GOST R 34.12-2015: Block Cipher "Kuznyechik"

Independent Submission                                  V. Dolmatov, Ed.
Request for Comments: 7801                  Research Computer Center MSU
Category: Informational                                       March 2016
ISSN: 2070-1721


              GOST R 34.12-2015: Block Cipher "Kuznyechik"

Abstract

   This document is intended to be a source of information about the
   Russian Federal standard GOST R 34.12-2015 describing the block
   cipher with a block length of n=128 bits and a key length of k=256
   bits, which is also referred to as "Kuznyechik".  This algorithm is
   one of the set of Russian cryptographic standard algorithms (called
   GOST algorithms).

Status of This Memo

   This document is not an Internet Standards Track specification; it is
   published for informational purposes.

   This is a contribution to the RFC Series, independently of any other
   RFC stream.  The RFC Editor has chosen to publish this document at
   its discretion and makes no statement about its value for
   implementation or deployment.  Documents approved for publication by
   the RFC Editor are not a candidate for any level of Internet
   Standard; see Section 2 of RFC 5741.

   Information about the current status of this document, any errata,
   and how to provide feedback on it may be obtained at
   http://www.rfc-editor.org/info/rfc7801.

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Table of Contents

   1.  Scope . . . . . . . . . . . . . . . . . . . . . . . . . . . .   2
   2.  General Information . . . . . . . . . . . . . . . . . . . . .   3
   3.  Definitions and Notations . . . . . . . . . . . . . . . . . .   3
     3.1.  Definitions . . . . . . . . . . . . . . . . . . . . . . .   3
     3.2.  Notations . . . . . . . . . . . . . . . . . . . . . . . .   4
   4.  Parameter Values  . . . . . . . . . . . . . . . . . . . . . .   6
     4.1.  Nonlinear Bijection . . . . . . . . . . . . . . . . . . .   6
     4.2.  Linear Transformation . . . . . . . . . . . . . . . . . .   7
     4.3.  Transformations . . . . . . . . . . . . . . . . . . . . .   8
     4.4.  Key Schedule  . . . . . . . . . . . . . . . . . . . . . .   9
     4.5.  Basic Encryption Algorithm  . . . . . . . . . . . . . . .   9
       4.5.1.  Encryption  . . . . . . . . . . . . . . . . . . . . .   9
       4.5.2.  Decryption  . . . . . . . . . . . . . . . . . . . . .   9
   5.  Examples (Informative)  . . . . . . . . . . . . . . . . . . .  10
     5.1.  Transformation S  . . . . . . . . . . . . . . . . . . . .  10
     5.2.  Transformation R  . . . . . . . . . . . . . . . . . . . .  10
     5.3.  Transformation L  . . . . . . . . . . . . . . . . . . . .  10
     5.4.  Key Schedule  . . . . . . . . . . . . . . . . . . . . . .  11
     5.5.  Test Encryption . . . . . . . . . . . . . . . . . . . . .  12
     5.6.  Test Decryption . . . . . . . . . . . . . . . . . . . . .  13
   6.  Security Considerations . . . . . . . . . . . . . . . . . . .  13
   7.  References  . . . . . . . . . . . . . . . . . . . . . . . . .  14
     7.1.  Normative References  . . . . . . . . . . . . . . . . . .  14
     7.2.  Informative References  . . . . . . . . . . . . . . . . .  14
   Author's Address  . . . . . . . . . . . . . . . . . . . . . . . .  14

1.  Scope

   The Russian Federal standard [GOST3412-2015] specifies basic block
   ciphers used as cryptographic techniques for information processing
   and information protection including the provision of
   confidentiality, authenticity, and integrity of information during
   information transmission, processing, and storage in computer-aided
   systems.

   The cryptographic algorithms specified in this standard are designed
   both for hardware and software implementation.  They comply with
   modern cryptographic requirements and put no restrictions on the
   confidentiality level of the protected information.

   The standard applies to development, operation, and modernization of
   the information systems of various purposes.

