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RFC 5905

 
 
 

Network Time Protocol Version 4: Protocol and Algorithms Specification

Part 2 of 5, p. 16 to 39
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7.  Data Structures

   The NTP state machines are defined in the following sections.  State
   variables are separated into classes according to their function in
   packet headers, peer and poll processes, the system process, and the
   clock discipline process.  Packet variables represent the NTP header
   values in transmitted and received packets.  Peer and poll variables
   represent the contents of the association for each server separately.
   System variables represent the state of the server as seen by its
   dependent clients.  Clock discipline variables represent the internal
   workings of the clock discipline algorithm.  An example is described
   in Appendix A.

7.1.  Structure Conventions

   In order to distinguish between different variables of the same name
   but used in different processes, the naming convention summarized in
   Figure 5 is adopted.  A receive packet variable v is a member of the
   packet structure r with fully qualified name r.v.  In a similar
   manner, x.v is a transmit packet variable, p.v is a peer variable,
   s.v is a system variable, and c.v is a clock discipline variable.
   There is a set of peer variables for each association; there is only
   one set of system and clock variables.

                   +------+---------------------------------+
                   | Name | Description                     |
                   +------+---------------------------------+
                   | r.   | receive packet header variable  |
                   | x.   | transmit packet header variable |
                   | p.   | peer/poll variable              |
                   | s.   | system variable                 |
                   | c.   | clock discipline variable       |
                   +------+---------------------------------+

                       Figure 5: Prefix Conventions

7.2.  Global Parameters

   In addition to the variable classes, a number of global parameters
   are defined in this document, including those shown with values in
   Figure 6.

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            +-----------+-------+----------------------------------+
            | Name      | Value | Description                      |
            +-----------+-------+----------------------------------+
            | PORT      | 123   | NTP port number                  |
            | VERSION   | 4     | NTP version number                   |
            | TOLERANCE | 15e-6 | frequency tolerance PHI (s/s)    |
            | MINPOLL   | 4     | minimum poll exponent (16 s)     |
            | MAXPOLL   | 17    | maximum poll exponent (36 h)     |
            | MAXDISP   | 16    | maximum dispersion (16 s)        |
            | MINDISP   | .005  | minimum dispersion increment (s) |
            | MAXDIST   | 1     | distance threshold (1 s)         |
            | MAXSTRAT  | 16    | maximum stratum number           |
            +-----------+-------+----------------------------------+

                        Figure 6: Global Parameters

   While these are the only global parameters needed for
   interoperability, a larger collection is necessary in any
   implementation.  Appendix A.1.1 contains those used by the skeleton
   for the mitigation algorithms, clock discipline algorithm, and
   related implementation-dependent functions.  Some of these parameter
   values are cast in stone, like the NTP port number assigned by the
   IANA and the version number assigned NTPv4 itself.  Others, like the
   frequency tolerance (also called PHI), involve an assumption about
   the worst-case behavior of a system clock once synchronized and then
   allowed to drift when its sources have become unreachable.  The
   minimum and maximum parameters define the limits of state variables
   as described in later sections of this document.

   While shown with fixed values in this document, some implementations
   may make them variables adjustable by configuration commands.  For
   instance, the reference implementation computes the value of
   PRECISION as log2 of the minimum time in several iterations to read
   the system clock.

7.3.  Packet Header Variables

   The most important state variables from an external point of view are
   the packet header variables described in Figure 7 and below.  The NTP
   packet header consists of an integral number of 32-bit (4 octet)
   words in network byte order.  The packet format consists of three
   components: the header itself, one or more optional extension fields,
   and an optional message authentication code (MAC).  The header
   component is identical to the NTPv3 header and previous versions.
   The optional extension fields are used by the Autokey public key
   cryptographic algorithms described in [RFC5906].  The optional MAC is
   used by both Autokey and the symmetric key cryptographic algorithm
   described in this RFC.

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               +-----------+------------+-----------------------+
               | Name      | Formula    | Description           |
               +-----------+------------+-----------------------+
               | leap      | leap       | leap indicator (LI)   |
               | version   | version    | version number (VN)   |
               | mode      | mode       | mode                  |
               | stratum   | stratum    | stratum               |
               | poll      | poll       | poll exponent         |
               | precision | rho        | precision exponent    |
               | rootdelay | delta_r    | root delay            |
               | rootdisp  | epsilon_r  | root dispersion       |
               | refid     | refid      | reference ID          |
               | reftime   | reftime    | reference timestamp   |
               | org       | T1         | origin timestamp      |
               | rec       | T2         | receive timestamp     |
               | xmt       | T3         | transmit timestamp    |
               | dst       | T4         | destination timestamp |
               | keyid     | keyid      | key ID                |
               | dgst      | dgst       | message digest        |
               +-----------+------------+-----------------------+

                     Figure 7: Packet Header Variables

   The NTP packet is a UDP datagram [RFC0768].  Some fields use multiple
   words and others are packed in smaller fields within a word.  The NTP
   packet header shown in Figure 8 has 12 words followed by optional
   extension fields and finally an optional message authentication code
   (MAC) consisting of the Key Identifier field and Message Digest
   field.

