Using GOST ciphers in ESP and IKEv2
draft-smyslov-esp-gost-06

Document Type Active Internet-Draft (individual)
Author Valery Smyslov 
Last updated 2021-08-25
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Network Working Group                                         V. Smyslov
Internet-Draft                                                ELVIS-PLUS
Intended status: Informational                           August 25, 2021
Expires: February 26, 2022

                  Using GOST ciphers in ESP and IKEv2
                       draft-smyslov-esp-gost-06

Abstract

   This document defines a set of encryption transforms for use in the
   Encapsulating Security Payload (ESP) and in the Internet Key Exchange
   version 2 (IKEv2) protocols.  The transforms are based on Russian
   cryptographic standard algorithms (GOST) in a Multilinear Galois Mode
   (MGM).

Status of This Memo

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   provisions of BCP 78 and BCP 79.

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Table of Contents

   1.  Introduction  . . . . . . . . . . . . . . . . . . . . . . . .   2
   2.  Requirements Language . . . . . . . . . . . . . . . . . . . .   2
   3.  Overview  . . . . . . . . . . . . . . . . . . . . . . . . . .   3
   4.  Transforms Description  . . . . . . . . . . . . . . . . . . .   3
     4.1.  Tree-based External Re-Keying . . . . . . . . . . . . . .   4
     4.2.  Initialization Vector Format  . . . . . . . . . . . . . .   5
     4.3.  Nonce Format for MGM  . . . . . . . . . . . . . . . . . .   5
       4.3.1.  MGM Nonce Format for "Kuznyechik" based Transforms  .   6
       4.3.2.  MGM Nonce Format for "Magma" based Transforms . . . .   6
     4.4.  Keying Material . . . . . . . . . . . . . . . . . . . . .   7
     4.5.  Integrity Check Value . . . . . . . . . . . . . . . . . .   7
     4.6.  Plaintext Padding . . . . . . . . . . . . . . . . . . . .   8
     4.7.  AAD Construction  . . . . . . . . . . . . . . . . . . . .   8
       4.7.1.  ESP AAD . . . . . . . . . . . . . . . . . . . . . . .   8
       4.7.2.  IKEv2 AAD . . . . . . . . . . . . . . . . . . . . . .   9
     4.8.  Using Transforms  . . . . . . . . . . . . . . . . . . . .  10
   5.  Security Considerations . . . . . . . . . . . . . . . . . . .  10
   6.  IANA Considerations . . . . . . . . . . . . . . . . . . . . .  11
   7.  References  . . . . . . . . . . . . . . . . . . . . . . . . .  11
     7.1.  Normative References  . . . . . . . . . . . . . . . . . .  11
     7.2.  Informative References  . . . . . . . . . . . . . . . . .  12
   Appendix A.  Test Vectors . . . . . . . . . . . . . . . . . . . .  13
   Author's Address  . . . . . . . . . . . . . . . . . . . . . . . .  21

1.  Introduction

   This document defines four transforms for the Encapsulating Security
   Payload protocol (ESP) [RFC4303] and for the Internet Key Exchange
   protocol version 2 (IKEv2) [RFC7296].  These document is based on
   Russian Standard [GOST-ESP], which describes how Russian
   cryptographic standard algorithms are used in ESP and IKEv2.
   Transforms defined in this document are based on two block ciphers
   from Russian cryptographic standard algorithms (often called "GOST"
   algorithms) - "Kuznyechik" [GOST3412-2015][RFC7801] and "Magma"
   [GOST3412-2015][RFC8891] in Multilinear Galois Mode (MGM)
   [GOST-MGM][RFC9058].  These transforms provide Authenticated
   Encryption with Associated Data (AEAD).  An external re-keying
   mechanism, described in [RFC8645] is also used in these transforms to
   limit load on session keys.

2.  Requirements Language

   The key words "MUST", "MUST NOT", "REQUIRED", "SHALL", "SHALL NOT",
   "SHOULD", "SHOULD NOT", "RECOMMENDED", "NOT RECOMMENDED", "MAY", and
   "OPTIONAL" in this document are to be interpreted as described in BCP

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   14 [RFC2119] [RFC8174] when, and only when, they appear in all
   capitals, as shown here.

3.  Overview

   Russian cryptographic standard algorithms, often referred as "GOST"
   algorithms, constitute a set of cryptographic algorithms of different
   types - ciphers, hash functions, digital signatures etc.  In
   particular, Russian cryptographic standard [GOST3412-2015] defines
   two block ciphers - "Kuznyechik" (also defined in [RFC7801]) and
   "Magma" (also defined in [RFC8891]).  Both ciphers use 256-bit key.
   "Kuznyechik" has a block size of 128 bits, while "Magma" has a 64-bit
   block.

   Multilinear Galois Mode (MGM) is an AEAD mode defined in
   [GOST-MGM][RFC9058].  It is claimed to provide defense against some
   attacks on well-known AEAD modes, like Galois Counter Mode (GCM).

   [RFC8645] defines mechanisms that can be used to limit the number of
   times any particular session key is used.  One of these mechanisms,
   called external re-keying with tree-based construction (defined in
   Section 5.2.3 of [RFC8645]), is used in the defined transforms.  For
   the purpose of deriving subordinate keys a Key Derivation Function
   (KDF) KDF_GOSTR3411_2012_256 defined in Section 4.5 of [RFC7836], is
   used.  This KDF is based on an HMAC [RFC2104] in a combination with a
   Russian GOST hash function defined in Russian cryptographic standard
   [GOST3411-2012] (also defined in [RFC6986]).

