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Guidelines on the cryptographic algorithms, accompanying the usage of standards GOST R 34.10-2012 and GOST R 34.11-2012
draft-smyshlyaev-gost-usage-00

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This is an older version of an Internet-Draft that was ultimately published as RFC 7836.
Authors Stanislav V. Smyshlyaev , Vladimir Popov , Evgeny Alekseev , Igor Oshkin
Last updated 2015-06-23
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draft-smyshlyaev-gost-usage-00
Network Working Group                                 S. Smyshlyaev, Ed.
Internet-Draft                                                  V. Popov
Intended status: Informational                               E. Alekseev
Expires: December 25, 2015                                     I. Oshkin
                                                              CRYPTO-PRO
                                                           June 23, 2015

 Guidelines on the cryptographic algorithms, accompanying the usage of
           standards GOST R 34.10-2012 and GOST R 34.11-2012
                     draft-smyshlyaev-gost-usage-00

Abstract

   The usage of cryptographic algorithms, that are defined by GOST R
   34.10-2012 [GOST3410-2012] and GOST R 34.11-2012 [GOST3411-2012]
   standards, for protection of the information is carried out, as a
   rule, within the cryptographic protocols based on the accompanying
   algorithms.

   This memo contains a description of the accompanying algorithms for
   defining the pseudorandom functions, the key derivation functions,
   the key agreement protocols based on the Diffie-Hellman algorithm and
   the keying material export algorithms.

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
   Task Force (IETF).  Note that other groups may also distribute
   working documents as Internet-Drafts.  The list of current Internet-
   Drafts is at http://datatracker.ietf.org/drafts/current/.

   Internet-Drafts are draft documents valid for a maximum of six months
   and may be updated, replaced, or obsoleted by other documents at any
   time.  It is inappropriate to use Internet-Drafts as reference
   material or to cite them other than as "work in progress."

   This Internet-Draft will expire on December 25, 2015.

Copyright Notice

   Copyright (c) 2015 IETF Trust and the persons identified as the
   document authors.  All rights reserved.

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   This document is subject to BCP 78 and the IETF Trust's Legal
   Provisions Relating to IETF Documents
   (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  . . . . . . . . . . . . . . . . . . . . . . . .   2
   2.  Scope . . . . . . . . . . . . . . . . . . . . . . . . . . . .   3
   3.  Conventions used in This Document . . . . . . . . . . . . . .   3
     3.1.  Mathematical objects  . . . . . . . . . . . . . . . . . .   3
     3.2.  Basic terms and definitions . . . . . . . . . . . . . . .   4
   4.  Algorithm descriptions  . . . . . . . . . . . . . . . . . . .   6
     4.1.  HMAC functions  . . . . . . . . . . . . . . . . . . . . .   6
     4.2.  PRF . . . . . . . . . . . . . . . . . . . . . . . . . . .   8
     4.3.  VKO algorithms for key agreement  . . . . . . . . . . . .  11
     4.4.  Key derivation function KDF_GOSTR3411_2012_256  . . . . .  12
     4.5.  Key derivation function KDF_TREE_GOSTR3411_2012_256 . . .  13
     4.6.  Key wrap and unwrap . . . . . . . . . . . . . . . . . . .  14
   5.  References  . . . . . . . . . . . . . . . . . . . . . . . . .  15
     5.1.  Normative References  . . . . . . . . . . . . . . . . . .  15
     5.2.  Informative References  . . . . . . . . . . . . . . . . .  16
   Appendix A.  Test examples  . . . . . . . . . . . . . . . . . . .  17
   Authors' Addresses  . . . . . . . . . . . . . . . . . . . . . . .  28

1.  Introduction

   The usage of cryptographic algorithms, that are defined by the GOST R
   34.10-2012 [GOST3410-2012] and GOST R 34.11-2012 [GOST3411-2012]
   standards, for protection of the information is carried out, as a
   rule, within the cryptographic protocols based on the accompanying
   algorithms.

   The specifications of algorithms and parameters proposed in this memo
   are defined on the basis of experience in the development of
   cryptographic protocols, as described in the [RFC4357], [RFC4490] and
   [RFC4491].

   This memo contains a description of the accompanying algorithms for
   defining the pseudorandom functions, the key derivation functions,
   the key agreement protocols based on the Diffie-Hellman algorithm and
   the keying material export algorithms.

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   This memo does not specify the cryptographic algorithms GOST R
   34.10-2012 [GOST3410-2012] and GOST R 34.11-2012 [GOST3411-2012].
   These algorithms are defined by the national standards GOST R
   34.10-2012 [GOST3410-2012] and GOST R 34.11-2012 [GOST3411-2012] and
   described in [RFC7091] and [RFC6986] (an English version of Russian
   national standards).

   The need to ensure compatibility of the cryptographic protocol
   implementations based on the Russian cryptographic standards GOST R
   34.10-2012 [GOST3410-2012] and GOST R 34.11-2012 [GOST3411-2012]
   served as the main reason for the development of this document.

2.  Scope

   This memo is recommended for use in encrypting and protecting the
   authenticity of the data, based on the use of digital signature
   algorithms GOST R 34.10-2012 [GOST3410-2012] and hash function GOST R
   34.11-2012 [GOST3411-2012], in public and corporate networks to
   protect information that does not contain a classified information.

3.  Conventions used in This Document

   The key words "MUST", "MUST NOT", "REQUIRED", "SHALL", "SHALL NOT",
   "SHOULD", "SHOULD NOT", "RECOMMENDED", "MAY", and "OPTIONAL" in this
   document are to be interpreted as described in [RFC2119].