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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
      +-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+
      |LI | VN  |Mode |    Stratum     |     Poll      |  Precision   |
      +-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+
      |                         Root Delay                            |
      +-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+
      |                         Root Dispersion                       |
      +-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+
      |                          Reference ID                         |
      +-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+
      |                                                               |
      +                     Reference Timestamp (64)                  +
      |                                                               |
      +-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+
      |                                                               |
      +                      Origin Timestamp (64)                    +
      |                                                               |
      +-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+
      |                                                               |
      +                      Receive Timestamp (64)                   +
      |                                                               |
      +-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+
      |                                                               |
      +                      Transmit Timestamp (64)                  +
      |                                                               |
      +-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+
      |                                                               |
      .                                                               .
      .                    Extension Field 1 (variable)               .
      .                                                               .
      |                                                               |
      +-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+
      |                                                               |
      .                                                               .
      .                    Extension Field 2 (variable)               .
      .                                                               .
      |                                                               |
      +-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+
      |                          Key Identifier                       |
      +-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+
      |                                                               |
      |                            dgst (128)                         |
      |                                                               |
      +-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+

                      Figure 8: Packet Header Format

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   The extension fields are used to add optional capabilities, for
   example, the Autokey security protocol [RFC5906].  The extension
   field format is presented in order for the packet to be parsed
   without the knowledge of the extension field functions.  The MAC is
   used by both Autokey and the symmetric key authentication scheme.

   A list of the packet header variables is shown in Figure 7 and
   described in detail below.  Except for a minor variation when using
   the IPv6 address family, these fields are backwards compatible with
   NTPv3.  The packet header fields apply to both transmitted packets (x
   prefix) and received packets (r prefix).  In Figure 8, the size of
   some multiple-word fields is shown in bits if not the default 32
   bits.  The basic header extends from the beginning of the packet to
   the end of the Transmit Timestamp field.

   The fields and associated packet variables (in parentheses) are
   interpreted as follows:

   LI Leap Indicator (leap): 2-bit integer warning of an impending leap
   second to be inserted or deleted in the last minute of the current
   month with values defined in Figure 9.

           +-------+----------------------------------------+
           | Value | Meaning                                |
           +-------+----------------------------------------+
           | 0     | no warning                             |
           | 1     | last minute of the day has 61 seconds  |
           | 2     | last minute of the day has 59 seconds  |
           | 3     | unknown (clock unsynchronized)         |
           +-------+----------------------------------------+

                         Figure 9: Leap Indicator

   VN Version Number (version): 3-bit integer representing the NTP
   version number, currently 4.

   Mode (mode): 3-bit integer representing the mode, with values defined
   in Figure 10.

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                      +-------+--------------------------+
                      | Value | Meaning                  |
                      +-------+--------------------------+
                      | 0     | reserved                 |
                      | 1     | symmetric active         |
                      | 2     | symmetric passive        |
                      | 3     | client                   |
                      | 4     | server                   |
                      | 5     | broadcast                |
                      | 6     | NTP control message      |
                      | 7     | reserved for private use |
                      +-------+--------------------------+

                       Figure 10: Association Modes

   Stratum (stratum): 8-bit integer representing the stratum, with
   values defined in Figure 11.

        +--------+-----------------------------------------------------+
        | Value  | Meaning                                             |
        +--------+-----------------------------------------------------+
        | 0      | unspecified or invalid                              |
        | 1      | primary server (e.g., equipped with a GPS receiver) |
        | 2-15   | secondary server (via NTP)                          |
        | 16     | unsynchronized                                      |
        | 17-255 | reserved                                            |
        +--------+-----------------------------------------------------+

                         Figure 11: Packet Stratum

   It is customary to map the stratum value 0 in received packets to
   MAXSTRAT (16) in the peer variable p.stratum and to map p.stratum
   values of MAXSTRAT or greater to 0 in transmitted packets.  This
   allows reference clocks, which normally appear at stratum 0, to be
   conveniently mitigated using the same clock selection algorithms used
   for external sources (see Appendix A.5.5.1 for an example).

   Poll: 8-bit signed integer representing the maximum interval between
   successive messages, in log2 seconds.  Suggested default limits for
   minimum and maximum poll intervals are 6 and 10, respectively.

   Precision: 8-bit signed integer representing the precision of the
   system clock, in log2 seconds.  For instance, a value of -18
   corresponds to a precision of about one microsecond.  The precision
   can be determined when the service first starts up as the minimum
   time of several iterations to read the system clock.

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   Root Delay (rootdelay): Total round-trip delay to the reference
   clock, in NTP short format.

   Root Dispersion (rootdisp): Total dispersion to the reference clock,
   in NTP short format.

   Reference ID (refid): 32-bit code identifying the particular server
   or reference clock.  The interpretation depends on the value in the
   stratum field.  For packet stratum 0 (unspecified or invalid), this
   is a four-character ASCII [RFC1345] string, called the "kiss code",
   used for debugging and monitoring purposes.  For stratum 1 (reference
   clock), this is a four-octet, left-justified, zero-padded ASCII
   string assigned to the reference clock.  The authoritative list of
   Reference Identifiers is maintained by IANA; however, any string
   beginning with the ASCII character "X" is reserved for unregistered
   experimentation and development.  The identifiers in Figure 12 have
   been used as ASCII identifiers:

     +------+----------------------------------------------------------+
     | ID   | Clock Source                                             |
     +------+----------------------------------------------------------+
     | GOES | Geosynchronous Orbit Environment Satellite               |
     | GPS  | Global Position System                                   |
     | GAL  | Galileo Positioning System                               |
     | PPS  | Generic pulse-per-second                                 |
     | IRIG | Inter-Range Instrumentation Group                        |
     | WWVB | LF Radio WWVB Ft. Collins, CO 60 kHz                     |
     | DCF  | LF Radio DCF77 Mainflingen, DE 77.5 kHz                  |
     | HBG  | LF Radio HBG Prangins, HB 75 kHz                         |
     | MSF  | LF Radio MSF Anthorn, UK 60 kHz                          |
     | JJY  | LF Radio JJY Fukushima, JP 40 kHz, Saga, JP 60 kHz       |
     | LORC | MF Radio LORAN C station, 100 kHz                        |
     | TDF  | MF Radio Allouis, FR 162 kHz                             |
     | CHU  | HF Radio CHU Ottawa, Ontario                             |
     | WWV  | HF Radio WWV Ft. Collins, CO                             |
     | WWVH | HF Radio WWVH Kauai, HI                                  |
     | NIST | NIST telephone modem                                     |
     | ACTS | NIST telephone modem                                     |
     | USNO | USNO telephone modem                                     |
     | PTB  | European telephone modem                                 |
     +------+----------------------------------------------------------+

                     Figure 12: Reference Identifiers

   Above stratum 1 (secondary servers and clients): this is the
   reference identifier of the server and can be used to detect timing
   loops.  If using the IPv4 address family, the identifier is the four-
   octet IPv4 address.  If using the IPv6 address family, it is the

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   first four octets of the MD5 hash of the IPv6 address.  Note that,
   when using the IPv6 address family on an NTPv4 server with a NTPv3
   client, the Reference Identifier field appears to be a random value
   and a timing loop might not be detected.

   Reference Timestamp: Time when the system clock was last set or
   corrected, in NTP timestamp format.

   Origin Timestamp (org): Time at the client when the request departed
   for the server, in NTP timestamp format.

   Receive Timestamp (rec): Time at the server when the request arrived
   from the client, in NTP timestamp format.

   Transmit Timestamp (xmt): Time at the server when the response left
   for the client, in NTP timestamp format.

   Destination Timestamp (dst): Time at the client when the reply
   arrived from the server, in NTP timestamp format.

   Note: The Destination Timestamp field is not included as a header
   field; it is determined upon arrival of the packet and made available
   in the packet buffer data structure.

   If the NTP has access to the physical layer, then the timestamps are
   associated with the beginning of the symbol after the start of frame.
   Otherwise, implementations should attempt to associate the timestamp
   to the earliest accessible point in the frame.

   The MAC consists of the Key Identifier followed by the Message
   Digest.  The message digest, or cryptosum, is calculated as in
   [RFC1321] over all NTP-header and optional extension fields, but not
   the MAC itself.

   Extension Field n: See Section 7.5 for a description of the format of
   this field.

   Key Identifier (keyid): 32-bit unsigned integer used by the client
   and server to designate a secret 128-bit MD5 key.

   Message Digest (digest): 128-bit MD5 hash computed over the key
   followed by the NTP packet header and extensions fields (but not the
   Key Identifier or Message Digest fields).

   It should be noted that the MAC computation used here differs from
   those defined in [RFC1305] and [RFC4330] but is consistent with how
   existing implementations generate a MAC.

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7.4.  The Kiss-o'-Death Packet

   If the Stratum field is 0, which implies unspecified or invalid, the
   Reference Identifier field can be used to convey messages useful for
   status reporting and access control.  These are called Kiss-o'-Death
   (KoD) packets and the ASCII messages they convey are called kiss
   codes.  The KoD packets got their name because an early use was to
   tell clients to stop sending packets that violate server access
   controls.  The kiss codes can provide useful information for an
   intelligent client, either NTPv4 or SNTPv4.  Kiss codes are encoded
   in four-character ASCII strings that are left justified and zero
   filled.  The strings are designed for character displays and log
   files.  A list of the currently defined kiss codes is given in
   Figure 13.  Recipients of kiss codes MUST inspect them and, in the
   following cases, take these actions:

   a.  For kiss codes DENY and RSTR, the client MUST demobilize any
       associations to that server and stop sending packets to that
       server;

   b.  For kiss code RATE, the client MUST immediately reduce its
       polling interval to that server and continue to reduce it each
       time it receives a RATE kiss code.

   c.  Kiss codes beginning with the ASCII character "X" are for
       unregistered experimentation and development and MUST be ignored
       if not recognized.

   d.  Other than the above conditions, KoD packets have no protocol
       significance and are discarded after inspection.

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   +------+------------------------------------------------------------+
   | Code |                           Meaning                          |
   +------+------------------------------------------------------------+
   | ACST | The association belongs to a unicast server.               |
   | AUTH | Server authentication failed.                              |
   | AUTO | Autokey sequence failed.                                   |
   | BCST | The association belongs to a broadcast server.             |
   | CRYP | Cryptographic authentication or identification failed.     |
   | DENY | Access denied by remote server.                            |
   | DROP | Lost peer in symmetric mode.                               |
   | RSTR | Access denied due to local policy.                         |
   | INIT | The association has not yet synchronized for the first     |
   |      | time.                                                      |
   | MCST | The association belongs to a dynamically discovered server.|
   | NKEY | No key found. Either the key was never installed or is     |
   |      | not trusted.                                               |
   | RATE | Rate exceeded. The server has temporarily denied access    |
   |      | because the client exceeded the rate threshold.            |
   | RMOT | Alteration of association from a remote host running       |
   |      | ntpdc.                                                     |
   | STEP | A step change in system time has occurred, but the         |
   |      | association has not yet resynchronized.                    |
   +------+------------------------------------------------------------+

                           Figure 13: Kiss Codes

   The Receive Timestamp and the Transmit Timestamp (set by the server)
   are undefined when in a KoD packet and MUST NOT be relied upon to
   have valid values and MUST be discarded.