4.  Transforms Description

   This document defines four transforms for use in ESP and IKEv2.  All
   of them use MGM mode of operation with tree-based external re-keying.
   The transforms differ in underlying ciphers and in cryptographic
   services they provide.

   o  ENCR_KUZNYECHIK_MGM_KTREE (Transform ID 32) is an AEAD transform
      based on "Kuznyechik" algorithm; it provides confidentiality and
      message authentication and thus can be used both in ESP and IKEv2

   o  ENCR_MAGMA_MGM_KTREE (Transform ID 33) is an AEAD transform based
      on "Magma" algorithm; it provides confidentiality and message
      authentication and thus can be used both in ESP and IKEv2

   o  ENCR_KUZNYECHIK_MGM_MAC_KTREE (Transform ID 34) is a MAC-only
      transform based on "Kuznyechik" algorithm; it provides no
      confidentiality and thus can only be used in ESP, but not in IKEv2

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   o  ENCR_MAGMA_MGM_MAC_KTREE (Transform ID 35) is a MAC-only transform
      based on "Magma" algorithm; it provides no confidentiality and
      thus can only be used in ESP, but not in IKEv2

4.1.  Tree-based External Re-Keying

   All four transforms use the same tree-based external re-keying
   mechanism.  The idea is that the key that is provided for the
   transform (Child SA key derived from KEYMAT in case of ESP or SK_ei/
   SK_er in case of IKEv2) is not directly used to protect messages.
   Instead a tree of keys is derived using this key as a root.  This
   tree may have several levels.  The leaf keys are used for messages
   protection, while intermediate nodes keys are used to derive lower
   level keys (including leaf keys).  See Section 5.2.3 of [RFC8645] for
   more details.  This construction allows to protect a large amount of
   data, at the same time providing a bound on a number of times any
   particular key in the tree is used, thus defending from some side
   channel attacks.

   The transforms defined in this document use three-level tree.  The
   leaf key that protects a message is computed as follows:

            K_msg = KDF (KDF (KDF (K, l1, i1), l2, i2), l3, i3)

   where:

   KDF (k, l, s)   Key Derivation Function KDF_GOSTR3411_2012_256
                   defined in Section 4.5 of [RFC7836], which accepts
                   three input parameters - a key (k), a label (l) and a
                   seed (s) and provides a new key as an output;

   K               the key for the transform (ESP SA key derived from
                   KEYMAT or SK_ei/SK_er in case of IKEv2);

   l1, l2, l3      labels defined as 6 octet ASCII strings without null
                   termination:

                      l1 = "level1"

                      l2 = "level2"

                      l3 = "level3"

   i1, i2, i3      parameters that determine which keys out of the tree
                   are used on each level, altogether they determine a
                   leaf key that is used for message protection; these
                   parameters are two octet integers in network byte
                   order;

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   This construction allows to generate up to 2^16 keys on each level,
   but due to IV construction (see Section 4.2) the number of possible
   keys on the level 1 is limited to 2^8.  So, the total number of
   possible leaf keys generated from one SA key is 2^40.

   This specifications doesn't impose any requirements on the frequency
   the external re-keying takes place.  It is expected that sending
   application will follow its own policy dictating how many times the
   keys on each level must be used.

4.2.  Initialization Vector Format

   Each message protected by the defined transforms must contain
   Initialization Vector (IV).  The IV has a size of 64 bits and
   consists of the four fields, three of which are i1, i2 and i3
   parameters that determine the particular leaf key this message was
   protected with (see Section 4.1), and the fourh is a counter,
   representing the message number for this key.

                          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
     +-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+
     |      i1       |               i2              |      i3       |
     +-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+
     |   i3 (cont)   |                     pnum                      |
     +-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+

                            Figure 1: IV Format

   where:

   o  i1 (1 octet), i2 (2 octets), i3 (2 octets) - parameters,
      determining the particular key used to protect this message;
      2-octets parameters are integers in network byte order

   o  pnum (3 octets) - message counter in network byte order for the
      leaf key protecting this message; up to 2^24 messages may be
      protected using a single leaf key

   For any given SA the IV MUST NOT repeat, but there is no requirement
   that IV is unpredictable.

4.3.  Nonce Format for MGM

   MGM requires a per-message nonce (called Initial Counter Nonce, ICN,
   in the [RFC9058]) that must be unique in the context of any leaf key.
   The size of the ICN is n-1 bits, where n is the block size of the
   underlying cipher.  The two ciphers used in the transforms defined in

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   this document have different block sizes, so two different formats
   for the ICN are defined.

   MGM specification requires that the nonce be n-1 bits in size, where
   n is a block size of underlying cipher.  This document defines MGM
   nonces that are n bits in size, because that makes them having a
   whole number of bytes.  When used inside MGM the most significant bit
   of the first octet of the nonce (represented as an octet string) is
   dropped, making an effective size of the nonce equal to n-1 bits.
   Note, that the dropped bit is a part of zero field (see Figure 2 and
   Figure 3) which is always set to 0, so no information is lost when it
   is dropped.

4.3.1.  MGM Nonce Format for "Kuznyechik" based Transforms

   For transforms based on "Kuznyechik" cipher
   (ENCR_KUZNYECHIK_MGM_KTREE and ENCR_KUZNYECHIK_MGM_MAC_KTREE) the ICN
   consists of a zero octet, a 24-bit message counter and a 96-bit
   secret salt, that is fixed for SA and is not transmitted.