3.1.  Mathematical objects

   This document uses the following notation for the sets and operations
   on the elements of these sets in accordance with GOST R 34.11-2012
   [GOST3411-2012]:

   (xor)   exclusive-or of two binary vectors of the same length;

   V_n     the finite-dimensional vector space over GF(2) of dimension n
           with the (xor) operation, for n = 0 the V_0 space consists of
           a single empty element of size 0;

   U       the element of V_n; in the binary representation U =
           (u_(n-1), u_(n-2), ..., u_1, u_0), where u_i in {0, 1};

   A|B     concatenation of vectors A, B, i.e., if A in V_n1, B in V_n2,
           A = (a_(n1-1), a_(n1-2), ..., a_0), and B = (b_(n2-1),
           b_(n2-2), ..., b_0), then A|B = (a_(n1-1), a_(n1-2), ...,
           a_0, b_(n2-1), b_(n2-2), ..., b_0) is an element of
           V_(n1+n2);

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   V_(8, r)  the set of byte strings of size r; if W is an element of
           V(8, r), then W = (w^0, w^1, ..., w^(r-1)), where w^0, w^1,
           ..., w^(r-1) are elements of V_8; if A in V_(8, r1), B in
           V_(8, r2), A = (a^0, a^1, ..., a^(r1-1)), and B = (b^0, b^1,
           ..., b^(r2-1)), then A|B = (a^0, a^1, ..., a^(r1-1), b^0,
           b^1, ..., b^(r2-1)) is an element of V_(8, r1+r2);

   Bit representation  the bit representation of the element W = (w^0,
           w^1, ..., w^(r-1)) of V_(8, r), where w^0 = (w_7, w_6, ...,
           w_0), w^1 = (w_15, w_14, ..., w_8), ..., w^(r-1) = (w_(8r-1),
           w_(8r-2), ..., w_(8r-8)) are elements of V_8, is an element
           (w_(8r-1), w_(8r-2), ..., w_1, w_0) of V_(8*r);

   Byte representation  if n is a multiple of 8, r = n/8, then the byte
           representation of the element W = (w_(n-1), w_(n-2), ...,
           w_0) of V_n is a byte string (w^0, w^1, ..., w^(r-1)) of
           V_(8, r), where w^0 = (w_7, w_6, ..., w_0), w^1 = (w_15,
           w_14, ..., w_8), ..., w^(r-1) = (w_(8r-1), w_(8r-2), ...,
           w_(8r-8)) are elements of V_8;

   K (key) arbitrary element of V_n; if K in V_n, then its size (in
           bits) is equal to n, where n can be an arbitrary natural
           number.

   Note: It is proposed to interpret and edit the formulas in accordance
   with the above definitions.

3.2.  Basic terms and definitions

   This memo uses the following terms, abbreviations and symbols:

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   +----------+--------------------------------------------------------+
   | Symbols  | Meaning                                                |
   +----------+--------------------------------------------------------+
   | H_256    | GOST R 34.11-2012 hash function, 256-bit               |
   |          |                                                        |
   | H_512    | GOST R 34.11-2012 hash function, 512-bit               |
   |          |                                                        |
   | HMAC     | a function for calculating a message authentication    |
   |          | code (based on some hash function)                     |
   |          |                                                        |
   | HMAC_256 | a function based on the hash function H_256, intended  |
   |          | for computing a message authentication code            |
   |          |                                                        |
   | HMAC_512 | a function based on the hash function H_512, intended  |
   |          | for computing a message authentication code            |
   |          |                                                        |
   | PRF      | a pseudorandom function, i.e., a transformation that   |
   |          | allows to generate pseudorandom sequence of bytes      |
   |          |                                                        |
   | KDF      | a key derivation function, i.e., a transformation,     |
   |          | that allows to derive keys and keying material for the |
   |          | root key and random data using a pseudorandom function |
   +----------+--------------------------------------------------------+

   To produce a byte sequence of the size N with functions that give a
   longer output the input should be taken from the output sequence of
   the first N bytes.  This remark applies to the following functions:

   o  the functions described in Section 4.2;

   o  KDF_TREE_GOSTR3411_2012_256.

   When n is multiple of 8, an element of V_n can be represented in the
   bit and byte form.  The result of operation <<|>>, applied to the
   elements in the bit representation is described in the bit
   representation.  The result of the operation <<|>>, applied to the
   same elements in their byte representation is described in the byte
   representation.  Thus, the symbol <<|>> is used to refer to two
   different operations, depending on the form of their arguments.
   Selecting one of these operations is uniquely determined by the
   representation of arguments.

   Hereinafter all data (the elements of V_n) unless otherwise
   specified, are considered given in the byte representation.
   Operation <<|>> on the arguments of functions, unless explicitly
   stated otherwise, is performed on their byte representation.

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   If the function is defined outside this document (eg, H_256) and its
   definition is using arguments in bit representation, it is assumed
   that the bit representation of the argument is formed immediately
   before the calculation of the function (in particular, only after the
   application of the operation <<|>> to the byte representation of the
   arguments).

   If as the argument of the function defined below is used the output
   of another function that is defined outside of this document and has
   output value in bit representation, it is assumed that the output
   value will be translated into the byte representation before
   substitution in arguments.

4.  Algorithm descriptions

   For algorithms described in this paper, the possible values of the
   functions are limited by the permissibility of applying them as the
   input parameter of the transformations and are assigned by the
   protocols.

4.1.  HMAC functions

   This section defines the HMAC transformations based on GOST R
   34.11-2012 [GOST3411-2012] algorithm with different size of the
   output value.

4.1.1.  HMAC_GOSTR3411_2012_256

   This HMAC transformation is based on GOST R 34.11-2012
   [GOST3411-2012] algorithm, 256-bit output.  The identifier of this
   transformation is shown below:

      id-tc26-hmac-gost-3411-12-256, <<1.2.643.7.1.1.4.1>>.

   The calculation of HMAC_256(K, T) for the data T of arbitrary length
   and the key K of n bits size is the forming of the 64-byte string K*
   and the transformation on K* and T using the hash function H_256.

   The size n can take any value in the interval from 256 to 512.

   For the formation of the key K*: if n < 512, take the string K* equal
   to the byte representation of the bit string K | A, where A = (0, 0,
   ..., 0) in V_(512-n); if n = 512, take K* equal to the byte
   representation of the key K.

   The value of HMAC_256 (K, T) is given by:

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      HMAC_256 (K, T) = H_256 (K* (xor) opad | H_256 (K* (xor) ipad |
      T)),

   where byte representations are:

      ipad = (0x36 | 0x36 | ... | 0x36) in V_(8, 64),
      opad = (0x5C | 0x5C | ... | 0x5C) in V_(8, 64).

