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Network Working Group                                            W. Eddy
Internet-Draft                                               MTI Systems
Intended status: Informational                                 E. Davies
Expires: April 14, 2011                                 Folly Consulting
                                                        October 11, 2010

           Using Self-Delimiting Numeric Values in Protocols


   Self-Delimiting Numeric Values (SDNVs) have recently been introduced
   as a field type in proposed Delay-Tolerant Networking protocols.
   SDNVs encode an arbitrary-length non-negative integer or arbitrary-
   length bit-string with minimum overhead.  They are intended to
   provide protocol flexibility without sacrificing economy, and to
   assist in future-proofing protocols under development.  This document
   describes formats and algorithms for SDNV encoding and decoding,
   along with notes on implementation and usage.  This document is a
   product of the Delay Tolerant Networking Research Group and has been
   reviewed by that group.  No objections to its publication as an RFC
   were raised.

Status of this Memo

   This Internet-Draft is submitted in full conformance with the
   provisions of BCP 78 and BCP 79.

   Internet-Drafts are working documents of the Internet Engineering
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   This Internet-Draft will expire on April 14, 2011.

Copyright Notice

   Copyright (c) 2010 IETF Trust and the persons identified as the
   document authors.  All rights reserved.

   This document is subject to BCP 78 and the IETF Trust's Legal
   Provisions Relating to IETF Documents

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   (http://trustee.ietf.org/license-info) in effect on the date of
   publication of this document.  Please review these documents
   carefully, as they describe your rights and restrictions with respect
   to this document.  Code Components extracted from this document must
   include Simplified BSD License text as described in Section 4.e of
   the Trust Legal Provisions and are provided without warranty as
   described in the Simplified BSD License.

Table of Contents

   1.  Introduction . . . . . . . . . . . . . . . . . . . . . . . . .  3
     1.1.  Problems with Fixed Value Fields . . . . . . . . . . . . .  3
     1.2.  SDNVs for DTN Protocols  . . . . . . . . . . . . . . . . .  4
     1.3.  SDNV Usage . . . . . . . . . . . . . . . . . . . . . . . .  5
   2.  Definition of SDNVs  . . . . . . . . . . . . . . . . . . . . .  7
   3.  Basic Algorithms . . . . . . . . . . . . . . . . . . . . . . .  9
     3.1.  Encoding Algorithm . . . . . . . . . . . . . . . . . . . .  9
     3.2.  Decoding Algorithm . . . . . . . . . . . . . . . . . . . .  9
     3.3.  Limitations of Implementations . . . . . . . . . . . . . . 10
   4.  Comparison to Alternatives . . . . . . . . . . . . . . . . . . 11
   5.  Security Considerations  . . . . . . . . . . . . . . . . . . . 15
   6.  IANA Considerations  . . . . . . . . . . . . . . . . . . . . . 16
   7.  Acknowledgements . . . . . . . . . . . . . . . . . . . . . . . 17
   8.  Informative References . . . . . . . . . . . . . . . . . . . . 18
   Appendix A.  SNDV Python Source Code . . . . . . . . . . . . . . . 20
   Authors' Addresses . . . . . . . . . . . . . . . . . . . . . . . . 22

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1.  Introduction

   This document is a product of the Internet Research Task Force (IRTF)
   Delay-Tolerant Networking (DTN) Research Group (DTNRG).  The document
   has received review and support within the DTNRG, as discussed in the
   Acknowledgements section of this document.

   This document begins by describing the drawbacks of using fixed-width
   protocol fields.  It then provides some background on the Self-
   Delimiting Numeric Values (SDNVs) proposed for use in DTN protocols,
   and motivates their potential applicability in other networking
   protocols.  One example of SDNVs being used outside of the DTN
   protocols is in Hixie's Web Socket protocol
   [I-D.hixie-thewebsocketprotocol], which includes a binary frame
   length indicator field identical to an SDNV.  The DTNRG has created
   SDNVs to meet the challenges it attempts to solve, and it has been
   noted that SDNVs closely resemble certain constructs within ASN.1 and
   even older ITU protocols, so the problems are not new or unique to
   DTN.  SDNVs focus strictly on numeric values or bitstrings, while
   other mechanisms have been developed for encoding more complex data
   structures, such as ASN.1 encoding rules, and Haverty's MSDTP
   [RFC0713].  Because of this focus, SDNVs are can be quickly
   implemented with only a small amount of code.