                          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
     +-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+
     |     zero      |                     pnum                      |
     +-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+
     |                                                               |
     |                             salt                              |
     |                                                               |
     +-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+

         Figure 2: Nonce format for "Kuznyechik" based transforms

   where:

   o  zero (1 octet) - set to 0

   o  pnum (3 octets) - the counter for the messages protected by the
      given leaf key; this field MUST be equal to the pnum field in the
      IV

   o  salt (12 octets) - secret salt

4.3.2.  MGM Nonce Format for "Magma" based Transforms

   For transforms based on "Magma" cipher (ENCR_MAGMA_MGM_KTREE and
   ENCR_MAGMA_MGM_MAC_KTREE) the ICN consists of a zero octet, a 24-bit
   message counter and a 32-bit secret salt, that is fixed for SA and is
   not transmitted.

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                          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
     +-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+
     |     zero      |                     pnum                      |
     +-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+
     |                             salt                              |
     +-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+

            Figure 3: Nonce format for "Magma" based transforms

   where:

   o  zero (1 octet) - set to 0

   o  pnum (3 octets) - the counter for the messages protected by the
      given leaf key; this field MUST be equal to the pnum field in the
      IV

   o  salt (4 octets) - secret salt

4.4.  Keying Material

   The key for ENCR_KUZNYECHIK_MGM_KTREE and
   ENCR_KUZNYECHIK_MGM_MAC_KTREE transforms consists of 352 bits, of
   which the first 256 bits is a root key for the tree (denoted as K in
   Section 4.1) and the remaining 96 bits is a secret salt (see
   Section 4.3.1).

   The key for ENCR_MAGMA_MGM_KTREE and ENCR_MAGMA_MGM_MAC_KTREE
   transforms consists of 288 bits, of which the first 256 bits is a
   root key for the tree (denoted as K in Section 4.1) and the remaining
   32 bits is a secret salt (see Section 4.3.2).

   The keys in case ESP are extracted from the KEYMAT, and in case IKEv2
   they are SK_ei/SK_er keys.  Note, that since these transforms provide
   authenticated encryption, no additional keys are needed for
   authentication.  It means that in case of IKEv2 the keys SK_ai/SK_ar
   are not used.

4.5.  Integrity Check Value

   The MGM computes authentication tag equal to the block size of the
   underlying cipher.  For "Kuznyechik" based transforms
   (ENCR_KUZNYECHIK_MGM_KTREE and ENCR_KUZNYECHIK_MGM_MAC_KTREE) the
   resulting Integrity Check Value (ICV) is truncated to 96 bits by
   dropping the last 4 octets of the produced authentication tag.  For
   "Magma" based transforms (ENCR_MAGMA_MGM_KTREE and

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   ENCR_MAGMA_MGM_MAC_KTREE) the full 64-bit authentication tag is used
   as ICV.

4.6.  Plaintext Padding

   Transforms defined in this document don't require any plaintext
   padding, as specified in [RFC9058].  It means, that only those
   padding requirements that are imposed by the protocol are applied (4
   bytes for ESP, no padding for IKEv2).

4.7.  AAD Construction

4.7.1.  ESP AAD

   Additional Authenticated Data (AAD) in ESP is constructed differently
   depending on the transform being used and whether Extended Sequence
   Number (ESN) is in use or not.  The ENCR_KUZNYECHIK_MGM_KTREE and
   ENCR_MAGMA_MGM_KTREE provide confidentiality, so the content of the
   ESP body is encrypted and AAD consists of the ESP SPI and (E)SN.  The
   AAD is constructed similarly to the one in [RFC4106].

   On the other hand the ENCR_KUZNYECHIK_MGM_MAC_KTREE and
   ENCR_MAGMA_MGM_MAC_KTREE don't provide confidentiality, they provide
   only message authentication.  For this purpose the IV and the part of
   ESP packet that is normally encrypted are included in the AAD.  For
   these transforms encryption capability provided by MGM is not used.
   The AAD is constructed similarly to the one in [RFC4543].

                          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
     +-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+
     |                               SPI                             |
     +-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+
     |                     32-bit Sequence Number                    |
     +-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+

             Figure 4: AAD for AEAD transforms with 32-bit SN

                          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
     +-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+
     |                               SPI                             |
     +-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+
     |                 64-bit Extended Sequence Number               |
     |                                                               |
     +-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+

             Figure 5: AAD for AEAD transforms with 64-bit ESN

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                          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
     +-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+
     |                               SPI                             |
     +-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+
     |                     32-bit Sequence Number                    |
     +-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+
     |                               IV                              |
     |                                                               |
     +-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+
     |                                                               |
     ~                     Payload Data (variable)                   ~
     |                                                               |
     +-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+
     |                    Padding (0-255 bytes)                      |
     +                               +-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+
     |                               |  Pad Length   | Next Header   |
     +-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+

      Figure 6: AAD for authentication only transforms with 32-bit SN

                          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
     +-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+
     |                               SPI                             |
     +-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+
     |                 64-bit Extended Sequence Number               |
     |                                                               |
     +-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+
     |                               IV                              |
     |                                                               |
     +-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+
     |                                                               |
     ~                     Payload Data (variable)                   ~
     |                                                               |
     +-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+
     |                    Padding (0-255 bytes)                      |
     +                               +-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+
     |                               |  Pad Length   | Next Header   |
     +-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+

     Figure 7: AAD for authentication only transforms with 64-bit ESN

4.7.2.  IKEv2 AAD

   For IKEv2 the AAD consists of the IKEv2 Header, any unencrypted
   payloads followed it (if they are present) and the Encrypted (or the

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   Encrypted Fragment) payload header.  The AAD is constructed similar
   to one in [RFC5282].