   This algorithm uses H_256 as a hash function for HMAC, described in
   [RFC2104].  The method of forming the values of ipad and opad is also
   given in [RFC2104].  The size of the HMAC_256 output in bytes is
   equal to 32, the block size of the iterative procedure for the H_256
   compression function in bytes is equal to 64 (in the notation of
   [RFC2104], L = 32 and B = 64, respectively).

4.1.2.  HMAC_GOSTR3411_2012_512

   This HMAC transformation is based on GOST R 34.11-2012
   [GOST3411-2012], 512-bit output.  The identifier of this
   transformation is shown below:

      id-tc26-hmac-gost-3411-12-512, <<1.2.643.7.1.1.4.2>>.

   The calculation of HMAC_512(K, T) for the data T of arbitrary length
   and the key K of n bits size is the forming of the 64-byte string K*
   and the transformation on K* and T using the hash function H_512.

   The size n can take any value in the interval from 256 to 512.  The
   recommended value is 512.

   For the formation of the key K*: if n < 512, take the string K* equal
   to the byte representation of the bit string K | A, where A = (0, 0,
   ..., 0) in V_(512-n); if n = 512, take K* equal to the byte
   representation of the K key.

   The value of HMAC_512 (K, T) is given by:

      HMAC_512 (K, T) = H_512 (K* (xor) opad | H_512 (K* (xor) ipad |
      T)),

   where byte representations are:

      ipad = (0x36|0x36|...|0x36) in V_(8, 64),
      opad = (0x5C|0x5C|...|0x5C) in V_(8, 64).

   This algorithm uses H_512 as a hash function for HMAC, described in
   [RFC2104].  The method of forming the values of ipad and opad is also
   given in [RFC2104].  The size of the HMAC_512 output in bytes is

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   equal to 64, the block size of the iterative procedure for the H_512
   compression function in bytes is equal to 64 (in the notation of
   [RFC2104], L = 64 and B = 64, respectively).

4.2.  PRF

   This section defines six based on HMAC PRF transformations that are
   recommended for the use.  Two of them are for the TLS protocol and
   four for IPsec.

   To obtain a set of values of the total size of m bytes using any of
   the following PRF it should be taken equal to the corresponding
   sequential values from the first m bytes of the used PRF output in
   the byte representation.

4.2.1.  PRFs for the TLS protocol

4.2.1.1.  PRF_TLS_GOSTR3411_2012_256

   This is the transformation to implement the pseudorandom function of
   the TLS protocol; the transformation uses the HMAC_256 values based
   on GOST R 34.11-2012 [GOST3411-2012], 256-bit output.

      PRF_TLS_GOSTR3411_2012_256 (secret, label, seed) =
      = P_GOSTR3411_2012_256 (secret, label | seed),

      P_GOSTR3411_2012_256 (secret, S) =
      = HMAC_256 (secret, A_1 | S) | HMAC_256 (secret, A_2 | S) |
      HMAC_256 (secret, A_3 | S) | ...

   The A_i parameters are determined sequentially as follows:

      A_0 = S,
      A_i = HMAC_256 (secret, A_(i-1)).

   P_GOSTR3411_2012_256 function uses HMAC_256 and corresponds to the
   method of method of specifying the arguments and the output value of
   P_hash data expansion function, given in Section 5 of [RFC2246] and
   kept in [RFC5246].

4.2.1.2.  PRF_TLS_GOSTR3411_2012_512

   This is the transformation to implement the pseudorandom function of
   the TLS protocol; the transformation uses the HMAC_512 values based
   on GOST R 34.11-2012 [GOST3411-2012], 512-bit output.

      PRF_TLS_GOSTR3411_2012_512 (secret, label, seed) =
      = P_GOSTR3411_2012_512 (secret, label | seed),

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      P_GOSTR3411_2012_512 (secret, S) =
      = HMAC_512 (secret, A_1 | S) | HMAC_512 (secret, A_2 | S) |
      HMAC_512 (secret, A_3 | S) | ...

   The A_i parameters are determined sequentially as follows:

      A_0 = S,
      A_i = HMAC_512 (secret, A_(i-1)).

   P_GOSTR3411_2012_512 function uses HMAC_512 and corresponds to the
   method of method of specifying the arguments and the output value for
   P_hash data expansion function, given in Section 5 of [RFC2246] and
   kept in [RFC5246].

4.2.2.  PRFs for the IPsec protocols based on GOST R 34.11-2012, 256-bit

4.2.2.1.  PRF_IPSEC_KEYMAT_GOSTR3411_2012_256

   This pseudorandom function for the keying material generation is
   defined as follows (the arguments are the byte strings K and S):

      PRF_IPSEC_KEYMAT_GOSTR3411_2012_256 (K, S) = T1| T2| T3| T4|...,

   where

      T1 = HMAC_256 (K, S),
      T2 = HMAC_256 (K, T1 | S),
      T3 = HMAC_256 (K, T2 | S),
      T4 = HMAC_256 (K, T3 | S),
      ...

   PRF_IPSEC_KEYMAT_GOSTR3411_2012_256 function is similar to KEYMAT
   function in [RFC2409] regarding the assignment scheme for the
   arguments in the iterations.

4.2.2.2.  PRF_IPSEC_PRFPLUS_GOSTR3411_2012_256

   This pseudorandom function for the keying material generation is
   defined as follows (the arguments are the byte strings K and S)

      PRF_IPSEC_PRFPLUS_GOSTR3411_2012_256 (K, S) = T1| T2| T3| T4|...,

   where

      T1 = HMAC_256 (K, S | 0x01),
      T2 = HMAC_256 (K, T1 | S | 0x02),
      T3 = HMAC_256 (K, T2 | S | 0x03),
      T4 = HMAC_256 (K, T3 | S | 0x04),

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      ...

   PRF_IPSEC_PRFPLUS_GOSTR3411_2012_256 output size is not more than
   255*256 bits, which corresponds to the output sequence T1| T2| T3|
   T4| ... | T255.

   PRF_IPSEC_PRFPLUS_GOSTR3411_2012_256 is similar to the prf+ function
   in [RFC5996] regarding the assignment scheme for the arguments in
   iterations.