   SDNVs are tersely defined in both the bundle protocol [RFC5050] and
   LTP [RFC5326] specifications, due to the flow of document production
   in the DTNRG.  This document clarifies and further explains the
   motivations and engineering decisions behind SDNVs.

1.1.  Problems with Fixed Value Fields

   Protocol designers commonly face an optimization problem in
   determining the proper size for header fields.  There is a strong
   desire to keep fields as small as possible, in order to reduce the
   protocol's overhead, and also allow for fast processing.  Since
   protocols can be used many years (even decades) after they are
   designed, and networking technology has tended to change rapidly, it
   is not uncommon for the use, deployment, or performance of a
   particular protocol to be limited or infringed upon by the length of
   some header field being too short.  Two well-known examples of this
   phenomenon are the TCP advertised receive window, and the IPv4
   address length.

   TCP segments contain an advertised receive window field that is fixed
   at 16 bits [RFC0793], encoding a maximum value of around 65
   kilobytes.  The purpose of this value is to provide flow control, by
   allowing a receiver to specify how many sent bytes its peer can have
   outstanding (unacknowledged) at any time, thus allowing the receiver

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   to limit its buffer size.  As network speeds have grown by several
   orders of magnitude since TCP's inception, the combination of the 65
   kilobyte maximum advertised window and long round-trip times
   prevented TCP senders from being able to achieve the high throughput
   that the underlying network supported.  This limitation was remedied
   through the use of the Window Scale option [RFC1323], which provides
   a multiplier for the advertised window field.  However, the Window
   Scale multiplier is fixed for the duration of the connection,
   requires support from each end of a TCP connection, and limits the
   precision of the advertised receive window, so this is certainly a
   less-than-ideal solution.  Because of the field width limit in the
   original design however, the Window Scale is necessary for TCP to
   reach high sending rates.

   An IPv4 address is fixed at 32 bits [RFC0791] (as a historical note,
   an early version 0 IP header format specification in [IEN21] used
   variable-length addresses in multiples of 8-bits up to 120-bits).
   Due to the way that subnetting and assignment of address blocks was
   performed, the number of IPv4 addresses has been seen as a limit to
   the growth of the Internet [Hain05].  Two divergent paths to solve
   this problem have been the use of Network Address Translators (NATs)
   and the development of IPv6.  NATs have caused a number of other
   issues and problems [RFC2993], leading to increased complexity and
   fragility, as well as forcing work-arounds to be engineered for many
   other protocols to function within a NATed environment.  The IPv6
   solution's transitional work has been underway for several years, but
   has still only just begun to have visible impact on the global

   Of course, in both the case of the TCP receive window and IPv4
   address length, the field size chosen by the designers seemed like a
   good idea at the time.  The fields were more than big enough for the
   originally perceived usage of the protocols, and yet were small
   enough to allow the headers to remain compact and relatively easy and
   efficient to parse on machines of the time.  The fixed sizes that
   were defined represented a tradeoff between the scalability of the
   protocol versus the overhead and efficiency of processing.  In both
   cases, these engineering decisions turned out to be painfully
   restrictive in the longer term.