                          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
     +-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+
     ~                         IKEv2 Header                          ~
     +-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+
     ~                   Unencrypted IKE Payloads                    ~
     +-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+
     | Next Payload  |C|  RESERVED   |         Payload Length        |
     +-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+

                          Figure 8: AAD for IKEv2

4.8.  Using Transforms

   When SA is established the i1, i2 and i3 parameters are set to 0 by
   the sender and a leaf key is calculated.  The pnum parameter starts
   from 0 and is incremented with each message protected by the same
   leaf key.  When sender decides that the leaf should be changed, it
   increments i3 parameter and generates a new leaf key.  The pnum
   parameter for the new leaf key is reset to 0 and the process
   continues.  If the sender decides, that 3-rd level key corresponding
   to i3 is used enough times, it increments i2, resets i3 to 0 and
   calculates a new leaf key.  The pnum is reset to 0 (as with every new
   leaf key) and the process continues.  Similar procedure is used when
   2-nd level key needs to be changed.

   The receiver always uses i1, i2 and i3 from the received message.  If
   they differ from the values in previously received packets, a new
   leaf key is calculated.  The pnum parameter is always used from the
   received packet.  To improve performance implementations may cache
   recently used leaf key.  When new leaf key is calculated (based on
   the values from received message) the old key may be kept for some
   time to improve performance in case of possible packet reordering
   (when packets protected by the old leaf key are delayed and arrive
   later).

5.  Security Considerations

   The most important security consideration for MGM is that the nonce
   MUST NOT repeat for a given key.  For this reason the transforms
   defined in this document MUST NOT be used with manual keying.

   Security properties of MGM are discussed in [MGM-SECURITY].

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6.  IANA Considerations

   IANA has assigned four Transform IDs in the "Transform Type 1 -
   Encryption Algorithm Transform IDs" registry (where RFCXXXX is this
   document):

   Number   Name                          ESP Reference  IKEv2 Reference
   ---------------------------------------------------------------------
    32    ENCR_KUZNYECHIK_MGM_KTREE       [RFCXXXX]       [RFCXXXX]
    33    ENCR_MAGMA_MGM_KTREE            [RFCXXXX]       [RFCXXXX]
    34    ENCR_KUZNYECHIK_MGM_MAC_KTREE   [RFCXXXX]      Not allowed
    35    ENCR_MAGMA_MGM_MAC_KTREE        [RFCXXXX]      Not allowed

7.  References

7.1.  Normative References

   [RFC2119]  Bradner, S., "Key words for use in RFCs to Indicate
              Requirement Levels", BCP 14, RFC 2119,
              DOI 10.17487/RFC2119, March 1997,
              <https://www.rfc-editor.org/info/rfc2119>.

   [RFC8174]  Leiba, B., "Ambiguity of Uppercase vs Lowercase in RFC
              2119 Key Words", BCP 14, RFC 8174, DOI 10.17487/RFC8174,
              May 2017, <https://www.rfc-editor.org/info/rfc8174>.

   [RFC4303]  Kent, S., "IP Encapsulating Security Payload (ESP)",
              RFC 4303, DOI 10.17487/RFC4303, December 2005,
              <https://www.rfc-editor.org/info/rfc4303>.

   [RFC7296]  Kaufman, C., Hoffman, P., Nir, Y., Eronen, P., and T.
              Kivinen, "Internet Key Exchange Protocol Version 2
              (IKEv2)", STD 79, RFC 7296, DOI 10.17487/RFC7296, October
              2014, <https://www.rfc-editor.org/info/rfc7296>.

   [RFC6986]  Dolmatov, V., Ed. and A. Degtyarev, "GOST R 34.11-2012:
              Hash Function", RFC 6986, DOI 10.17487/RFC6986, August
              2013, <https://www.rfc-editor.org/info/rfc6986>.

   [RFC7801]  Dolmatov, V., Ed., "GOST R 34.12-2015: Block Cipher
              "Kuznyechik"", RFC 7801, DOI 10.17487/RFC7801, March 2016,
              <https://www.rfc-editor.org/info/rfc7801>.

   [RFC8891]  Dolmatov, V., Ed. and D. Baryshkov, "GOST R 34.12-2015:
              Block Cipher "Magma"", RFC 8891, DOI 10.17487/RFC8891,
              September 2020, <https://www.rfc-editor.org/info/rfc8891>.

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   [RFC9058]  Smyshlyaev, S., Ed., Nozdrunov, V., Shishkin, V., and E.
              Griboedova, "Multilinear Galois Mode (MGM)", RFC 9058,
              DOI 10.17487/RFC9058, June 2021,
              <https://www.rfc-editor.org/info/rfc9058>.

   [RFC7836]  Smyshlyaev, S., Ed., Alekseev, E., Oshkin, I., Popov, V.,
              Leontiev, S., Podobaev, V., and D. Belyavsky, "Guidelines
              on the Cryptographic Algorithms to Accompany the Usage of
              Standards GOST R 34.10-2012 and GOST R 34.11-2012",
              RFC 7836, DOI 10.17487/RFC7836, March 2016,
              <https://www.rfc-editor.org/info/rfc7836>.