4.2.3.  PRFs for the IPsec protocols based on GOST R 34.11-2012, 512-bit

4.2.3.1.  PRF_IPSEC_KEYMAT_GOSTR3411_2012_512

   This pseudorandom function for the keying material generation is
   defined as follows (the arguments are the byte strings K and S):

      PRF_IPSEC_KEYMAT_GOSTR3411_2012_512 (K, S) = T1| T2| T3| T4|...,

   where

      T1 = HMAC_512 (K, S),
      T2 = HMAC_512 (K, T1 | S),
      T3 = HMAC_512 (K, T2 | S),
      T4 = HMAC_512 (K, T3 | S),
      ...

   PRF_IPSEC_KEYMAT_GOSTR3411_2012_512 is similar to KEYMAT function in
   [RFC2409] regarding the assignment scheme for the arguments in
   iterations.

4.2.3.2.  PRF_IPSEC_PRFPLUS_GOSTR3411_2012_512

   This pseudorandom function for the keying material generation is
   defined as follows (the arguments are the byte strings K and S):

      PRF_IPSEC_PRFPLUS_GOSTR3411_2012_512 (K, S) = T1| T2| T3| T4|...,

   where

      T1 = HMAC_512 (K, S | 0x01),
      T2 = HMAC_512 (K, T1 | S | 0x02),
      T3 = HMAC_512 (K, T2 | S | 0x03),
      T4 = HMAC_512 (K, T3 | S | 0x04),
      ...

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   PRF_IPSEC_PRFPLUS_GOSTR3411_2012_512 output size is not more than
   255*512 bits, which corresponds to the output sequence T1| T2| T3|
   T4|...| T255.

   The function PRF_IPSEC_PRFPLUS_GOSTR3411_2012_512 is similar to the
   prf+ function in [RFC5996] regarding the assignment scheme for the
   arguments in iterations.

4.3.  VKO algorithms for key agreement

   This section identifies the key agreement algorithms using GOST R
   34.10-2012 [GOST3410-2012].

4.3.1.  VKO_GOSTR3410_2012_256

   The 256-bit VKO GOST R 34.10-2012 algorithm is used for an agreement
   of the VKO 256-bit keys and based on GOST R 34.11-2012
   [GOST3411-2012], 256-bit.  The algorithm can be used for an agreement
   of the GOST R 34.10-2012 [GOST3410-2012] keys with the size of 256
   bits or 512 bits.

   The algorithm is designed to produce an encryption key or a keying
   material of size 256 bits to be used in the cryptographic protocols.
   Key or keying material KEK_VKO (x, y, UKM) is produced by the
   exchange participant from his private key x, the public key y*P of
   the opposite side and UKM value, considered as a number.

   The algorithm can be used for both static and ephemeral key with the
   public key size n >= 512 bits including the case where one side uses
   a static key and the other - ephemeral.

   UKM parameter is optional (the default UKM = 1) and can take any
   value from 1 to 2^(n/2)-1.  It is allowed to use a nonzero UKM of
   arbitrary size not exceeding n/2 bits.  UKM size of 64 bit or more is
   recommended for cases where the keys at least one of the parties are
   static.

      K (x, y, UKM) = (m/q*UKM*x mod q)*(y*P),

   where m and q - the parameters of the elliptic curve according GOST R
   34.10-2012 [GOST3410-2012] notation.

      KEK_VKO (x, y, UKM) = H_256 (K(x, y, UKM)).

   This algorithm is defined by analogy with Section 5.2 of [RFC4357],
   but instead of the hash function GOST R 34.11-94 [GOST3411-94]
   (referred as gostR3411) applies the hash function H_256 and K(x, y,

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   UKM) is calculated at the public key size n >= 512 bits and UKM size
   up to n/2 bits.

4.3.2.  VKO_GOSTR3410_2012_512

   The 512-bit VKO GOST R 34.10-2012 algorithm is used for an agreement
   of the VKO 512-bit keys and based on GOST R 34.11-2012
   [GOST3411-2012], 512-bit.  The algorithm can be used for an agreement
   of the GOST R 34.10-2012 [GOST3410-2012] keys with the size of 512
   bits.

   The algorithm is designed to produce an encryption key or keying
   material of size 512 bits to be used in cryptographic protocols.  Key
   or keying material KEK_VKO (x, y, UKM) is produced by the exchange
   participant from his private key x, the public key y*P of the
   opposite side and the UKM value, considered as a number.

   The algorithm can be used for both static and ephemeral key with the
   public key size n >= 1024 bits including the case where one side uses
   a static key and the other - ephemeral.

   UKM parameter is optional (the default UKM = 1) and can take any
   value from 1 to 2^(n/2)-1.  It is allowed to use a nonzero UKM of
   arbitrary size not exceeding n/2 bits.  UKM size of 128 bit or more
   is recommended for cases where the keys at least one of the parties
   are static.

      K (x, y, UKM) = (m/q*UKM*x mod q)*(y*P),

   where m and q - the parameters of the elliptic curve according GOST R
   34.10-2012 [GOST3410-2012] notation.

      KEK_VKO (x, y, UKM) = H_512 (K (x, y, UKM)).

   This algorithm is defined by analogy with Section 5.2 of [RFC4357],
   but instead of the hash function GOST R 34.11-94 [GOST3411-94]
   (referred as gostR3411) applies the hash function H_256, and K(x, y,
   UKM) is calculated at the public key size n >= 1024 bits and UKM size
   up to n/2 bits.

4.4.  Key derivation function KDF_GOSTR3411_2012_256

   The key derivation function KDF_GOSTR3411_2012_256 based on HMAC_256
   function is designed to generate a 256-bit keying material and is
   given by:

      KDF (K_in, label, seed) = HMAC_256 (K_in, 0x01 | label | 0x00 |
      seed | 0x01 | 0x00),

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   where

   o  K_in -- derivation key,

   o  label, seed -- the parameters, fixed and assigned by a protocol.

   The key derivation function KDF_GOSTR3411_2012_256 is a special case
   of KDF_TREE_GOSTR3411_2012 function, described in the next section.