7.5.  NTP Extension Field Format

   In NTPv4, one or more extension fields can be inserted after the
   header and before the MAC, which is always present when an extension
   field is present.  Other than defining the field format, this
   document makes no use of the field contents.  An extension field
   contains a request or response message in the format shown in
   Figure 14.

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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
      +-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+
      |          Field Type           |            Length             |
      +-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+
      .                                                               .
      .                            Value                              .
      .                                                               .
      +-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+
      |                       Padding (as needed)                     |
      +-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+

                     Figure 14: Extension Field Format

   All extension fields are zero-padded to a word (four octets)
   boundary.  The Field Type field is specific to the defined function
   and is not elaborated here.  While the minimum field length
   containing required fields is four words (16 octets), a maximum field
   length remains to be established.

   The Length field is a 16-bit unsigned integer that indicates the
   length of the entire extension field in octets, including the Padding
   field.

8.  On-Wire Protocol

   The heart of the NTP on-wire protocol is the core mechanism that
   exchanges time values between servers, peers, and clients.  It is
   inherently resistant to lost or duplicate packets.  Data integrity is
   provided by the IP and UDP checksums.  No flow control or
   retransmission facilities are provided or necessary.  The protocol
   uses timestamps, which are either extracted from packet headers or
   struck from the system clock upon the arrival or departure of a
   packet.  Timestamps are precision data and should be restruck in the
   case of link-level retransmission and corrected for the time to
   compute a MAC in transmit.

   NTP messages make use of two different communication modes, one-to-
   one and one-to-many, commonly referred to as unicast and broadcast.
   For the purposes of this document, the term broadcast is interpreted
   as any available one-to-many mechanism.  For IPv4, this equates to
   either IPv4 broadcast or IPv4 multicast.  For IPv6, this equates to
   IPv6 multicast.  For this purpose, IANA has allocated the IPv4
   multicast address 224.0.1.1 and the IPv6 multicast address ending
   :101, with the prefix determined by scoping rules.  Any other non-
   allocated multicast address may also be used in addition to these
   allocated multicast addresses.

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   The on-wire protocol uses four timestamps numbered t1 through t4 and
   three state variables org, rec, and xmt, as shown in Figure 15.  This
   figure shows the most general case where each of two peers, A and B,
   independently measure the offset and delay relative to the other.
   For purposes of illustration, the packet timestamps are shown in
   lowercase, while the state variables are shown in uppercase.  The
   state variables are copied from the packet timestamps upon arrival or
   departure of a packet.

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             t2            t3           t6            t7
        +---------+   +---------+   +---------+   +---------+
        |    0    |   |    t1   |   |   t3    |   |    t5   |
        +---------+   +---------+   +---------+   +---------+
        |    0    |   |    t2   |   |   t4    |   |    t6   |  Packet
        +---------+   +---------+   +---------+   +---------+ Timestamps
        |   t1    |   |t3=clock |   |   t5    |   |t7=clock |
        +---------+   +---------+   +---------+   +---------+
        |t2=clock |                 |t6=clock |
        +---------+                 +---------+
                                                               Peer B
        +---------+   +---------+   +---------+   +---------+
   org  |   T1    |   |    T1   |   | t5<>T1? |   |    T5   |
        +---------+   +---------+   +---------+   +---------+   State
   rec  |   T2    |   |    T2   |   |   T6    |   |    T6   | Variables
        +---------+   +---------+   +---------+   +---------+
   xmt  |    0    |   |    T3   |   |  t3=T3? |   |    T7   |
        +---------+   +---------+   +---------+   +---------+

                  t2      t3                 t6          t7
        ---------------------------------------------------------
                 /\         \                 /\            \
                 /           \                /              \
                /             \              /                \
               /               \/           /                 \/
        ---------------------------------------------------------
             t1                t4         t5                  t8

            t1            t4            t5             t8
        +---------+   +---------+   +---------+   +---------+
        |    0    |   |    t1   |   |   t3    |   |    t5   |
        +---------+   +---------+   +---------+   +---------+
        |    0    |   |    t2   |   |   t4    |   |    t6   |  Packet
        +---------+   +---------+   +---------+   +---------+ Timestamps
        |t1=clock |   |    t3   |   |t5=clock |   |    t7   |
        +---------+   +---------+   +---------+   +---------+
                      |t4=clock |                 |t8=clock |
                      +---------+                 +---------+
                                                               Peer A
        +---------+   +---------+   +---------+   +---------+
   org  |    0    |   |  t3<>0? |   |   T3    |   | t7<>T3? |
        +---------+   +---------+   +---------+   +---------+   State
   rec  |    0    |   |    T4   |   |   T4    |   |    T8   | Variables
        +---------+   +---------+   +---------+   +---------+
   xmt  |   T1    |   |  t1=T1? |   |   T5    |   |  t5=T5? |
        +---------+   +---------+   +---------+   +---------+

                        Figure 15: On-Wire Protocol

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   In the figure, the first packet transmitted by A contains only the
   origin timestamp t1, which is then copied to T1.  B receives the
   packet at t2 and copies t1 to T1 and the receive timestamp t2 to T2.
   At this time or some time later at t3, B sends a packet to A
   containing t1 and t2 and the transmit timestamp t3.  All three
   timestamps are copied to the corresponding state variables.  A
   receives the packet at t4 containing the three timestamps t1, t2, and
   t3 and the destination timestamp t4.  These four timestamps are used
   to compute the offset and delay of B relative to A, as described
   below.