7.2.  Informative References

   [GOST3411-2012]
              Federal Agency on Technical Regulating and Metrology,
              "Information technology. Cryptographic Data Security.
              Hashing function", GOST R 34.11-2012, 2012.

              (In Russian)

   [GOST3412-2015]
              Federal Agency on Technical Regulating and Metrology,
              "Information technology. Cryptographic data security.
              Block ciphers", GOST R 34.12-2015, 2015.

              (In Russian)

   [GOST-MGM]
              Federal Agency on Technical Regulating and Metrology,
              "Information technology. Cryptographic data security.
              Authenticated encryption block cipher operation modes",
              R 1323565.1.026-2019, 2019.

              (In Russian)

   [GOST-ESP]
              Federal Agency on Technical Regulating and Metrology,
              "Information technology. Cryptographic data security.
              Using Russian cryptographic algorithms in data security
              protocol ESP", R 1323565.1.035-2021, 2021.

              (In Russian)

   [RFC2104]  Krawczyk, H., Bellare, M., and R. Canetti, "HMAC: Keyed-
              Hashing for Message Authentication", RFC 2104,
              DOI 10.17487/RFC2104, February 1997,
              <https://www.rfc-editor.org/info/rfc2104>.

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   [RFC4106]  Viega, J. and D. McGrew, "The Use of Galois/Counter Mode
              (GCM) in IPsec Encapsulating Security Payload (ESP)",
              RFC 4106, DOI 10.17487/RFC4106, June 2005,
              <https://www.rfc-editor.org/info/rfc4106>.

   [RFC4543]  McGrew, D. and J. Viega, "The Use of Galois Message
              Authentication Code (GMAC) in IPsec ESP and AH", RFC 4543,
              DOI 10.17487/RFC4543, May 2006,
              <https://www.rfc-editor.org/info/rfc4543>.

   [RFC5282]  Black, D. and D. McGrew, "Using Authenticated Encryption
              Algorithms with the Encrypted Payload of the Internet Key
              Exchange version 2 (IKEv2) Protocol", RFC 5282,
              DOI 10.17487/RFC5282, August 2008,
              <https://www.rfc-editor.org/info/rfc5282>.

   [RFC8645]  Smyshlyaev, S., Ed., "Re-keying Mechanisms for Symmetric
              Keys", RFC 8645, DOI 10.17487/RFC8645, August 2019,
              <https://www.rfc-editor.org/info/rfc8645>.

   [MGM-SECURITY]
              Akhmetzyanova, L., Alekseev, E., Karpunin, G., and V.
              Nozdrunov, "Security of Multilinear Galois Mode (MGM)",
              2019, <https://eprint.iacr.org/2019/123.pdf>.

Appendix A.  Test Vectors

   1.  ENCR_KUZNYECHIK_MGM_KTREE, example 1:

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   K:
       b6 18 0c 14 5c 51 2d bd 69 d9 ce a9 2c ac 1b 5c
       e1 bc fa 73 79 2d 61 af 0b 44 0d 84 b5 22 cc 38
   i1 = 00, i2 = 0000, i3 = 0000, pnum = 000000
   K_msg:
       2f f1 c9 0e de 78 6e 06 1e 17 b3 74 d7 82 af 7b
       d8 80 bd 52 7c 66 a2 ba dc 3e 56 9a ab 27 1d a4
   salt [12]:
       7b 67 e6 f2 44 f9 7f 06 78 95 2e 45
   nonce [16]:
       00 00 00 00 7b 67 e6 f2 44 f9 7f 06 78 95 2e 45
   IV [8]:
       00 00 00 00 00 00 00 00
   AAD [8]:
       51 46 53 6b 00 00 00 01
   plaintext [64]:
       45 00 00 3c 23 35 00 00 7f 01 ee cc 0a 6f 0a c5
       0a 6f 0a 1d 08 00 f3 5b 02 00 58 00 61 62 63 64
       65 66 67 68 69 6a 6b 6c 6d 6e 6f 70 71 72 73 74
       75 76 77 61 62 63 64 65 66 67 68 69 01 02 02 04
   ciphertext [64]:
       18 9d 12 88 b7 18 f9 ea be 55 4b 23 9b ee 65 96
       c6 d4 ea fd 31 64 96 ef 90 1c ac 31 60 05 aa 07
       62 97 b2 24 bf 6d 2b e3 5f d6 f6 7e 7b 9d eb 31
       85 ff e9 17 9c a9 bf 0b db af c2 3e ae 4d a5 6f
   ESP ICV [12]:
       50 b0 70 a1 5a 2b d9 73 86 89 f8 ed
   ESP packet [112]:
       45 00 00 70 00 4d 00 00 ff 32 91 4f 0a 6f 0a c5
       0a 6f 0a 1d 51 46 53 6b 00 00 00 01 00 00 00 00
       00 00 00 00 18 9d 12 88 b7 18 f9 ea be 55 4b 23
       9b ee 65 96 c6 d4 ea fd 31 64 96 ef 90 1c ac 31
       60 05 aa 07 62 97 b2 24 bf 6d 2b e3 5f d6 f6 7e
       7b 9d eb 31 85 ff e9 17 9c a9 bf 0b db af c2 3e
       ae 4d a5 6f 50 b0 70 a1 5a 2b d9 73 86 89 f8 ed