4.5.  Key derivation function KDF_TREE_GOSTR3411_2012_256

   The key derivation function KDF_TREE_GOSTR3411_2012_256 based on
   HMAC_256 and is given by:

      KDF_TREE (K_in, label, seed, R) = K(1)| K(2)| K(3)| K(4)|...,

      K(i) = HMAC_256 (K_in, [i]_2 | label | 0x00 | seed| [L]2), i >= 1,

   where

   R       a fixed external parameter, with possible values of 1, 2, 3
           or 4;

   K_in    derivation key;

   L       the required size (in bits) of the generated keying material
           (an integer, not exceeding 256*(2^(8*R)-1));

   [L]_2   byte representation of L, in network byte order;

   i       iteration counter;

   [i]_2   byte representation of the iteration counter (in the network
           byte order), the number of bytes in the representation [i]_2
           is equal to R (no more than 4 bytes);

   label, seed  the parameters, fixed and assigned by a protocol.

   The key derivation function KDF_TREE_GOSTR3411_2012_256 is intended
   for generating a keying material in size of L, not exceeding
   256*(2^(8*R)-1) bits, and utilizes general principles of the input
   and output for the key derivation function that are outlined in
   Section 5.1 of NIST SP 800-108 [NISTSP800-108].  HMAC_256 algorithm
   with 256-bit output described in Section 4.1 is selected as a
   pseudorandom function.

   When R = 1 and L = 256 the function KDF_TREE_GOSTR3411_2012_256 is
   equivalent to KDF_GOSTR3411_2012_256 from the previous section.

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   Each key derived from the keying material, which was formed with the
   derivation key K_in (0-level key) may be a 1-level diversification
   key and may used to generate a new keying material.  The keying
   material derived from the 1-level derivation key, can be broken down
   into the 2nd level derivation keys.  The application of this
   procedure leads to the construction of the key tree with the root key
   and the formation of the key material to the hierarchy of the levels,
   as described in Section 6 of NIST SP 800-108 [NISTSP800-108].  The
   partitioning procedure for keying material at each level is defined
   in the protocols.

4.6.  Key wrap and unwrap

   Wrapped representation of the secret key K (GOST R 34.10-2012
   [GOST3410-2012] key or GOST 28147-89 [GOST28147-89] key) is formed as
   follows by using a given export key K_e (GOST 28147-89 [GOST28147-89]
   key) and the random UKM vector from 8 to 16 bytes in size:

   1.  Generates a random UKM vector.

   2.  With the key derivation function, using export key K_e as a
       derivation key, and a UKM vector as the value of seed, generates
       a key, denoted by KEK_e (UKM), where

          KEK_e (UKM) = KDF (K_e, label, UKM).

   3.  MAC value GOST 28147-89 (4-byte) for the data K and the key KEK_e
       (UKM) is calculated, initialization vector (IV) in this case is
       equal to the first 8 bytes of UKM.  The resulting value is
       denoted as CEK_MAC.

   4.  The key K is encrypted by the GOST 28147-89 algorithm in the
       Electronic Codebook (ECB) mode with the key KEK_e (UKM).  The
       encoding result denoted as CEK_ENC.

   5.  The wrapped representation of the key is considered (UKM |
       CEK_ENC | CEK_MAC).

   Where as a key derivation function is used KDF function (see previous
   section) for the fixed value

      label = (0x26 | 0xBD | 0xB8 | 0x78)

   and the seed value that is equal to UKM.

   During key import the value of key K is restored as follows from the
   wrapped representation of the key (GOST R 34.10-2012 [GOST3410-2012]
   key or GOST 28147-89 key [GOST28147-89] key) and the export key K_e:

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   1.  From the wrapped representation of the key selects the sets UKM,
       CEK_ENC, and CEK_MAC.

   2.  With the key derivation function, using the export key K_e as a
       derivation key, and a random UKM value as the value of seed,
       generates a key, denoted by KEK_e(UKM), where

          KEK_e (UKM) = KDF (K_e, label, UKM).

   3.  The CEK_ENC set is decrypted by the GOST 28147-89 algorithm in
       the Electronic Codebook (ECB) mode with the key KEK_e(UKM).  The
       unwrapped key K is assumed to be equal to the result of
       decryption.

   4.  MAC value GOST 28147-89 (4-byte) for the data K and the key
       KEK_e(UKM) is calculated, initialization vector (IV) in this case
       is equal to the first 8 bytes of UKM.  If the result does not
       equal to CEK_MAC, an error is returned.

   The algorithms for wrapping and unwrapping of the GOST R 34.10-2012
   [GOST3410-2012] keys are modifications of CryptoPro Key Wrap and
   CryptoPro Key Unwrap algorithms, described in Sections 6.3 and 6.4 of
   [RFC4357].

5.  References

5.1.  Normative References

   [GOST28147-89]
              Gosudarstvennyi Standard of USSR, Government Committee of
              the USSR for Standards, "Systems of information
              processing.  Cryptographic data security.  Algorithms of
              cryptographic transformation", GOST 28147-89, 1989.

   [GOST3410-2012]
              Federal Agency on Technical Regulating and Metrology,
              "Information technology. Cryptographic data security.
              Signature and verification processes of [electronic]
              digital signature", GOST R 34.10-2012, 2012.

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

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   [GOST3411-94]
              Federal Agency on Technical Regulating and Metrology,
              "Information technology. Cryptographic Data Security.
              Hashing function", GOST R 34.11-94, 1994.

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

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

   [RFC4357]  Popov, V., Kurepkin, I., and S. Leontiev, "Additional
              Cryptographic Algorithms for Use with GOST 28147-89, GOST
              R 34.10-94, GOST R 34.10-2001, and GOST R 34.11-94
              Algorithms", RFC 4357, January 2006.

5.2.  Informative References

   [NISTSP800-108]
              National Institute of Standards and Technology,
              "Recommendation for Key Derivation Using Pseudorandom
              Functions", NIST SP 800-108, October 2009.

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

   [RFC2409]  Harkins, D. and D. Carrel, "The Internet Key Exchange
              (IKE)", RFC 2409, November 1998.

   [RFC4490]  Leontiev, S. and G. Chudov, "Using the GOST 28147-89, GOST
              R 34.11-94, GOST R 34.10-94, and GOST R 34.10-2001
              Algorithms with Cryptographic Message Syntax (CMS)", RFC
              4490, May 2006.

