1997.

   [RFC2119]       Bradner, S., "Key words for use in RFCs to Indicate
                   Requirement Levels", BCP 14, RFC 2119, March 1997.

   [RFC2330]       Paxson, V., Almes, G., Mahdavi, J., and M. Mathis,
                   "Framework for IP Performance Metrics", RFC 2330, May
                   1998.

   [RFC2474]       Nichols, K., Blake, S., Baker, F., and D. Black,
                   "Definition of the Differentiated Services Field (DS
                   Field) in the IPv4 and IPv6 Headers", RFC 2474,
                   December 1998.

   [RFC2679]       Almes, G., Kalidindi, S., and M. Zekauskas, "A One-
                   way Delay Metric for IPPM", RFC 2679, September 1999.

   [RFC2680]       Almes, G., Kalidindi, S., and M. Zekauskas, "A One-
                   way Packet Loss Metric for IPPM", RFC 2680, September
                   1999.

   [RFC2836]       Brim, S., Carpenter, B., and F. Le Faucheur, "Per Hop
                   Behavior Identification Codes", RFC 2836, May 2000.

   [RFC2898]       Kaliski, B., "PKCS #5: Password-Based Cryptography
                   Specification Version 2.0", RFC 2898, September 2000.






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10.2.  Informative References

   [APAN]          Z. Shu and K. Kobayashi, "HOTS: An OWAMP-Compliant
                   Hardware Packet Timestamper", In Proceedings of PAM
                   2005, http://www.springerlink.com/index/
                   W4GBD39YWC11GQTN.pdf

   [BRIX]          Brix Networks, http://www.brixnet.com/

   [ZIGG]          J. H. Ahrens, U. Dieter, "Computer methods for
                   sampling from the exponential and normal
                   distributions", Communications of ACM, volume 15,
                   issue 10, 873-882, 1972.
                   http://doi.acm.org/10.1145/355604.361593

   [MENEZES]       A. J. Menezes, P. C. van Oorschot, and S. A.
                   Vanstone, Handbook of Applied Cryptography, CRC
                   Press, revised reprint with updates, 1997.

   [KNUTH]         D. Knuth, The Art of Computer Programming, vol.2, 3rd
                   edition, 1998.

   [Abilene]       One-way Latency Measurement (OWAMP),
                   http://e2epi.internet2.edu/owamp/

   [RIJN]          Reference ANSI C Implementation of Rijndael,
                   http://www.esat.kuleuven.ac.be/~rijmen/
                   rijndael/rijndaelref.zip

   [RIPE]          RIPE NCC Test-Traffic Measurements home,
                   http://www.ripe.net/test-traffic/.

   [SURVEYOR]      Surveyor Home Page,
                   http://www.advanced.org/surveyor/.

   [SURVEYOR-INET] S. Kalidindi and M. Zekauskas, "Surveyor: An
                   Infrastructure for Network Performance Measurements",
                   Proceedings of INET'99, June 1999.
                   http://www.isoc.org/inet99/proceedings/4h/4h_2.htm

   [RFC1305]       Mills, D., "Network Time Protocol (Version 3)
                   Specification, Implementation and Analysis", RFC
                   1305, March 1992.

   [RFC2246]       Dierks, T. and C. Allen, "The TLS Protocol Version
                   1.0", RFC 2246, January 1999.





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   [RFC2401]       Kent, S. and R. Atkinson, "Security Architecture for
                   the Internet Protocol", RFC 2401, November 1998.

   [RFC3546]       Blake-Wilson, S., Nystrom, M., Hopwood, D.,
                   Mikkelsen, J., and T. Wright, "Transport Layer
                   Security (TLS) Extensions", RFC 3546, June 2003.

   [RFC4086]       Eastlake, D., 3rd, Schiller, J., and S. Crocker,
                   "Randomness Requirements for Security", BCP 106, RFC
                   4086, June 2005.









































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Appendix A: Sample C Code for Exponential Deviates

   The values in array Q[] are the exact values that MUST be used by all
   implementations (see Sections 5.1 and 5.2).  This appendix only
   serves for illustrative purposes.

   /*
   ** Example usage: generate a stream of exponential (mean 1)
   ** random quantities (ignoring error checking during initialization).
   ** If a variate with some mean mu other than 1 is desired, the output
   ** of this algorithm can be multiplied by mu according to the rules
   ** of arithmetic we described.