   2.  ENCR_KUZNYECHIK_MGM_KTREE, example 2:

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   K:
       b6 18 0c 14 5c 51 2d bd 69 d9 ce a9 2c ac 1b 5c
       e1 bc fa 73 79 2d 61 af 0b 44 0d 84 b5 22 cc 38
   i1 = 00, i2 = 0001, i3 = 0001, pnum = 000000
   K_msg:
       9a ba c6 57 78 18 0e 6f 2a f6 1f b8 d5 71 62 36
       66 c2 f5 13 0d 54 e2 11 6c 7d 53 0e 6e 7d 48 bc
   salt [12]:
       7b 67 e6 f2 44 f9 7f 06 78 95 2e 45
   nonce [16]:
       00 00 00 00 7b 67 e6 f2 44 f9 7f 06 78 95 2e 45
   IV [8]:
       00 00 01 00 01 00 00 00
   AAD [8]:
       51 46 53 6b 00 00 00 10
   plaintext [64]:
       45 00 00 3c 23 48 00 00 7f 01 ee b9 0a 6f 0a c5
       0a 6f 0a 1d 08 00 e4 5b 02 00 67 00 61 62 63 64
       65 66 67 68 69 6a 6b 6c 6d 6e 6f 70 71 72 73 74
       75 76 77 61 62 63 64 65 66 67 68 69 01 02 02 04
   ciphertext [64]:
       78 0a 2c 62 62 32 15 7b fe 01 76 32 f3 2d b4 d0
       a4 fa 61 2f 66 c2 bf 79 d5 e2 14 9b ac 1d fc 4b
       15 4b 69 03 4d c2 1d ef 20 90 6d 59 62 81 12 7c
       ff 72 56 ab f0 0b a1 22 bb 5e 6c 71 a4 d4 9a 4d
   ESP ICV [12]:
       c2 2f 87 40 83 8e 3d fa ce 91 cc b8
   ESP packet [112]:
       45 00 00 70 00 5c 00 00 ff 32 91 40 0a 6f 0a c5
       0a 6f 0a 1d 51 46 53 6b 00 00 00 10 00 00 01 00
       01 00 00 00 78 0a 2c 62 62 32 15 7b fe 01 76 32
       f3 2d b4 d0 a4 fa 61 2f 66 c2 bf 79 d5 e2 14 9b
       ac 1d fc 4b 15 4b 69 03 4d c2 1d ef 20 90 6d 59
       62 81 12 7c ff 72 56 ab f0 0b a1 22 bb 5e 6c 71
       a4 d4 9a 4d c2 2f 87 40 83 8e 3d fa ce 91 cc b8

   3.  ENCR_MAGMA_MGM_KTREE, example 1:

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   K:
       5b 50 bf 33 78 87 02 38 f3 ca 74 0f d1 24 ba 6c
       22 83 ef 58 9b e6 f4 6a 89 4a a3 5d 5f 06 b2 03
   i1 = 00, i2 = 0000, i3 = 0000, pnum = 000000
   K_msg:
       25 65 21 e2 70 b7 4a 16 4d fc 26 e6 bf 0c ca 76
       5e 9d 41 02 7d 4b 7b 19 76 2b 1c c9 01 dc de 7f
   salt [4]:
       cf 36 63 12
   nonce [8]:
       00 00 00 00 cf 36 63 12
   IV [8]:
       00 00 00 00 00 00 00 00
   AAD [8]:
       c8 c2 b2 8d 00 00 00 01
   plaintext [64]:
       45 00 00 3c 24 2d 00 00 7f 01 ed d4 0a 6f 0a c5
       0a 6f 0a 1d 08 00 de 5b 02 00 6d 00 61 62 63 64
       65 66 67 68 69 6a 6b 6c 6d 6e 6f 70 71 72 73 74
       75 76 77 61 62 63 64 65 66 67 68 69 01 02 02 04
   ciphertext [64]:
       fa 08 40 33 2c 4f 3f c9 64 4d 8c 2c 4a 91 7e 0c
       d8 6f 8e 61 04 03 87 64 6b b9 df bd 91 50 3f 4a
       f5 d2 42 69 49 d3 5a 22 9e 1e 0e fc 99 ac ee 9e
       32 43 e2 3b a4 d1 1e 84 5c 91 a7 19 15 52 cc e8
   ESP ICV [8]:
       5f 4a fa 8b 02 94 0f 5c
   ESP packet [108]:
       45 00 00 6c 00 62 00 00 ff 32 91 3e 0a 6f 0a c5
       0a 6f 0a 1d c8 c2 b2 8d 00 00 00 01 00 00 00 00
       00 00 00 00 fa 08 40 33 2c 4f 3f c9 64 4d 8c 2c
       4a 91 7e 0c d8 6f 8e 61 04 03 87 64 6b b9 df bd
       91 50 3f 4a f5 d2 42 69 49 d3 5a 22 9e 1e 0e fc
       99 ac ee 9e 32 43 e2 3b a4 d1 1e 84 5c 91 a7 19
       15 52 cc e8 5f 4a fa 8b 02 94 0f 5c