1.2.  SDNVs for DTN Protocols

   In specifications for the DTN Bundle Protocol (BP) [RFC5050] and
   Licklider Transmission Protocol (LTP) [RFC5326], SDNVs have been used
   for several fields including identifiers, payload/header lengths, and
   serial (sequence) numbers.  SDNVs were developed for use in these
   types of fields, to avoid sending more bytes than needed, as well as
   avoiding fixed sizes that may not end up being appropriate.  For

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   example, since LTP is intended primarily for use in long-delay
   interplanetary communications [RFC5325], where links may be fairly
   low in capacity, it is desirable to avoid the header overhead of
   routinely sending a 64-bit field where a 16-bit field would suffice.
   Since many of the nodes implementing LTP are expected to be beyond
   the current range of human spaceflight, upgrading their on-board LTP
   implementations to use longer values if the defined fields are found
   to be too short would also be problematic.  Furthermore, extensions
   similar in mechanism to TCP's Window Scale option are unsuitable for
   use in DTN protocols since, due to high delays, DTN protocols must
   avoid handshaking and configuration parameter negotiation to the
   greatest extent possible.  All of these reasons make the choice of
   SDNVs for use in DTN protocols attractive.

1.3.  SDNV Usage

   In short, an SDNV is simply a way of representing non-negative
   integers (both positive integers of arbitrary magnitude and 0),
   without expending much unnecessary space.  This definition allows
   SDNVs to represent many common protocol header fields, such as:

   o  Random identification fields as used in the IPsec Security
      Parameters Index or in IP headers for fragment reassembly (Note:
      the 16-bit IP ID field for fragment reassembly was recently found
      to be too short in some environments [RFC4963]),

   o  Sequence numbers as in TCP or SCTP,

   o  Values used in cryptographic algorithms such as RSA keys, Diffie-
      Hellman key-agreement, or coordinates of points on elliptic

   o  Message lengths as used in file transfer protocols.

   o  Nonces and cookies.

   o  Etc.

   As any bit-field can be interpreted as an unsigned integer, SDNVs can
   also encode arbitrary-length bit-fields, including bit-fields
   representing signed integers or other data types; however, this
   document assumes SDNV encoding and decoding in terms of unsigned
   integers.  Implementations may differ in the interface that they
   provide to SDNV encoding and decoding functions, in terms of whether
   the values are numeric, bit-fields, etc.; this detail does not alter
   the representation or algorithms described in this document.

   The use of SDNVs rather than fixed length fields gives protocol

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   designers the ability to ameliorate the consequences of making
   difficult-to-reverse field-sizing decisions, as the SDNV format grows
   and shrinks depending on the particular value encoded.  SDNVs do not
   necessarily provide optimal encodings for values of any particular
   length, however they allow protocol designers to avoid potential
   blunders in assigning fixed lengths, and remove the complexity
   involved with either negotiating field lengths or constructing
   protocol extensions.

   To our knowledge, at this time, no IETF transport or network-layer
   protocol designed for use outside of the DTN domain has proposed to
   use SDNVs; however there is no inherent reason not to use SDNVs more
   broadly in the future.  The two examples cited here, of fields that
   have proven too small in general Internet protocols, are only a small
   sampling of the much larger set of similar instances that the authors
   can think of.  Outside the Internet protocols, within ASN.1 and
   previous ITU protocols, constructs very similar to SDNVs have been
   used for many years due to engineering concerns very similar to those
   facing the DTNRG.

   Many protocols use a Type-Length-Value method for encoding variable
   length fields (e.g.  TCP's options format, or many of the fields in
   IKEv2).  An SDNV is equivalent to combining the length and value
   portions of this type of field, with the overhead of the length
   portion amortized out over the bytes of the value.  The penalty paid
   for this in an SDNV may be several extra bytes for long values (e.g.
   1024 bit RSA keys).  See Section 4 for further discussion and a

   As is shown in later sections, for large values, the current SDNV
   scheme is fairly inefficient in terms of space (1/8 of the bits are
   overhead) and not particularly easy to encode/decode in comparison to
   alternatives.  The best use of SDNVs may often be to define the
   Length field of a TLV structure to be an SDNV whose value is the
   length of the TLV's Value field.  In this way, one can avoid forcing
   large numbers from being directly encoded as an SDNV, yet retain the
   extensibility that using SDNVs grants.