   Before the xmt and org state variables are updated, two sanity checks
   are performed in order to protect against duplicate, bogus, or
   replayed packets.  In the exchange above, a packet is duplicate or
   replay if the transmit timestamp t3 in the packet matches the org
   state variable T3.  A packet is bogus if the origin timestamp t1 in
   the packet does not match the xmt state variable T1.  In either of
   these cases, the state variables are updated, then the packet is
   discarded.  To protect against replay of the last transmitted packet,
   the xmt state variable is set to zero immediately after a successful
   bogus check.

   The four most recent timestamps, T1 through T4, are used to compute
   the offset of B relative to A

   theta = T(B) - T(A) = 1/2 * [(T2-T1) + (T3-T4)]

   and the round-trip delay

   delta = T(ABA) = (T4-T1) - (T3-T2).

   Note that the quantities within parentheses are computed from 64-bit
   unsigned timestamps and result in signed values with 63 significant
   bits plus sign.  These values can represent dates from 68 years in
   the past to 68 years in the future.  However, the offset and delay
   are computed as sums and differences of these values, which contain
   62 significant bits and two sign bits, so they can represent
   unambiguous values from 34 years in the past to 34 years in the
   future.  In other words, the time of the client must be set within 34
   years of the server before the service is started.  This is a
   fundamental limitation with 64-bit integer arithmetic.

   In implementations where floating double arithmetic is available, the
   first-order differences can be converted to floating double and the
   second-order sums and differences computed in that arithmetic.  Since

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   the second-order terms are typically very small relative to the
   timestamp magnitudes, there is no loss in significance, yet the
   unambiguous range is restored from 34 years to 68 years.

   In some scenarios where the initial frequency offset of the client is
   relatively large and the actual propagation time small, it is
   possible for the delay computation to become negative.  For instance,
   if the frequency difference is 100 ppm and the interval T4-T1 is 64
   s, the apparent delay is -6.4 ms.  Since negative values are
   misleading in subsequent computations, the value of delta should be
   clamped not less than s.rho, where s.rho is the system precision
   described in Section 11.1, expressed in seconds.

   The discussion above assumes the most general case where two
   symmetric peers independently measure the offsets and delays between
   them.  In the case of a stateless server, the protocol can be
   simplified.  A stateless server copies T3 and T4 from the client
   packet to T1 and T2 of the server packet and tacks on the transmit
   timestamp T3 before sending it to the client.  Additional details for
   filling in the remaining protocol fields are given in a Section 9 and
   following sections and in the appendix.

   Note that the on-wire protocol as described resists replay of a
   server response packet.  However, it does not resist replay of the
   client request packet, which would result in a server reply packet
   with new values of T2 and T3 and result in incorrect offset and
   delay.  This vulnerability can be avoided by setting the xmt state
   variable to zero after computing the offset and delay.

9.  Peer Process

   The process descriptions to follow include a listing of the important
   state variables followed by an overview of the process operations
   implemented as routines.  Frequent reference is made to the skeleton
   in the appendix.  The skeleton includes C-language fragments that
   describe the functions in more detail.  It includes the parameters,
   variables, and declarations necessary for a conforming NTPv4
   implementation.  However, many additional variables and routines may
   be necessary in a working implementation.

   The peer process is called upon arrival of a server or peer packet.
   It runs the on-wire protocol to determine the clock offset and round-
   trip delay and computes statistics used by the system and poll
   processes.  Peer variables are instantiated in the association data
   structure when the structure is initialized and updated by arriving
   packets.  There is a peer process, poll process, and association
   process for each server.

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9.1.  Peer Process Variables

   Figures 16, 17, 18, and 19 summarize the common names, formula names,
   and a short description of the peer variables.  The common names and
   formula names are interchangeable; formula names are intended to
   increase readability of equations in this specification.  Unless
   noted otherwise, all peer variables have assumed prefix p.