   4.  ENCR_MAGMA_MGM_KTREE, example 2:

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   K:
       5b 50 bf 33 78 87 02 38 f3 ca 74 0f d1 24 ba 6c
       22 83 ef 58 9b e6 f4 6a 89 4a a3 5d 5f 06 b2 03
   i1 = 00, i2 = 0001, i3 = 0001, pnum = 000000
   K_msg:
       20 e0 46 d4 09 83 9b 23 f0 66 a5 0a 7a 06 5b 4a
       39 24 4f 0e 29 ef 1e 6f 2e 5d 2e 13 55 f5 da 08
   salt [4]:
       cf 36 63 12
   nonce [8]:
       00 00 00 00 cf 36 63 12
   IV [8]:
       00 00 01 00 01 00 00 00
   AAD [8]:
       c8 c2 b2 8d 00 00 00 10
   plaintext [64]:
       45 00 00 3c 24 40 00 00 7f 01 ed c1 0a 6f 0a c5
       0a 6f 0a 1d 08 00 cf 5b 02 00 7c 00 61 62 63 64
       65 66 67 68 69 6a 6b 6c 6d 6e 6f 70 71 72 73 74
       75 76 77 61 62 63 64 65 66 67 68 69 01 02 02 04
   ciphertext [64]:
       7a 71 48 41 a5 34 b7 58 93 6a 8e ab 26 91 40 a8
       25 a7 f3 5d b9 e4 37 1f e7 6c 99 9c 9b 88 db 72
       1d c7 59 f6 56 b5 b3 ea b6 b1 4d 6b d7 7a 07 1d
       4b 93 78 bd 08 97 6c 33 ed 9a 01 91 bf fe a1 dd
   ESP ICV [8]:
       dd 5d 50 9a fd b8 09 98
   ESP packet [108]:
       45 00 00 6c 00 71 00 00 ff 32 91 2f 0a 6f 0a c5
       0a 6f 0a 1d c8 c2 b2 8d 00 00 00 10 00 00 01 00
       01 00 00 00 7a 71 48 41 a5 34 b7 58 93 6a 8e ab
       26 91 40 a8 25 a7 f3 5d b9 e4 37 1f e7 6c 99 9c
       9b 88 db 72 1d c7 59 f6 56 b5 b3 ea b6 b1 4d 6b
       d7 7a 07 1d 4b 93 78 bd 08 97 6c 33 ed 9a 01 91
       bf fe a1 dd dd 5d 50 9a fd b8 09 98

   5.  ENCR_KUZNYECHIK_MGM_MAC_KTREE, example 1:

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   K:
       98 bd 34 ce 3b e1 9a 34 65 e4 87 c0 06 48 83 f4
       88 cc 23 92 63 dc 32 04 91 9b 64 3f e7 57 b2 be
   i1 = 00, i2 = 0000, i3 = 0000, pnum = 000000
   K_msg:
       98 f1 03 01 81 0a 04 1c da dd e1 bd 85 a0 8f 21
       8b ac b5 7e 00 35 e2 22 c8 31 e3 e4 f0 a2 0c 8f
   salt [12]:
       6c 51 cb ac 93 c4 5b ea 99 62 79 1d
   nonce [16]:
       00 00 00 00 6c 51 cb ac 93 c4 5b ea 99 62 79 1d
   IV [8]:
       00 00 00 00 00 00 00 00
   AAD [80]:
       3d ac 92 6a 00 00 00 01 00 00 00 00 00 00 00 00
       45 00 00 3c 0c f1 00 00 7f 01 05 11 0a 6f 0a c5
       0a 6f 0a 1d 08 00 48 5c 02 00 03 00 61 62 63 64
       65 66 67 68 69 6a 6b 6c 6d 6e 6f 70 71 72 73 74
       75 76 77 61 62 63 64 65 66 67 68 69 01 02 02 04
   plaintext [0]:
   ciphertext [0]:
   ESP ICV [12]:
       ca c5 8c e5 e8 8b 4b f3 2d 6c f0 4d
   ESP packet [112]:
       45 00 00 70 00 01 00 00 ff 32 91 9b 0a 6f 0a c5
       0a 6f 0a 1d 3d ac 92 6a 00 00 00 01 00 00 00 00
       00 00 00 00 45 00 00 3c 0c f1 00 00 7f 01 05 11
       0a 6f 0a c5 0a 6f 0a 1d 08 00 48 5c 02 00 03 00
       61 62 63 64 65 66 67 68 69 6a 6b 6c 6d 6e 6f 70
       71 72 73 74 75 76 77 61 62 63 64 65 66 67 68 69
       01 02 02 04 ca c5 8c e5 e8 8b 4b f3 2d 6c f0 4d