   ** Assume that a 16-octet 'seed' has been initialized
   ** (as the shared secret in OWAMP, for example)
   ** unsigned char seed[16];

   ** OWPrand_context next;

   ** (initialize state)
   ** OWPrand_context_init(&next, seed);

   ** (generate a sequence of exponential variates)
   ** while (1) {
   **    u_int64_t num = OWPexp_rand64(&next);
         <do something with num here>
                    ...
   ** }
   */

   #include <stdlib.h>

   typedef u_int64_t u_int64_t;

   /* (K - 1) is the first k such that Q[k] > 1 - 1/(2^32). */
   #define K 12

   #define BIT31   0x80000000UL    /* See if first bit in the lower
                                      32 bits is zero. */
   #define MASK32(n)       ((n) & 0xFFFFFFFFUL)

   #define EXP2POW32       0x100000000ULL

   typedef struct OWPrand_context {
           unsigned char counter[16];/* Counter (network byte order).*/
           keyInstance key;          /* Key to encrypt the counter.*/
           unsigned char out[16];    /* The encrypted block.*/




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   } OWPrand_context;

   /*
   ** The array has been computed according to the formula:
   **
   **       Q[k] = (ln2)/(1!) + (ln2)^2/(2!) + ... + (ln2)^k/(k!)
   **
   ** as described in algorithm S. (The values below have been
   ** multiplied by 2^32 and rounded to the nearest integer.)
   ** These exact values MUST be used so that different implementation
   ** produce the same sequences.
   */
   static u_int64_t Q[K] = {
           0,        /* Placeholder - so array indices start from 1. */
           0xB17217F8,
           0xEEF193F7,
           0xFD271862,
           0xFF9D6DD0,
           0xFFF4CFD0,
           0xFFFEE819,
           0xFFFFE7FF,
           0xFFFFFE2B,
           0xFFFFFFE0,
           0xFFFFFFFE,
           0xFFFFFFFF
   };

   /* this element represents ln2 */
   #define LN2 Q[1]

   /*
   ** Convert an unsigned 32-bit integer into a u_int64_t number.
   */
   u_int64_t
   OWPulong2num64(u_int32_t a)
   {
           return ((u_int64_t)1 << 32) * a;
   }

   /*
   ** Arithmetic functions on u_int64_t numbers.
   */

   /*
   ** Addition.
   */
   u_int64_t
   OWPnum64_add(u_int64_t x, u_int64_t y)



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   {
           return x + y;
   }

   /*
   ** Multiplication.  Allows overflow.  Straightforward implementation
   ** of Algorithm 4.3.1.M (p.268) from [KNUTH].
   */
   u_int64_t
   OWPnum64_mul(u_int64_t x, u_int64_t y)
   {
           unsigned long w[4];
           u_int64_t xdec[2];
           u_int64_t ydec[2];

           int i, j;
           u_int64_t k, t, ret;

           xdec[0] = MASK32(x);
           xdec[1] = MASK32(x>>32);
           ydec[0] = MASK32(y);
           ydec[1] = MASK32(y>>32);

           for (j = 0; j < 4; j++)
                   w[j] = 0;

           for (j = 0; j < 2; j++) {
                   k = 0;
                   for (i = 0; ; ) {
                           t = k + (xdec[i]*ydec[j]) + w[i + j];
                           w[i + j] = t%EXP2POW32;
                           k = t/EXP2POW32;
                           if (++i < 2)
                                   continue;
                           else {
                                   w[j + 2] = k;
                                   break;
                           }
                   }
           }

           ret = w[2];
           ret <<= 32;
           return w[1] + ret;
   }


   /*



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   ** Seed the random number generator using a 16-byte quantity 'seed'
   ** (== the session ID in OWAMP). This function implements step U1
   ** of algorithm Unif.
   */

   void
   OWPrand_context_init(OWPrand_context *next, unsigned char *seed)
   {
           int i;

           /* Initialize the key */
           rijndaelKeyInit(next->key, seed);

           /* Initialize the counter with zeros */
           memset(next->out, 0, 16);
           for (i = 0; i < 16; i++)
                   next->counter[i] = 0UL;
   }


   /*
   ** Random number generating functions.
   */

   /*
   ** Generate and return a 32-bit uniform random value (saved in the
   **less significant half of the u_int64_t).  This function implements
   **steps U2-U4 of the algorithm Unif.
   */
   u_int64_t
   OWPunif_rand64(OWPrand_context *next)
   {
           int j;
           u_int8_t  *buf;
           u_int64_t  ret = 0;