   [RFC4491]  Leontiev, S. and D. Shefanovski, "Using the GOST R
              34.10-94, GOST R 34.10-2001, and GOST R 34.11-94
              Algorithms with the Internet X.509 Public Key
              Infrastructure Certificate and CRL Profile", RFC 4491, May
              2006.

   [RFC5246]  Dierks, T. and E. Rescorla, "The Transport Layer Security
              (TLS) Protocol Version 1.2", RFC 5246, August 2008.

   [RFC5996]  Kaufman, C., Hoffman, P., Nir, Y., and P. Eronen,
              "Internet Key Exchange Protocol Version 2 (IKEv2)", RFC
              5996, September 2010.

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   [RFC6986]  Dolmatov, V. and A. Degtyarev, "GOST R 34.11-2012: Hash
              Function", RFC 6986, August 2013.

   [RFC7091]  Dolmatov, V. and A. Degtyarev, "GOST R 34.10-2012: Digital
              Signature Algorithm", RFC 7091, December 2013.

Appendix A.  Test examples

   1) HMAC_GOSTR3411_2012_256

   Key K:

   00 01 02 03 04 05 06 07 08 09 0a 0b 0c 0d 0e 0f
   10 11 12 13 14 15 16 17 18 19 1a 1b 1c 1d 1e 1f

   T:

   01 26 bd b8 78 00 af 21 43 41 45 65 63 78 01 00

   HMAC_256(K, T) value:

   a1 aa 5f 7d e4 02 d7 b3 d3 23 f2 99 1c 8d 45 34
   01 31 37 01 0a 83 75 4f d0 af 6d 7c d4 92 2e d9

   2) HMAC_GOSTR3411_2012_512

   Key K:

   00 01 02 03 04 05 06 07 08 09 0a 0b 0c 0d 0e 0f
   10 11 12 13 14 15 16 17 18 19 1a 1b 1c 1d 1e 1f

   T:

   01 26 bd b8 78 00 af 21 43 41 45 65 63 78 01 00

   HMAC_256(K, T) value:

   a5 9b ab 22 ec ae 19 c6 5f bd e6 e5 f4 e9 f5 d8
   54 9d 31 f0 37 f9 df 9b 90 55 00 e1 71 92 3a 77
   3d 5f 15 30 f2 ed 7e 96 4c b2 ee dc 29 e9 ad 2f
   3a fe 93 b2 81 4f 79 f5 00 0f fc 03 66 c2 51 e6

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   3) PRF_TLS_GOSTR3411_2012_256

   Key K:

   00 01 02 03 04 05 06 07 08 09 0a 0b 0c 0d 0e 0f
   10 11 12 13 14 15 16 17 18 19 1a 1b 1c 1d 1e 1f

   Seed:

   18 47 1d 62 2d c6 55 c4 d2 d2 26 96 91 ca 4a 56
   0b 50 ab a6 63 55 3a f2 41 f1 ad a8 82 c9 f2 9a

   Label:

   11 22 33 44 55

   Output T1:

   ff 09 66 4a 44 74 58 65 94 4f 83 9e bb 48 96 5f
   15 44 ff 1c c8 e8 f1 6f 24 7e e5 f8 a9 eb e9 7f

   Output T2:

   c4 e3 c7 90 0e 46 ca d3 db 6a 01 64 30 63 04 0e
   c6 7f c0 fd 5c d9 f9 04 65 23 52 37 bd ff 2c 02

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   4) PRF_TLS_GOSTR3411_2012_512

   Key K:

   00 01 02 03 04 05 06 07 08 09 0a 0b 0c 0d 0e 0f
   10 11 12 13 14 15 16 17 18 19 1a 1b 1c 1d 1e 1f

   Seed:

   18 47 1d 62 2d c6 55 c4 d2 d2 26 96 91 ca 4a 56
   0b 50 ab a6 63 55 3a f2 41 f1 ad a8 82 c9 f2 9a

   Label:

   11 22 33 44 55

   Output T1:

   f3 51 87 a3 dc 96 55 11 3a 0e 84 d0 6f d7 52 6c
   5f c1 fb de c1 a0 e4 67 3d d6 d7 9d 0b 92 0e 65
   ad 1b c4 7b b0 83 b3 85 1c b7 cd 8e 7e 6a 91 1a
   62 6c f0 2b 29 e9 e4 a5 8e d7 66 a4 49 a7 29 6d

   Output T2:

   e6 1a 7a 26 c4 d1 ca ee cf d8 0c ca 65 c7 1f 0f
   88 c1 f8 22 c0 e8 c0 ad 94 9d 03 fe e1 39 57 9f
   72 ba 0c 3d 32 c5 f9 54 f1 cc cd 54 08 1f c7 44
   02 78 cb a1 fe 7b 7a 17 a9 86 fd ff 5b d1 5d 1f

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   5) PRF_IPSEC_KEYMAT_GOSTR3411_2012_256

   Key K:

   c9 a9 a7 73 20 e2 cc 55 9e d7 2d ce 6f 47 e2 19
   2c ce a9 5f a6 48 67 05 82 c0 54 c0 ef 36 c2 21

   Data of S:

   01 26 bd b8 78 00 1d 80 60 3c 85 44 c7 27 01 00

   Output T1:

   21 01 d8 0c 47 db 54 bc 3c 82 9b 8c 30 7c 47 55
   50 88 83 a6 d6 9e 60 1b f7 aa fb 0a bc a4 ed 95

   Output T2:

   33 b8 4e d0 8f 93 56 f8 1d f8 d2 79 f0 79 c9 02
   87 cb 45 2c 81 d4 1e 80 38 43 08 86 c1 92 12 aa

   6) PRF_IPSEC_PRFPLUS_GOSTR3411_2012_256

   Key K:

   c9 a9 a7 73 20 e2 cc 55 9e d7 2d ce 6f 47 e2 19
   2c ce a9 5f a6 48 67 05 82 c0 54 c0 ef 36 c2 21

   Data of S:

   01 26 bd b8 78 00 1d 80 60 3c 85 44 c7 27 01 00

   Output T1:

   2d e5 ee 84 e1 3d 7b e5 36 16 67 39 13 37 0a b0
   54 c0 74 b7 9b 69 a8 a8 46 82 a9 f0 4f ec d5 87