2.  General Information

   The block cipher "Kuznyechik" [GOST3412-2015] was developed by the
   Center for Information Protection and Special Communications of the
   Federal Security Service of the Russian Federation with participation
   of the Open Joint-Stock company "Information Technologies and
   Communication Systems" (InfoTeCS JSC).  GOST R 34.12-2015 was
   approved and introduced by Decree #749 of the Federal Agency on
   Technical Regulating and Metrology on June 19, 2015.

   Terms and concepts in the standard comply with the following
   international standards:

   o  ISO/IEC 10116 [ISO-IEC10116] and

   o  series of standards ISO/IEC 18033 [ISO-IEC18033-1]
      [ISO-IEC18033-3].

3.  Definitions and Notations

   The following terms and their corresponding definitions are used in
   the standard.

3.1.  Definitions

   Definitions

      encryption algorithm: process that transforms plaintext into
      ciphertext (Section 2.19 of [ISO-IEC18033-1]),

      decryption algorithm: process that transforms ciphertext into
      plaintext (Section 2.14 of [ISO-IEC18033-1]),

      basic block cipher: block cipher that for a given key provides a
      single invertible mapping of the set of fixed-length plaintext
      blocks into ciphertext blocks of the same length,

      block: string of bits of a defined length (Section 2.6 of
      [ISO-IEC18033-1]),

      block cipher: symmetric encipherment system with the property that
      the encryption algorithm operates on a block of plaintext, i.e., a
      string of bits of a defined length, to yield a block of ciphertext
      (Section 2.7 of [ISO-IEC18033-1]),

         Note: In GOST R 34.12-2015, it is established that the terms
         "block cipher" and "block encryption algorithm" are synonyms.

      encryption: reversible transformation of data by a cryptographic
      algorithm to produce ciphertext, i.e., to hide the information
      content of the data (Section 2.18 of [ISO-IEC18033-1]),

      round key: sequence of symbols that is calculated from the key and
      controls a transformation for one round of a block cipher,

      key: sequence of symbols that controls the operation of a
      cryptographic transformation (e.g., encipherment and decipherment)
      (Section 2.21 of [ISO-IEC18033-1]),

         Note: In GOST R 34.12-2015, the key must be a binary sequence.

      plaintext: unencrypted information (Section 3.11 of
      [ISO-IEC10116]),

      key schedule: calculation of round keys from the key,

      decryption: reversal of a corresponding encipherment (Section 2.13
      of [ISO-IEC18033-1]),

      symmetric cryptographic technique: cryptographic technique that
      uses the same secret key for both the originator's and the
      recipient's transformation (Section 2.32 of [ISO-IEC18033-1]),

      cipher: alternative term for encipherment system (Section 2.20 of
      [ISO-IEC18033-1]), and

      ciphertext: data that has been transformed to hide its information
      content (Section 3.3 of [ISO-IEC10116]).

3.2.  Notations

   The following notations are used in the standard:

   V*      the set of all binary vector strings of a finite length
           (hereinafter referred to as the strings) including the empty
           string,

   V_s     the set of all binary strings of length s, where s is a non-
           negative integer; substrings and string components are
           enumerated from right to left starting from zero,

   U[*]W   direct (Cartesian) product of two sets, U and W,

   |A|     the number of components (the length) of a string A belonging
           to V* (if A is an empty string, then |A| = 0),

   A||B    concatenation of strings A and B both belonging to V*, i.e.,
           a string from V_(|A|+|B|), where the left substring from
           V_|A| is equal to A, and the right substring from V_|B| is
           equal to B,

   Z_(2^n) ring of residues modulo 2^n,

   Q       finite field GF(2)[x]/p(x), where p(x)=x^8+x^7+x^6+x+1
           belongs to GF(2)[x]; elements of field Q are represented by
           integers in such way that element
           z_0+z_1*theta+...+z_7*theta^7 belonging to Q corresponds to
           integer z_0+2*z_1+...+2^7*z_7, where z_i=0 or z_i=1,
           i=0,1,...,7 and theta denotes a residue class modulo p(x)
           containing x,