                 +---------+----------+-----------------------+
                 | Name    | Formula  | Description           |
                 +---------+----------+-----------------------+
                 | srcaddr | srcaddr  | source address        |
                 | srcport | srcport  | source port           |
                 | dstaddr | dstaddr  | destination address   |
                 | dstport | destport | destination port      |
                 | keyid   | keyid    | key identifier key ID |
                 +---------+----------+-----------------------+

              Figure 16: Peer Process Configuration Variables


                +-----------+------------+---------------------+
                | Name      | Formula    | Description         |
                +-----------+------------+---------------------+
                | leap      | leap       | leap indicator      |
                | version   | version    | version number      |
                | mode      | mode       | mode                |
                | stratum   | stratum    | stratum             |
                | ppoll     | ppoll      | peer poll exponent  |
                | rootdelay | delta_r    | root delay          |
                | rootdisp  | epsilon_r  | root dispersion     |
                | refid     | refid      | reference ID        |
                | reftime   | reftime    | reference timestamp |
                +-----------+------------+---------------------+

                 Figure 17: Peer Process Packet Variables


                     +------+---------+--------------------+
                     | Name | Formula | Description        |
                     +------+---------+--------------------+
                     | org  | T1      | origin timestamp   |
                     | rec  | T2      | receive timestamp  |
                     | xmt  | T3      | transmit timestamp |
                     | t    | t       | packet time        |
                     +------+---------+--------------------+

                Figure 18: Peer Process Timestamp Variables

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                     +--------+---------+-----------------+
                     | Name   | Formula | Description     |
                     +--------+---------+-----------------+
                     | offset | theta   | clock offset    |
                     | delay  | delta   | round-trip delay|
                     | disp   | epsilon | dispersion      |
                     | jitter | psi     | jitter          |
                     | filter | filter  | clock filter    |
                     | tp     | t_p     | filter time     |
                     +--------+---------+-----------------+

               Figure 19: Peer Process Statistics Variables

   The following configuration variables are normally initialized when
   the association is mobilized, either from a configuration file or
   upon the arrival of the first packet for an unknown association.

   srcaddr: IP address of the remote server or reference clock.  This
   becomes the destination IP address in packets sent from this
   association.

   srcport: UDP port number of the server or reference clock.  This
   becomes the destination port number in packets sent from this
   association.  When operating in symmetric modes (1 and 2), this field
   must contain the NTP port number PORT (123) assigned by the IANA.  In
   other modes, it can contain any number consistent with local policy.

   dstaddr: IP address of the client.  This becomes the source IP
   address in packets sent from this association.

   dstport: UDP port number of the client, ordinarily the NTP port
   number PORT (123) assigned by the IANA.  This becomes the source port
   number in packets sent from this association.

   keyid: Symmetric key ID for the 128-bit MD5 key used to generate and
   verify the MAC.  The client and server or peer can use different
   values, but they must map to the same key.

   The variables defined in Figure 17 are updated from the packet header
   as each packet arrives.  They are interpreted in the same way as the
   packet variables of the same names.  It is convenient for later
   processing to convert the NTP short format packet values r.rootdelay
   and r.rootdisp to floating doubles as peer variables.

   The variables defined in Figure 18 include the timestamps exchanged
   by the on-wire protocol in Section 8.  The t variable is the seconds
   counter c.t associated with these values.  The c.t variable is
   maintained by the clock-adjust process described in Section 12.  It

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   counts the seconds since the service was started.  The variables
   defined in Figure 19 include the statistics computed by the
   clock_filter() routine described in Section 10.  The tp variable is
   the seconds counter associated with these values.

9.2.  Peer Process Operations

   The receive routine defines the process flow upon the arrival of a
   packet.  An example is described by the receive() routine in
   Appendix A.5.1.  There is no specific method required for access
   control, although it is recommended that implementations include such
   a scheme, which is similar to many others now in widespread use.  The
   access() routine in Appendix A.5.4 describes a method of implementing
   access restrictions using an access control list (ACL).  Format
   checks require correct field length and alignment, acceptable version
   number (1-4), and correct extension field syntax, if present.

   There is no specific requirement for authentication; however, if
   authentication is implemented, then the MD5-keyed hash algorithm
   described in [RFC1321] must be supported.

   Next, the association table is searched for matching source address
   and source port, for example, using the find_assoc() routine in
   Appendix A.5.1.  Figure 20 is a dispatch table where the columns
   correspond to the packet mode and rows correspond to the association
   mode.  The intersection of the association and packet modes
   dispatches processing to one of the following steps.

           +------------------+---------------------------------------+
           |                  |              Packet Mode              |
           +------------------+-------+-------+-------+-------+-------+
           | Association Mode |   1   |   2   |   3   |   4   |   5   |
           +------------------+-------+-------+-------+-------+-------+
           | No Association 0 | NEWPS | DSCRD | FXMIT | MANY  | NEWBC |
           | Symm. Active   1 | PROC  | PROC  | DSCRD | DSCRD | DSCRD |
           | Symm. Passive  2 | PROC  | ERR   | DSCRD | DSCRD | DSCRD |
           | Client         3 | DSCRD | DSCRD | DSCRD | PROC  | DSCRD |
           | Server         4 | DSCRD | DSCRD | DSCRD | DSCRD | DSCRD |
           | Broadcast      5 | DSCRD | DSCRD | DSCRD | DSCRD | DSCRD |
           | Bcast Client   6 | DSCRD | DSCRD | DSCRD | DSCRD | PROC  |
           +------------------+-------+-------+-------+-------+-------+

                      Figure 20: Peer Dispatch Table

   DSCRD.  This indicates a non-fatal violation of protocol as the
   result of a programming error, long-delayed packet, or replayed
   packet.  The peer process discards the packet and exits.

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   ERR.  This indicates a fatal violation of protocol as the result of a
   programming error, long-delayed packet, or replayed packet.  The peer
   process discards the packet, demobilizes the symmetric passive
   association, and exits.