   Output T2:

   29 f6 0d da 45 7b f2 19 aa 2e f9 5d 7a 59 be 95
   4d e0 08 f4 a5 0d 50 4d bd b6 90 be 68 06 01 53

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   7) PRF_IPSEC_KEYMAT_GOSTR3411_2012_512

   Key K:

   c9 a9 a7 73 20 e2 cc 55 9e d7 2d ce 6f 47 e2 19
   2c ce a9 5f a6 48 67 05 82 c0 54 c0 ef 36 c2 21

   Data of S:

   01 26 bd b8 78 00 1d 80 60 3c 85 44 c7 27 01 00

   Output T1:

   b9 55 5b 29 91 75 4b 37 9d a6 8e 60 98 f5 b6 0e
   df 91 8a 56 20 4b ff f3 a8 37 6d 1f 57 ed b2 34
   a5 12 32 81 23 cd 6c 03 0b 54 14 2e 1e c7 78 2b
   03 00 be a5 7c c2 a1 4c a3 b4 f0 85 a4 5c d6 ca

   Output T2:

   37 b1 e0 86 52 43 a4 fb 29 14 8d 27 4d 30 63 fc
   bf b0 f2 f4 68 d5 27 e4 3b ca 41 fa 6b b5 3e c8
   df 21 bf c4 62 3a 2e 76 8b 64 54 03 3e 09 52 32
   d1 8c 86 a6 8f 00 98 d3 31 81 75 f6 59 05 ae db

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   8) PRF_IPSEC_ PRFPLUS_GOSTR3411_2012_512

   Key K:

   c9 a9 a7 73 20 e2 cc 55 9e d7 2d ce 6f 47 e2 19
   2c ce a9 5f a6 48 67 05 82 c0 54 c0 ef 36 c2 21

   Data of S:

   01 26 bd b8 78 00 1d 80 60 3c 85 44 c7 27 01 00

   Output T1:

   5d a6 71 43 a5 f1 2a 6d 6e 47 42 59 6f 39 24 3f
   cc 61 57 45 91 5b 32 59 10 06 ff 78 a2 08 63 d5
   f8 8e 4a fc 17 fb be 70 b9 50 95 73 db 00 5e 96
   26 36 98 46 cb 86 19 99 71 6c 16 5d d0 6a 15 85

   Output T2:

   48 34 49 5a 43 74 6c b5 3f 0a ba 3b c4 6e bc f8
   77 3c a6 4a d3 43 c1 22 ee 2a 57 75 57 03 81 57
   ee 9c 38 8d 96 ef 71 d5 8b e5 c1 ef a1 af a9 5e
   be 83 e3 9d 00 e1 9a 5d 03 dc d6 0a 01 bc a8 e3

   9) VKO_GOSTR3410_2012_256 with 256-bit output on the GOST R
   34.10-2012 keys (512-bit output) with id-tc26-gost-
   3410-12-512-paramSetA

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   UKM value:

   1d 80 60 3c 85 44 c7 27

   Private key x of A:

   c9 90 ec d9 72 fc e8 4e c4 db 02 27 78 f5 0f ca
   c7 26 f4 67 08 38 4b 8d 45 83 04 96 2d 71 47 f8
   c2 db 41 ce f2 2c 90 b1 02 f2 96 84 04 f9 b9 be
   6d 47 c7 96 92 d8 18 26 b3 2b 8d ac a4 3c b6 67

   Public key x*P of A (curve point (X, Y)):

   aa b0 ed a4 ab ff 21 20 8d 18 79 9f b9 a8 55 66
   54 ba 78 30 70 eb a1 0c b9 ab b2 53 ec 56 dc f5
   d3 cc ba 61 92 e4 64 e6 e5 bc b6 de a1 37 79 2f
   24 31 f6 c8 97 eb 1b 3c 0c c1 43 27 b1 ad c0 a7
   91 46 13 a3 07 4e 36 3a ed b2 04 d3 8d 35 63 97
   1b d8 75 8e 87 8c 9d b1 14 03 72 1b 48 00 2d 38
   46 1f 92 47 2d 40 ea 92 f9 95 8c 0f fa 4c 93 75
   64 01 b9 7f 89 fd be 0b 5e 46 e4 a4 63 1c db 5a

   Private key y of part B:

   48 c8 59 f7 b6 f1 15 85 88 7c c0 5e c6 ef 13 90
   cf ea 73 9b 1a 18 c0 d4 66 22 93 ef 63 b7 9e 3b
   80 14 07 0b 44 91 85 90 b4 b9 96 ac fe a4 ed fb
   bb cc cc 8c 06 ed d8 bf 5b da 92 a5 13 92 d0 db

   Public key y*P of B (curve point (X, Y)):

   19 2f e1 83 b9 71 3a 07 72 53 c7 2c 87 35 de 2e
   a4 2a 3d bc 66 ea 31 78 38 b6 5f a3 25 23 cd 5e
   fc a9 74 ed a7 c8 63 f4 95 4d 11 47 f1 f2 b2 5c
   39 5f ce 1c 12 91 75 e8 76 d1 32 e9 4e d5 a6 51
   04 88 3b 41 4c 9b 59 2e c4 dc 84 82 6f 07 d0 b6
   d9 00 6d da 17 6c e4 8c 39 1e 3f 97 d1 02 e0 3b
   b5 98 bf 13 2a 22 8a 45 f7 20 1a ba 08 fc 52 4a
   2d 77 e4 3a 36 2a b0 22 ad 40 28 f7 5b de 3b 79

   KEK_VKO value:

   c9 a9 a7 73 20 e2 cc 55 9e d7 2d ce 6f 47 e2 19
   2c ce a9 5f a6 48 67 05 82 c0 54 c0 ef 36 c2 21

   10) VKO_GOSTR3410_2012_512 with 512-bit output on the GOST R
   34.10-2012 keys (512-bit output) with id-tc26-gost-

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   3410-12-512-paramSetA

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   UKM value:

   1d 80 60 3c 85 44 c7 27

   Private key x of A:

   c9 90 ec d9 72 fc e8 4e c4 db 02 27 78 f5 0f ca
   c7 26 f4 67 08 38 4b 8d 45 83 04 96 2d 71 47 f8
   c2 db 41 ce f2 2c 90 b1 02 f2 96 84 04 f9 b9 be
   6d 47 c7 96 92 d8 18 26 b3 2b 8d ac a4 3c b6 67