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2.  Definition of SDNVs

   Early in the work of the DTNRG, it was agreed that the properties of
   an SDNV were useful for DTN protocols.  The exact SDNV format used by
   the DTNRG evolved somewhat over time before the publication of the
   initial RFCs on LTP and the BP.  An ealier version bore resemblance
   to the ASN.1 [ASN1] Basic Encoding Rules (BER) [ASN1-BER] for lengths
   (Section 8.1.3 of X.690).  The current SDNV format is the one used by
   ASN.1 BER for encoding tag identifiers greater than or equal to 31
   (Section of X.690).  A comparison between the current SDNV
   format and the early SDNV format is made in Section 4.

   The format currently used is very simple.  Before encoding, an
   integer is represented as a left-to-right bitstring beginning with
   its most significant bit, and ending with its least signifcant bit.
   If the bitstring's length is not a multiple of 7, then the string is
   left-padded with zeros.  When transmitted, the bits are encoded into
   a series of bytes.  The low-order 7 bits of each byte in the encoded
   format are taken left-to-right from the integer's bitstring
   representation.  The most significant bit of each byte specifies
   whether it is the final byte of the encoded value (when it holds a
   0), or not (when it holds a 1).

   For example:

   o  1 (decimal) is represented by the bitstring "0000001" and encoded
      as the single byte 0x01 (in hexadecimal)

   o  128 is represented by the bitstring "10000001 00000000" and
      encoded as the bytes 0x81 followed by 0x00.

   o  Other values can be found in the test vectors of the source code
      in Appendix A

   To be perfectly clear, and avoid potential interoperability issues
   (as have occurred with ASN.1 BER time values), we explicitly state
   two considerations regarding zero-padding. (1) When encoding SDNVs,
   any leading (most significant) zero bits in the input number might be
   discarded by the SDNV encoder.  Protocols that use SDNVs should not
   rely on leading-zeros being retained after encoding and decoding
   operations. (2) When decoding SDNVs, the relevant number of leading
   zeros required to pad up to a machine word or other natural data unit
   might be added.  These are put in the most-significant positions in
   order to not change the value of the number.  Protocols using SDNVs
   should consider situations where lost zero-padding may be

   The issues of zero-padding are particularly relevant where an SDNV is

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   being used to represent a bit field to be transmitted by a protocol.
   The specification of the protocol and any associated IANA registry
   should specify the allocation and usage of bit positions within the
   unencoded field.  Both sender and receiver will know of this
   allocation so that they are implicitly aware of the width of the bit
   field.  Unassigned and reserved bits in the unencoded field will be
   treated as zeroes by the SDNV encoding prior to transmission.
   Assuming the bit positions are numbered starting from 0 at the least
   significant bit position in the integer representation, then if
   higher numbered positions in the field contain all zeroes, the
   encoding process may not transmit these bits explicitly (e.g., if all
   the bit positions numbered 7 or higher are zeroes then the
   transmitted SDNV can consist of just one octet).  On reception the
   decoding process will treat any untransmitted higher numbered bits as

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3.  Basic Algorithms

   This section describes some simple algorithms for creating and
   parsing SDNV fields.  These may not be the most efficient algorithms
   possible, however, they are easy to read, understand, and implement.
   Appendix A contains Python source code implementing the routines
   described here.

3.1.  Encoding Algorithm

   There is a very simple algorithm for the encoding operation that
   converts a non-negative integer (value n, of length 1+floor(log n)
   bits) into an SDNV.  This algorithm takes n as its only argument and
   returns a string of bytes:

   o  (Initial Step) Set a variable X to a byte sharing the least
      significant 7 bits of n, and with 0 in the most significant bit,
      and a variable Y to n, right-shifted by 7 bits.

   o  (Recursion Step) If Y == 0, return X. Otherwise, set Z to the
      bitwise-or of 0x80 with the 7 least significant bits of Y, and
      append Z to X. Right-shift Y by 7 bits and repeat the Recursion

   This encoding algorithm has time complexity of O(log n), since it
   takes a number of steps equal to ceil(n/7), and no additional space
   beyond the size of the result (8/7 log n) is required.  One aspect of
   this algorithm is that it assumes strings can be efficiently appended
   to new bytes.  One way to implement this is to allocate a buffer for
   the expected length of the result and fill that buffer one byte at a
   time from the right end.