   6.  ENCR_KUZNYECHIK_MGM_MAC_KTREE, example 2:

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   K:
       98 bd 34 ce 3b e1 9a 34 65 e4 87 c0 06 48 83 f4
       88 cc 23 92 63 dc 32 04 91 9b 64 3f e7 57 b2 be
   i1 = 00, i2 = 0000, i3 = 0001, pnum = 000000
   K_msg:
       02 c5 41 87 7c c6 23 f3 f1 35 91 9a 75 13 b6 f8
       a8 a1 8c b2 63 99 86 2f 50 81 4f 52 91 01 67 84
   salt [12]:
       6c 51 cb ac 93 c4 5b ea 99 62 79 1d
   nonce [16]:
       00 00 00 00 6c 51 cb ac 93 c4 5b ea 99 62 79 1d
   IV [8]:
       00 00 00 00 01 00 00 00
   AAD [80]:
       3d ac 92 6a 00 00 00 06 00 00 00 00 01 00 00 00
       45 00 00 3c 0c fb 00 00 7f 01 05 07 0a 6f 0a c5
       0a 6f 0a 1d 08 00 43 5c 02 00 08 00 61 62 63 64
       65 66 67 68 69 6a 6b 6c 6d 6e 6f 70 71 72 73 74
       75 76 77 61 62 63 64 65 66 67 68 69 01 02 02 04
   plaintext [0]:
   ciphertext [0]:
   ESP ICV [12]:
       ba bc 67 ec 72 a8 c3 1a 89 b4 0e 91
   ESP packet [112]:
       45 00 00 70 00 06 00 00 ff 32 91 96 0a 6f 0a c5
       0a 6f 0a 1d 3d ac 92 6a 00 00 00 06 00 00 00 00
       01 00 00 00 45 00 00 3c 0c fb 00 00 7f 01 05 07
       0a 6f 0a c5 0a 6f 0a 1d 08 00 43 5c 02 00 08 00
       61 62 63 64 65 66 67 68 69 6a 6b 6c 6d 6e 6f 70
       71 72 73 74 75 76 77 61 62 63 64 65 66 67 68 69
       01 02 02 04 ba bc 67 ec 72 a8 c3 1a 89 b4 0e 91

   7.  ENCR_MAGMA_MGM_MAC_KTREE, example 1:

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   K:
       d0 65 b5 30 fa 20 b8 24 c7 57 0c 1d 86 2a e3 39
       2c 1c 07 6d fa da 69 75 74 4a 07 a8 85 7d bd 30
   i1 = 00, i2 = 0000, i3 = 0000, pnum = 000000
   K_msg:
       4c 61 45 99 a0 a0 67 f1 94 87 24 0a e1 00 e1 b7
       ea f2 3e da f8 7e 38 73 50 86 1c 68 3b a4 04 46
   salt [4]:
       88 79 8f 29
   nonce [8]:
       00 00 00 00 88 79 8f 29
   IV [8]:
       00 00 00 00 00 00 00 00
   AAD [80]:
       3e 40 69 9c 00 00 00 01 00 00 00 00 00 00 00 00
       45 00 00 3c 0e 08 00 00 7f 01 03 fa 0a 6f 0a c5
       0a 6f 0a 1d 08 00 36 5c 02 00 15 00 61 62 63 64
       65 66 67 68 69 6a 6b 6c 6d 6e 6f 70 71 72 73 74
       75 76 77 61 62 63 64 65 66 67 68 69 01 02 02 04
   plaintext [0]:
   ciphertext [0]:
   ESP ICV [8]:
       4d d4 25 8a 25 35 95 df
   ESP packet [108]:
       45 00 00 6c 00 13 00 00 ff 32 91 8d 0a 6f 0a c5
       0a 6f 0a 1d 3e 40 69 9c 00 00 00 01 00 00 00 00
       00 00 00 00 45 00 00 3c 0e 08 00 00 7f 01 03 fa
       0a 6f 0a c5 0a 6f 0a 1d 08 00 36 5c 02 00 15 00
       61 62 63 64 65 66 67 68 69 6a 6b 6c 6d 6e 6f 70
       71 72 73 74 75 76 77 61 62 63 64 65 66 67 68 69
       01 02 02 04 4d d4 25 8a 25 35 95 df

   8.  ENCR_MAGMA_MGM_MAC_KTREE, example 2:

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   K:
       d0 65 b5 30 fa 20 b8 24 c7 57 0c 1d 86 2a e3 39
       2c 1c 07 6d fa da 69 75 74 4a 07 a8 85 7d bd 30
   i1 = 00, i2 = 0000, i3 = 0001, pnum = 000000
   K_msg:
       b4 f3 f9 0d c4 87 fa b8 c4 af d0 eb 45 49 f2 f0
       e4 36 32 b6 79 19 37 2e 1e 96 09 ea f0 b8 e2 28
   salt [4]:
       88 79 8f 29
   nonce [8]:
       00 00 00 00 88 79 8f 29
   IV [8]:
       00 00 00 00 01 00 00 00
   AAD [80]:
       3e 40 69 9c 00 00 00 06 00 00 00 00 01 00 00 00
       45 00 00 3c 0e 13 00 00 7f 01 03 ef 0a 6f 0a c5
       0a 6f 0a 1d 08 00 31 5c 02 00 1a 00 61 62 63 64
       65 66 67 68 69 6a 6b 6c 6d 6e 6f 70 71 72 73 74
       75 76 77 61 62 63 64 65 66 67 68 69 01 02 02 04
   plaintext [0]:
   ciphertext [0]:
   ESP ICV [8]:
       84 84 a9 23 30 a0 b1 96
   ESP packet [108]:
       45 00 00 6c 00 18 00 00 ff 32 91 88 0a 6f 0a c5
       0a 6f 0a 1d 3e 40 69 9c 00 00 00 06 00 00 00 00
       01 00 00 00 45 00 00 3c 0e 13 00 00 7f 01 03 ef
       0a 6f 0a c5 0a 6f 0a 1d 08 00 31 5c 02 00 1a 00
       61 62 63 64 65 66 67 68 69 6a 6b 6c 6d 6e 6f 70
       71 72 73 74 75 76 77 61 62 63 64 65 66 67 68 69
       01 02 02 04 84 84 a9 23 30 a0 b1 96

Author's Address

   Valery Smyslov
   ELVIS-PLUS
   PO Box 81
   Moscow (Zelenograd)  124460
   RU

   Phone: +7 495 276 0211
   Email: svan@elvis.ru

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