   Public key x*P of A (curve point (X, Y)):

   aa b0 ed a4 ab ff 21 20 8d 18 79 9f b9 a8 55 66
   54 ba 78 30 70 eb a1 0c b9 ab b2 53 ec 56 dc f5
   d3 cc ba 61 92 e4 64 e6 e5 bc b6 de a1 37 79 2f
   24 31 f6 c8 97 eb 1b 3c 0c c1 43 27 b1 ad c0 a7
   91 46 13 a3 07 4e 36 3a ed b2 04 d3 8d 35 63 97
   1b d8 75 8e 87 8c 9d b1 14 03 72 1b 48 00 2d 38
   46 1f 92 47 2d 40 ea 92 f9 95 8c 0f fa 4c 93 75
   64 01 b9 7f 89 fd be 0b 5e 46 e4 a4 63 1c db 5a

   Private key y of part B:

   48 c8 59 f7 b6 f1 15 85 88 7c c0 5e c6 ef 13 90
   cf ea 73 9b 1a 18 c0 d4 66 22 93 ef 63 b7 9e 3b
   80 14 07 0b 44 91 85 90 b4 b9 96 ac fe a4 ed fb
   bb cc cc 8c 06 ed d8 bf 5b da 92 a5 13 92 d0 db

   Public key y*P of B (curve point (X, Y)):

   19 2f e1 83 b9 71 3a 07 72 53 c7 2c 87 35 de 2e
   a4 2a 3d bc 66 ea 31 78 38 b6 5f a3 25 23 cd 5e
   fc a9 74 ed a7 c8 63 f4 95 4d 11 47 f1 f2 b2 5c
   39 5f ce 1c 12 91 75 e8 76 d1 32 e9 4e d5 a6 51
   04 88 3b 41 4c 9b 59 2e c4 dc 84 82 6f 07 d0 b6
   d9 00 6d da 17 6c e4 8c 39 1e 3f 97 d1 02 e0 3b
   b5 98 bf 13 2a 22 8a 45 f7 20 1a ba 08 fc 52 4a
   2d 77 e4 3a 36 2a b0 22 ad 40 28 f7 5b de 3b 79

   KEK_VKO value:

   79 f0 02 a9 69 40 ce 7b de 32 59 a5 2e 01 52 97
   ad aa d8 45 97 a0 d2 05 b5 0e 3e 17 19 f9 7b fa
   7e e1 d2 66 1f a9 97 9a 5a a2 35 b5 58 a7 e6 d9
   f8 8f 98 2d d6 3f c3 5a 8e c0 dd 5e 24 2d 3b df

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   11) Key derivation function KDF_GOSTR3411_2012_256:

   K_in key:

   00 01 02 03 04 05 06 07 08 09 0a 0b 0c 0d 0e 0f
   10 11 12 13 14 15 16 17 18 19 1a 1b 1c 1d 1e 1f

   Label:

   26 bd b8 78

   Seed:

   af 21 43 41 45 65 63 78

   KDF(K_in, label, seed) value:

   a1 aa 5f 7d e4 02 d7 b3 d3 23 f2 99 1c 8d 45 34
   01 31 37 01 0a 83 75 4f d0 af 6d 7c d4 92 2e d9

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   12) Key derivation function KDF_TREE_GOSTR3411_2012_256

   Output size of L:

   512

   K_in key:

   00 01 02 03 04 05 06 07 08 09 0a 0b 0c 0d 0e 0f
   10 11 12 13 14 15 16 17 18 19 1a 1b 1c 1d 1e 1f

   Label:

   26 bd b8 78

   Seed:

   af 21 43 41 45 65 63 78

   Value of K1:

   22 b6 83 78 45 c6 be f6 5e a7 16 72 b2 65 83 10
   86 d3 c7 6a eb e6 da e9 1c ad 51 d8 3f 79 d1 6b

   Value of K2:

   07 4c 93 30 59 9d 7f 8d 71 2f ca 54 39 2f 4d dd
   e9 37 51 20 6b 35 84 c8 f4 3f 9e 6d c5 15 31 f9

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   13) Key wrap and unwrap with the szOID_Gost28147_89_TC26_Z_ParamSet
   parameters

   Key K:

   00 01 02 03 04 05 06 07 08 09 0a 0b 0c 0d 0e 0f
   10 11 12 13 14 15 16 17 18 19 1a 1b 1c 1d 1e 1f

   UKM value:

   af 21 43 41 45 65 63 78

   Label:

   26 bd b8 78

   KEK_e(UKM) = KDF(K_e, label, UKM):

   a1 aa 5f 7d e4 02 d7 b3 d3 23 f2 99 1c 8d 45 34
   01 31 37 01 0a 83 75 4f d0 af 6d 7c d4 92 2e d9

   CEK_MAC:

   38 d5 8a a3

   CEK_ENC:

   b9 fb 92 42 95 0f 84 3f 0f bd 5b 9a 5e cf 9f 17
   f7 9e 6d 21 58 16 56 de 6d c5 85 dd 62 7a 44 0a

Authors' Addresses

   Stanislav Smyshlyaev (editor)
   CRYPTO-PRO
   18, Suschevsky val
   Moscow  127018
   Russian Federation

   Phone: +7 (495) 995-48-20
   Email: svs@cryptopro.ru

Smyshlyaev, et al.      Expires December 25, 2015              [Page 28]
Internet-Draft              Abbreviated Title                  June 2015

   Vladimir Popov
   CRYPTO-PRO
   18, Suschevsky val
   Moscow  127018
   Russian Federation

   Email: vpopov@cryptopro.ru

   Evgeny Alekseev
   CRYPTO-PRO
   18, Suschevsky val
   Moscow  127018
   Russian Federation

   Email: alekseev@cryptopro.ru

   Igor Oshkin
   CRYPTO-PRO
   18, Suschevsky val
   Moscow  127018
   Russian Federation

   Email: oshkin@cryptopro.ru

Smyshlyaev, et al.      Expires December 25, 2015              [Page 29]