   If, for some reason, an implementation requires an encoded SDNV to be
   some specific length (possibly related to a machine word), any
   leftmost zero-padding included needs to properly set the high-order
   bit in each byte of padding.

3.2.  Decoding Algorithm

   Decoding SNDVs is a more difficult operation than encoding them, due
   to the fact that no bound on the resulting value is known until the
   SDNV is parsed, at which point the value itself is already known.
   This means that if space is allocated for decoding the value of an
   SDNV into, it is never known whether this space will be overflowed
   until it is 7 bits away from happening.

   (Initial Step) Set the result to 0.  Set an index to the first byte
   of the encoded SDNV.

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   (Recursion Step) Shift the result left 7 bits.  Add the low-order 7
   bits of the value at the index to the result.  If the high-order bit
   under the pointer is a 1, advance the index by one byte within the
   encoded SDNV and repeat the Recursion Step, otherwise return the
   current value of the result.

   This decoding algorithm takes no more additional space than what is
   required for the result (7/8 the length of the SDNV) and the pointer.
   The complication is that before the result can be left-shifted in the
   Recursion Step, an implementation needs to first make sure that this
   won't cause any bits to be lost, and re-allocate a larger piece of
   memory for the result, if required.  The pure time complexity is the
   same as for the encoding algorithm given, but if re-allocation is
   needed due to the inability to predict the size of the result,
   decoding may be slower.

   These decoding steps include removal of any leftmost zero-padding
   that might be used by an encoder to create encodings of a certain

3.3.  Limitations of Implementations

   Because of efficiency considerations or convenience of internal
   representation of decoded integers, implementations may choose to
   limit the number of bits in SDNVs that they will handle.  To avoid
   interoperability problems any protocol that uses SDNVs must specify
   the largest number of bits in an SDNV that an implementation of that
   protocol is expected to handle.

   For example Section 4.1 of [RFC5050] specifies that implementations
   of the DTN Bundle Protocol are not required to handle SDNVs with more
   than 64 bits in their unencoded value.  Accordingly integer values
   transmitted in SDNVs have an upper limit and SDNV encoded flag fields
   must be limited to 64 bit positions in any future revisions of the
   protocol unless the restriction is altered.

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4.  Comparison to Alternatives

   This section compares three alternative ways of implementing the
   concept of SDNVs: (1) the TLV scheme commonly used in the Internet
   family, and many other families of protocols, (2) the old style of
   SDNVs (both the SDNV-8 and SDNV-16) defined in an early stage of
   LTP's development [BRF04], and (3) the current SDNV format.

   The TLV method uses two fixed-length fields to hold the Type and
   Length elements that then imply the syntax and semantics of the Value
   element.  This is only similar to an SDNV in that the value element
   can grow or shrink within the bounds capable of being conveyed by the
   Length field.  Two fundamental differences between TLVs and SDNVs are
   that through the Type element, TLVs also contain some notion of what
   their contents are semantically, while SDNVs are simply generic non-
   negative integers, and protocol engineers still have to choose fixed
   field lengths for the Type and Length fields in the TLV format.

   Some protocols use TLVs where the value conveyed within the Length
   field needs to be decoded into the actual length of the Value field.
   This may be accomplished through simple multiplication, left-
   shifting, or a look-up table.  In any case, this tactic limits the
   granularity of the possible Value lengths, and can contribute some
   degree of bloat if Values do not fit neatly within the available
   decoded Lengths.

   In the SDNV format originally used by LTP, parsing the first byte of
   the SDNV told an implementation how much space was required to hold
   the contained value.  There were two different types of SDNVs defined
   for different ranges of use.  The SDNV-8 type could hold values up to
   127 in a single byte, while the SDNV-16 type could hold values up to
   32,767 in 2 bytes.  Both formats could encode values requiring up to
   N bytes in N+2 bytes, where N<127.  The major difference between this
   old SDNV format and the current SDNV format is that the new format is
   not as easily decoded as the old format was, but the new format also
   has absolutely no limitation on its length.