           /* step U2 */
           u_int8_t i = next->counter[15] & (u_int8_t)3;
           if (!i)
                   rijndaelEncrypt(next->key, next->counter, next->out);

           /* Step U3.  Increment next.counter as a 16-octet single
              quantity in network byte order for AES counter mode. */
           for (j = 15; j >= 0; j--)
                   if (++next->counter[j])
                           break;

           /* Step U4.  Do output.  The last 4 bytes of ret now contain



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              the random integer in network byte order */
           buf = &next->out[4*i];
           for (j=0; j<4; j++) {
                   ret <<= 8;
                   ret += *buf++;
           }
           return ret;
   }

   /*
   ** Generate an exponential deviate with mean 1.
   */
   u_int64_t
   OWPexp_rand64(OWPrand_context *next)
   {
           unsigned long i, k;
           u_int32_t j = 0;
           u_int64_t U, V, J, tmp;

           /* Step S1. Get U and shift */
           U = OWPunif_rand64(next);

           while ((U & BIT31) && (j < 32)) { /* Shift until first 0. */
                   U <<= 1;
                   j++;
           }
           /* Remove the 0 itself. */
           U <<= 1;

           U = MASK32(U);  /* Keep only the fractional part. */
           J = OWPulong2num64(j);

           /* Step S2.  Immediate acceptance? */
           if (U < LN2)       /* return  (j*ln2 + U) */
                   return OWPnum64_add(OWPnum64_mul(J, LN2), U);

           /* Step S3.  Minimize. */
           for (k = 2; k < K; k++)
                   if (U < Q[k])
                           break;
           V = OWPunif_rand64(next);
           for (i = 2; i <= k; i++) {
                   tmp = OWPunif_rand64(next);
                   if (tmp < V)
                           V = tmp;
           }

           /* Step S4.  Return (j+V)*ln2 */



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           return OWPnum64_mul(OWPnum64_add(J, V), LN2);
   }

Appendix B: Test Vectors for Exponential Deviates

   It is important that the test schedules generated by different
   implementations from identical inputs be identical.  The non-trivial
   part is the generation of pseudo-random exponentially distributed
   deviates.  To aid implementors in verifying interoperability, several
   test vectors are provided.  For each of the four given 128-bit values
   of SID represented as hexadecimal numbers, 1,000,000 exponentially
   distributed 64-bit deviates are generated as described above.  As
   they are generated, they are all added to each other.  The sum of all
   1,000,000 deviates is given as a hexadecimal number for each SID.  An
   implementation MUST produce exactly these hexadecimal numbers.  To
   aid in the verification of the conversion of these numbers to values
   of delay in seconds, approximate values are given (assuming
   lambda=1).  An implementation SHOULD produce delay values in seconds
   that are close to the ones given below.

       SID = 0x2872979303ab47eeac028dab3829dab2
       SUM[1000000] = 0x000f4479bd317381 (1000569.739036 seconds)

       SID = 0x0102030405060708090a0b0c0d0e0f00
       SUM[1000000] = 0x000f433686466a62 (1000246.524512 seconds)

       SID = 0xdeadbeefdeadbeefdeadbeefdeadbeef
       SUM[1000000] = 0x000f416c8884d2d3 (999788.533277 seconds)

       SID = 0xfeed0feed1feed2feed3feed4feed5ab
       SUM[1000000] = 0x000f3f0b4b416ec8 (999179.293967 seconds)




















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Authors' Addresses

   Stanislav Shalunov
   Internet2
   1000 Oakbrook Drive, Suite 300
   Ann Arbor, MI 48104

   EMail: shalunov@internet2.edu
   WWW: http://www.internet2.edu/~shalunov/


   Benjamin Teitelbaum
   Internet2
   1000 Oakbrook Drive, Suite 300
   Ann Arbor, MI 48104

   EMail: ben@internet2.edu
   WWW: http://people.internet2.edu/~ben/


   Anatoly Karp
   Computer Sciences Department
   University of Wisconsin-Madison
   Madison, WI 53706

   EMail: akarp@cs.wisc.edu


   Jeff W. Boote
   Internet2
   1000 Oakbrook Drive, Suite 300
   Ann Arbor, MI 48104

   EMail: boote@internet2.edu


   Matthew J. Zekauskas
   Internet2
   1000 Oakbrook Drive, Suite 300
   Ann Arbor, MI 48104

   EMail: matt@internet2.edu









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RFC 4656          One-way Active Measurement Protocol     September 2006


Full Copyright Statement

   Copyright (C) The Internet Society (2006).

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