   FXMIT.  This indicates a client (mode 3) packet matching no
   association (mode 0).  If the destination address is not a broadcast
   address, the server constructs a server (mode 4) packet and returns
   it to the client without retaining state.  The server packet header
   is constructed.  An example is described by the fast_xmit() routine
   in Appendix A.5.3.  The packet header is assembled from the receive
   packet and system variables as shown in Figure 21.  If the
   s.rootdelay and s.rootdisp system variables are stored in floating
   double, they must be converted to NTP short format first.

                   +-----------------------------------+
                   | Packet Variable -->   Variable    |
                   +-----------------------------------+
                   | r.leap        -->     p.leap      |
                   | r.mode        -->     p.mode      |
                   | r.stratum     -->     p.stratum   |
                   | r.poll        -->     p.ppoll     |
                   | r.rootdelay   -->     p.rootdelay |
                   | r.rootdisp    -->     p.rootdisp  |
                   | r.refid       -->     p.refid     |
                   | r.reftime     -->     p.reftime   |
                   | r.keyid       -->     p.keyid     |
                   +-----------------------------------+

                     Figure 21: Receive Packet Header

   Note that, if authentication fails, the server returns a special
   message called a crypto-NAK.  This message includes the normal NTP
   header data shown in Figure 8, but with a MAC consisting of four
   octets of zeros.  The client MAY accept or reject the data in the
   message.  After these actions, the peer process exits.

   If the destination address is a multicast address, the sender is
   operating in manycast client mode.  If the packet is valid and the
   server stratum is less than the client stratum, the server sends an
   ordinary server (mode 4) packet, but one which uses its unicast
   destination address.  A crypto-NAK is not sent if authentication
   fails.  After these actions, the peer process exits.

   MANY: This indicates a server (mode 4) packet matching no
   association.  Ordinarily, this can happen only as the result of a
   manycast server reply to a previously sent multicast client packet.

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   If the packet is valid, an ordinary client (mode 3) association is
   mobilized and operation continues as if the association was mobilized
   by the configuration file.

   NEWBC.  This indicates a broadcast (mode 5) packet matching no
   association.  The client mobilizes either a client (mode 3) or
   broadcast client (mode 6) association.  Examples are shown in the
   mobilize() and clear() routines in Appendix A.2.  Then, the packet is
   validated and the peer variables initialized.  An example is provided
   by the packet() routine in Appendix A.5.1.1.

   If the implementation supports no additional security or calibration
   functions, the association mode is set to broadcast client (mode 6)
   and the peer process exits.  Implementations supporting public key
   authentication MAY run the Autokey or equivalent security protocol.
   Implementations SHOULD set the association mode to 3 and run a short
   client/server exchange to determine the propagation delay.  Following
   the exchange, the association mode is set to 6 and the peer process
   continues in listen-only mode.  Note the distinction between a mode-6
   packet, which is reserved for the NTP monitor and control functions,
   and a mode-6 association.

   NEWPS.  This indicates a symmetric active (mode 1) packet matching no
   association.  The client mobilizes a symmetric passive (mode 2)
   association.  An example is shown in the mobilize() and clear()
   routines in Appendix A.2.  Processing continues in the PROC section
   below.

   PROC.  This indicates a packet matching an existing association.  The
   packet timestamps are carefully checked to avoid invalid, duplicate,
   or bogus packets.  Additional checks are summarized in Figure 22.
   Note that all packets, including a crypto-NAK, are considered valid
   only if they survive these tests.

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   +--------------------------+----------------------------------------+
   | Packet Type              | Description                            |
   +--------------------------+----------------------------------------+
   | 1 duplicate packet       | The packet is at best an old duplicate |
   |                          | or at worst a replay by a hacker.      |
   |                          | This can happen in symmetric modes if  |
   |                          | the poll intervals are uneven.         |
   | 2 bogus packet           |                                        |
   | 3 invalid                | One or more timestamp fields are       |
   |                          | invalid. This normally happens in      |
   |                          | symmetric modes when one peer sends    |
   |                          | the first packet to the other and      |
   |                          | before the other has received its      |
   |                          | first reply.                           |
   | 4 access denied          | The access controls have blacklisted   |
   |                          | the source.                            |
   | 5 authentication failure | The cryptographic message digest does  |
   |                          | not match the MAC.                     |
   | 6 unsynchronized         | The server is not synchronized to a    |
   |                          | valid source.                          |
   | 7 bad header data        | One or more header fields are invalid. |
   +--------------------------+----------------------------------------+

                      Figure 22: Packet Error Checks

   Processing continues by copying the packet variables to the peer
   variables as shown in Figure 21.  An example is described by the
   packet() routine in Appendix A.5.1.1.  The receive() routine
   implements tests 1-5 in Figure 22; the packet() routine implements
   tests 6-7.  If errors are found, the packet is discarded and the peer
   process exits.

   The on-wire protocol calculates the clock offset theta and round-trip
   delay delta from the four most recent timestamps as described in
   Section 8.  While it is, in principle, possible to do all
   calculations except the first-order timestamp differences in fixed-
   point arithmetic, it is much easier to convert the first-order
   differences to floating doubles and do the remaining calculations in
   that arithmetic, and this will be assumed in the following
   description.

   Next, the 8-bit p.reach shift register in the poll process described
   in Section 13 is used to determine whether the server is reachable
   and the data are fresh.  The register is shifted left by one bit when
   a packet is sent and the rightmost bit is set to zero.  As valid
   packets arrive, the rightmost bit is set to one.  If the register
   contains any nonzero bits, the server is considered reachable;
   otherwise, it is unreachable.  Since the peer poll interval might

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   have changed since the last packet, the host poll interval is
   reviewed.  An example is provided by the poll_update() routine in
   Appendix A.5.7.2.