   The advantage in ease of parsing the old format manifests itself in
   two aspects: (1) the size of the value is determinable ahead of time,
   in a way equivalent to parsing a TLV, and (2) the actual value is
   directly encoded and decoded, without shifting and masking bits as is
   required in the new format.  For these reasons, the old format
   requires less computational overhead to deal with, but is also very
   limited, in that it can only hold a 1024-bit number, at maximum.
   Since according to IETF Best Current Practices, an asymmetric
   cryptography key needed to last for a long term requires using moduli
   of over 1228 bits [RFC3766], this could be seen as a severe
   limitation of the old-style of SDNVs, which the currently-used style

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   does not suffer from.

   Table 1 compares the maximum values that can be encoded into SDNVs of
   various lengths using the old SDNV-8/16 method and the current SDNV
   method.  The only place in this table where SDNV-16 is used rather
   than SDNV-8 is in the 2-byte row.  Starting with a single byte, the
   two methods are equivalent, but when using 2 bytes, the old method is
   a more compact encoding by one bit.  From 3 to 7 bytes of length
   though, the current SDNV format is more compact, since it only
   requires one bit per byte of overhead, whereas the old format used a
   full byte.  Thus, at 8 bytes, both schemes are equivalent in
   efficiency since they both use 8 bits of overhead.  Up to 129 bytes,
   the old format is more compact than the current one, although after
   this limit it becomes unusable.

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   | Bytes |   SDNV-8/16   |     SDNV    |   SDNV-8/16   |     SDNV    |
   |       | Maximum Value |   Maximum   | Overhead Bits |   Overhead  |
   |       |               |    Value    |               |     Bits    |
   |   1   |      127      |     127     |       1       |      1      |
   |       |               |             |               |             |
   |   2   |     32,767    |    16,383   |       1       |      2      |
   |       |               |             |               |             |
   |   3   |     65,535    |  2,097,151  |       8       |      3      |
   |       |               |             |               |             |
   |   4   |    2^24 - 1   |   2^28 - 1  |       8       |      4      |
   |       |               |             |               |             |
   |   5   |    2^32 - 1   |   2^35 - 1  |       8       |      5      |
   |       |               |             |               |             |
   |   6   |    2^40 - 1   |   2^42 - 1  |       8       |      6      |
   |       |               |             |               |             |
   |   7   |    2^48 - 1   |   2^49 - 1  |       8       |      7      |
   |       |               |             |               |             |
   |   8   |    2^56 - 1   |   2^56 - 1  |       8       |      8      |
   |       |               |             |               |             |
   |   9   |    2^64 - 1   |   2^63 - 1  |       8       |      9      |
   |       |               |             |               |             |
   |   10  |    2^72 - 1   |   2^70 - 1  |       8       |      10     |
   |       |               |             |               |             |
   |   16  |   2^120 - 1   |  2^112 - 1  |       8       |      16     |
   |       |               |             |               |             |
   |   32  |   2^248 - 1   |  2^224 - 1  |       8       |      32     |
   |       |               |             |               |             |
   |   64  |   2^504 - 1   |  2^448 - 1  |       8       |      64     |
   |       |               |             |               |             |
   |  128  |   2^1016 - 1  |  2^896 - 1  |       8       |     128     |
   |       |               |             |               |             |
   |  129  |   2^1024 - 1  |  2^903 - 1  |       8       |     129     |
   |       |               |             |               |             |
   |  130  |      N/A      |  2^910 - 1  |      N/A      |     130     |
   |       |               |             |               |             |
   |  256  |      N/A      |  2^1792 - 1 |      N/A      |     256     |

                                  Table 1

   In general, it seems like the most promising use of SDNVs may be to
   define the Length field of a TLV structure to be an SDNV whose value
   is the length of the TLV's Value field.  This leverages the strengths
   of the SDNV format and limits the effects of its weaknesses.