   (xor)   exclusive-or of the two binary strings of the same length,

   Vec_s: Z_(2^s) -> V_s  bijective mapping that maps an element from
           ring Z_(2^s) into its binary representation, i.e., for an
           element z of the ring Z_(2^s), represented by the residue z_0
           + (2*z_1) + ... + (2^(s-1)*z_(s-1)), where z_i in {0, 1}, i =
           0, ..., n-1, the equality Vec_s(z) = z_(s-1)||...||z_1||z_0
           holds,

   Int_s: V_s -> Z_(2^s)  the mapping inverse to the mapping Vec_s,
           i.e., Int_s = Vec_s^(-1),

   delta: V_8 -> Q  bijective mapping that maps a binary string from V_8
           into an element from field Q as follows: string
           z_7||...||z_1||z_0, where z_i in {0, 1}, i = 0, ..., 7,
           corresponds to the element z_0+(z_1*theta)+...+(z_7*theta^7)
           belonging to Z,

   nabla: Q -> V8  the mapping inverse to the mapping delta, i.e., delta
           = nabla^(-1),

   PS      composition of mappings, where the mapping S applies first,
           and

   P^s     composition of mappings P^(s-1) and P, where P^1=P.

4.  Parameter Values

4.1.  Nonlinear Bijection

   The bijective nonlinear mapping is a substitution: Pi =
   (Vec_8)Pi'(Int_8): V_8 -> V_8, where Pi': Z_(2^8) -> Z_(2^8).  The
   values of the substitution Pi' are specified below as an array Pi' =
   (Pi'(0), Pi'(1), ... , Pi'(255)):

    Pi' =
   (       252, 238, 221,  17, 207, 110,  49,  22, 251, 196, 250,
           218,  35, 197,   4,  77, 233, 119, 240, 219, 147,  46,
           153, 186,  23,  54, 241, 187,  20, 205,  95, 193, 249,
            24, 101,  90, 226,  92, 239,  33, 129,  28,  60,  66,
           139,   1, 142,  79,   5, 132,   2, 174, 227, 106, 143,
           160,   6,  11, 237, 152, 127, 212, 211,  31, 235,  52,
            44,  81, 234, 200,  72, 171, 242,  42, 104, 162, 253,
            58, 206, 204, 181, 112,  14,  86,   8,  12, 118,  18,
           191, 114,  19,  71, 156, 183,  93, 135,  21, 161, 150,
            41,  16, 123, 154, 199, 243, 145, 120, 111, 157, 158,
           178, 177,  50, 117,  25,  61, 255,  53, 138, 126, 109,
            84, 198, 128, 195, 189,  13,  87, 223, 245,  36, 169,
            62, 168,  67, 201, 215, 121, 214, 246, 124,  34, 185,
             3, 224,  15, 236, 222, 122, 148, 176, 188, 220, 232,
            40,  80,  78,  51,  10,  74, 167, 151,  96, 115,  30,
             0,  98,  68,  26, 184,  56, 130, 100, 159,  38,  65,
           173,  69,  70, 146,  39,  94,  85,  47, 140, 163, 165,
           125, 105, 213, 149,  59,   7,  88, 179,  64, 134, 172,
            29, 247,  48,  55, 107, 228, 136, 217, 231, 137, 225,
            27, 131,  73,  76,  63, 248, 254, 141,  83, 170, 144,
           202, 216, 133,  97,  32, 113, 103, 164,  45,  43,   9,
            91, 203, 155,  37, 208, 190, 229, 108,  82,  89, 166,
           116, 210, 230, 244, 180, 192, 209, 102, 175, 194,  57,
            75,  99, 182).

   Pi^(-1) is the inverse of Pi; the values of the substitution Pi^(-1)'
   are specified below as an array Pi^(-1)' = (Pi^(-1)'(0), Pi^(-1)'(1),
   ... , Pi^(-1)'(255)):