   The dispersion statistic epsilon(t) represents the maximum error due
   to the frequency tolerance and time since the last packet was sent.
   It is initialized

   epsilon(t_0) = r.rho + s.rho + PHI * (T4-T1)

   when the measurement is made at t_0 according to the seconds counter.
   Here, r.rho is the packet precision described in Section 7.3 and
   s.rho is the system precision described in Section 11.1, both
   expressed in seconds.  These terms are necessary to account for the
   uncertainty in reading the system clock in both the server and the
   client.

   The dispersion then grows at constant rate PHI; in other words, at
   time t, epsilon(t) = epsilon(t_0) + PHI * (t-t_0).  With the default
   value PHI = 15 ppm, this amounts to about 1.3 s per day.  With this
   understanding, the argument t will be dropped and the dispersion
   represented simply as epsilon.  The remaining statistics are computed
   by the clock filter algorithm described in the next section.

10.  Clock Filter Algorithm

   The clock filter algorithm is part of the peer process.  It grooms
   the stream of on-wire data to select the samples most likely to
   represent accurate time.  The algorithm produces the variables shown
   in Figure 19, including the offset (theta), delay (delta), dispersion
   (epsilon), jitter (psi), and time of arrival (t).  These data are
   used by the mitigation algorithms to determine the best and final
   offset used to discipline the system clock.  They are also used to
   determine the server health and whether it is suitable for
   synchronization.

   The clock filter algorithm saves the most recent sample tuples
   (theta, delta, epsilon, t) in the filter structure, which functions
   as an 8-stage shift register.  The tuples are saved in the order that
   packets arrive.  Here, t is the packet time of arrival according to
   the seconds counter and should not be confused with the peer variable
   tp.

   The following scheme is used to ensure sufficient samples are in the
   filter and that old stale data are discarded.  Initially, the tuples
   of all stages are set to the dummy tuple (0, MAXDISP, MAXDISP, 0).
   As valid packets arrive, tuples are shifted into the filter causing
   old tuples to be discarded, so eventually only valid tuples remain.

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   If the three low-order bits of the reach register are zero,
   indicating three poll intervals have expired with no valid packets
   received, the poll process calls the clock filter algorithm with a
   dummy tuple just as if the tuple had arrived from the network.  If
   this persists for eight poll intervals, the register returns to the
   initial condition.

   In the next step, the shift register stages are copied to a temporary
   list and the list sorted by increasing delta.  Let i index the stages
   starting with the lowest delta.  If the first tuple epoch t_0 is not
   later than the last valid sample epoch tp, the routine exits without
   affecting the current peer variables.  Otherwise, let epsilon_i be
   the dispersion of the ith entry, then

                     i=n-1
                     ---     epsilon_i
      epsilon =       \     ----------
                      /        (i+1)
                     ---     2
                     i=0

   is the peer dispersion p.disp.  Note the overload of epsilon, whether
   input to the clock filter or output, the meaning should be clear from
   context.

   The observer should note (a) if all stages contain the dummy tuple
   with dispersion MAXDISP, the computed dispersion is a little less
   than 16 s, (b) each time a valid tuple is shifted into the register,
   the dispersion drops by a little less than half, depending on the
   valid tuples dispersion, and (c) after the fourth valid packet the
   dispersion is usually a little less than 1 s, which is the assumed
   value of the MAXDIST parameter used by the selection algorithm to
   determine whether or not the peer variables are acceptable.

   Let the first stage offset in the sorted list be theta_0; then, for
   the other stages in any order, the jitter is the RMS average

                          +-----                 -----+^1/2
                          |  n-1                      |
                          |  ---                      |
                  1       |  \                     2  |
      psi   =  -------- * |  /    (theta_0-theta_j)   |
                (n-1)     |  ---                      |
                          |  j=1                      |
                          +-----                 -----+

   where n is the number of valid tuples in the filter (n > 1).  In
   order to ensure consistency and avoid divide exceptions in other

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   computations, the psi is bounded from below by the system precision
   s.rho expressed in seconds.  While not in general considered a major
   factor in ranking server quality, jitter is a valuable indicator of
   fundamental timekeeping performance and network congestion state.  Of
   particular importance to the mitigation algorithms is the peer
   synchronization distance, which is computed from the delay and
   dispersion.

   lambda = (delta / 2) + epsilon.

   Note that epsilon and therefore lambda increase at rate PHI.  The
   lambda is not a state variable, since lambda is recalculated at each
   use.  It is a component of the root synchronization distance used by
   the mitigation algorithms as a metric to evaluate the quality of time
   available from each server.

   It is important to note that, unlike NTPv3, NTPv4 associations do not
   show a timeout condition by setting the stratum to 16 and leap
   indicator to 3.  The association variables retain the values
   determined upon arrival of the last packet.  In NTPv4, lambda
   increases with time, so eventually the synchronization distance
   exceeds the distance threshold MAXDIST, in which case the association
   is considered unfit for synchronization.

   An example implementation of the clock filter algorithm is shown in
   the clock_filter() routine of Appendix A.5.2.



(page 39 continued on part 3)

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