   Another aspect of comparison between SDNVs and alternatives using

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   fixed-length fields is the result of errors in transmission.  Bit-
   errors in an SDNV can result in either errors in the decoded value,
   or parsing errors in subsequent fields of the protocol.  In fixed-
   length fields, bit errors always result in errors to the decoded
   value rather than parsing errors in subsequent fields.  If the
   decoded values from either type of field encoding (SDNV or fixed-
   length) are used as indexes, offsets, or lengths of further fields in
   the protocol, similar failures result.

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5.  Security Considerations

   The only security considerations with regards to SDNVs are that code
   which parses SDNVs should have bounds-checking logic and be capable
   of handling cases where an SDNV's value is beyond the code's ability
   to parse.  These precautions can prevent potential exploits involving
   SDNV decoding routines.

   Stephen Farrell noted that very early definitions of SDNVs also
   allowed negative integers.  This was considered a potential security
   hole, since it could expose implementations to underflow attacks
   during SDNV decoding.  There is a precedent in that many existing TLV
   decoders map the Length field to a signed integer and are vulnerable
   in this way.  An SDNV decoder should be based on unsigned types and
   not have this issue.

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6.  IANA Considerations

   This document has no IANA considerations.

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7.  Acknowledgements

   Scott Burleigh, Manikantan Ramadas, Michael Demmer, Stephen Farrell,
   and other members of the IRTF DTN Research Group contributed to the
   development and usage of SDNVs in DTN protocols.  George Jones and
   Keith Scott from Mitre, Lloyd Wood, Gerardo Izquierdo, Joel Halpern,
   Peter TB Brett, Kevin Fall, and Elwyn Davies also contributed useful
   comments on and criticisms of this document.  DTNRG last call
   comments on the draft were sent to the mailing list by Lloyd Wood,
   Will Ivancic, Jim Wyllie, William Edwards, Hans Kruse, Janico
   Greifenberg, Teemu Karkkainen, Stephen Farrell, and Scott Burleigh.
   Further constructive comments were incorporated from Dave Crocker.

   Work on this document was performed at NASA's Glenn Research Center,
   in support of the NASA Space Communications Architecture Working
   Group (SCAWG), NASA's Earth Science Technology Office (ESTO), and the
   FAA/Eurocontrol Future Communications Study (FCS) in the 2005-2007
   timeframe, while the editor was an employee of Verizon Federal
   Network Systems.

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8.  Informative References

   [ASN1]     ITU-T Rec. X.680, "Abstract Syntax Notation One (ASN.1).
              Specification of Basic Notation", ISO/IEC 8824-1:2002,

              ITU-T Rec. X.690, "Abstract Syntax Notation One (ASN.1).
              Encoding Rules: Specification of Basic Encoding Rules
              (BER), Canonical Encoding Rules (CER) and Distinguished
              Encoding Rules (DER)", ISO/IEC 8825-1:2002, 2002.

   [BRF04]    Burleigh, S., Ramadas, M., and S. Farrell, "Licklider
              Transmission Protocol",
              draft-irtf-dtnrg-ltp-00 (replaced), May 2004.

   [Hain05]   Hain, T., "A Pragmatic Report on IPv4 Address Space
              Consumption", Internet Protocol Journal Vol. 8, No. 3,
              September 2005.

              Hickson, I., "The WebSocket protocol",
              draft-hixie-thewebsocketprotocol-76 (work in progress),
              May 2010.

   [IEN21]    Cerf, V. and J. Postel, "Specification of Internetwork
              Transmission Control Program: TCP Version 3", Internet
              Experimental Note 21, January 1978.

   [RFC0713]  Haverty, J., "MSDTP-Message Services Data Transmission
              Protocol", RFC 713, April 1976.

   [RFC0791]  Postel, J., "Internet Protocol", STD 5, RFC 791,
              September 1981.

   [RFC0793]  Postel, J., "Transmission Control Protocol", STD 7,
              RFC 793, September 1981.

   [RFC1323]  Jacobson, V., Braden, B., and D. Borman, "TCP Extensions
              for High Performance", RFC 1323, May 1992.

   [RFC2993]  Hain, T., "Architectural Implications of NAT", RFC 2993,
              November 2000.

   [RFC3766]  Orman, H. and P. Hoffman, "Determining Strengths For
              Public Keys Used For Exchanging Symmetric Keys", BCP 86,
              RFC 3766, April 2004.

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   [RFC4963]  Heffner, J., Mathis, M., and B. Chandler, "IPv4 Reassembly
              Errors at High Data Rates", RFC 4963, July 2007.

   [RFC5050]  Scott, K. and S. Burleigh, "Bundle Protocol
              Specification", RFC 5050, November 2007.

   [RFC5325]  Burleigh, S., Ramadas, M., and S. Farrell, "Licklider
              Transmission Protocol - Motivation", RFC 5325,
              September 2008.

   [RFC5326]  Ramadas, M., Burleigh, S., and S. Farrell, "Licklider
              Transmission Protocol - Specification", RFC 5326,
              September 2008.

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Appendix A.  SNDV Python Source Code

   # sdnv_decode() takes a string argument (s), which is assumed to be
   #   an SDNV, and optionally a number (slen) for the maximum number of
   #   bytes to parse from the string.  The function returns a pair of
   #   the non-negative integer n that is the numeric value encoded in
   #   the SDNV, and integer that is the distance parsed into the input
   #   string.  If the slen argument is not given (or is not a non-zero
   #   number) then, s is parsed up to the first byte whose high-order
   #   bit is 0 -- the length of the SDNV portion of s does not have to
   #   be pre-computed by calling code.  If the slen argument is given
   #   as a non-zero value, then slen bytes of s are parsed.  The value
   #   for n of -1 is returned for any type of parsing error.
   # NOTE: In python, integers can be of arbitrary size.  In other
   #   languages, such as C, SDNV-parsing routines should take
   #   precautions to avoid overflow (e.g. by using the Gnu MP library,
   #   or similar).
   def sdnv_decode(s, slen=0):
     n = long(0)
     for i in range(0, len(s)):
       v = ord(s[i])
       n = n<<7
       n = n + (v & 0x7F)
       if v>>7 == 0:
         slen = i+1
       elif i == len(s)-1 or (slen != 0 and i > slen):
         n = -1 # reached end of input without seeing end of SDNV
     return (n, slen)

   # sdnv_encode() returns the SDNV-encoded string that represents n.
   #   An empty string is returned if n is not a non-negative integer
   def sdnv_encode(n):
     r = ""
     # validate input
     if n >= 0 and (type(n) in [type(int(1)), type(long(1))]):
       flag = 0
       done = False
       while not done:
         # encode lowest 7 bits from n
         newbits = n & 0x7F
         n = n>>7
         r = chr(newbits + flag) + r
         if flag == 0:
           flag = 0x80
         if n == 0:

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           done = True
     return r

   # test cases from LTP and BP internet-drafts, only print failures
   def sdnv_test():
     tests = [(0xABC, chr(0x95) + chr(0x3C)),
              (0x1234, chr(0xA4) + chr (0x34)),
              (0x4234, chr(0x81) + chr(0x84) + chr(0x34)),
              (0x7F, chr(0x7F))]

     for tp in tests:
       # test encoding function
       if sdnv_encode(tp[0]) != tp[1]:
         print "sdnv_encode fails on input %s" % hex(tp[0])
       # test decoding function
       if sdnv_decode(tp[1])[0] != tp[0]:
         print "sdnv_decode fails on input %s, giving %s" % \
               (hex(tp[0]), sdnv_decode(tp[1]))

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Authors' Addresses

   Wesley M. Eddy
   MTI Systems
   NASA Glenn Research Center
   MS 500-ASRC; 21000 Brookpark Rd
   Cleveland, OH  44135

   Phone: 216-433-6682
   Email: wes@mti-systems.com

   Elwyn Davies
   Folly Consulting

   Email: elwynd@folly.org.uk

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