    Pi^(-1)' =
   (    165,  45,  50, 143,  14,  48,  56, 192,  84, 230, 158,
         57,  85, 126,  82, 145, 100,   3,  87,  90,  28,  96,
          7,  24,  33, 114, 168, 209,  41, 198, 164,  63, 224,
         39, 141,  12, 130, 234, 174, 180, 154,  99,  73, 229,
         66, 228,  21, 183, 200,   6, 112, 157,  65, 117,  25,
        201, 170, 252,  77, 191,  42, 115, 132, 213, 195, 175,
         43, 134, 167, 177, 178,  91,  70, 211, 159, 253, 212,
         15, 156,  47, 155,  67, 239, 217, 121, 182,  83, 127,
        193, 240,  35, 231,  37,  94, 181,  30, 162, 223, 166,
        254, 172,  34, 249, 226,  74, 188,  53, 202, 238, 120,
          5, 107,  81, 225,  89, 163, 242, 113,  86,  17, 106,
        137, 148, 101, 140, 187, 119,  60, 123,  40, 171, 210,
         49, 222, 196,  95, 204, 207, 118,  44, 184, 216,  46,
         54, 219, 105, 179,  20, 149, 190,  98, 161,  59,  22,
        102, 233,  92, 108, 109, 173,  55,  97,  75, 185, 227,
        186, 241, 160, 133, 131, 218,  71, 197, 176,  51, 250,
        150, 111, 110, 194, 246,  80, 255,  93, 169, 142,  23,
         27, 151, 125, 236,  88, 247,  31, 251, 124,   9,  13,
        122, 103,  69, 135, 220, 232,  79,  29,  78,   4, 235,
        248, 243,  62,  61, 189, 138, 136, 221, 205,  11,  19,
        152,   2, 147, 128, 144, 208,  36,  52, 203, 237, 244,
        206, 153,  16,  68,  64, 146,  58,   1,  38,  18,  26,
         72, 104, 245, 129, 139, 199, 214,  32,  10,   8,   0,
         76, 215, 116 ).

4.2.  Linear Transformation

   The linear transformation is denoted by l: (V_8)^16 -> V_8, and
   defined as:

   l(a_15,...,a_0) = nabla(148*delta(a_15) + 32*delta(a_15) +
   133*delta(a_13) + 16*delta(a_12) + 194*delta(a_11) +
   192*delta(a_10) + 1*delta(a_9) + 251*delta(a_8) + 1*delta(a_7) +
   192*delta(a_6) + 194*delta(a_5) + 16*delta(a_4) + 133*delta(a_3) +
   32*delta(a_2) + 148*delta(a_1) +1*delta(a_0)),

   for all a_i belonging to V_8, i = 0, 1, ..., 15, where the addition
   and multiplication operations are in the field Q, and constants are
   elements of the field as defined above.

4.3.  Transformations

   The following transformations are applicable for encryption and
   decryption algorithms:

   X[x]:V_128->V_128  X[k](a)=k(xor)a, where k, a belong to V_128,

   S:V_128-> V_128  S(a)=(a_15||...||a_0)=pi(a_15)||...||pi(a_0), where
      a_15||...||a_0 belongs to V_128, a_i belongs to V_8, i=0,1,...,15,

   S^(-1):V_128-> V_128  the inverse transformation of S, which may be
      calculated, for example, as follows:
      S^(-1)(a_15||...||a_0)=pi^(-1) (a_15)||...||pi^(-1)(a_0), where
      a_15||...||a_0 belongs to V_128, a_i belongs to V_8, i=0,1,...,15,

   R:V_128-> V_128  R(a_15||...||a_0)=l(a_15,...,a_0)||a_15||...||a_1,
      where a_15||...||a_0 belongs to V_128, a_i belongs to V_8,
      i=0,1,...,15,

   L:V_128-> V_128  L(a)=R^(16)(a), where a belongs to V_128,

   R^(-1):V_128-> V_128  the inverse transformation of R, which may be
      calculated, for example, as follows: R^(-1)(a_15||...||a_0)=a_14||
      a_13||...||a_0||l(a_14,a_13,...,a_0,a_15), where a_15||...||a_0
      belongs to V_128, a_i belongs to V_8, i=0,1,...,15,

   L^(-1):V_128-> V_128  L^(-1)(a)=(R^(-1))(16)(a), where a belongs to
      V_128, and

   F[k]:V_128[*]V_128 -> V_128[*]V_128
      F[k](a_1,a_0)=(LSX[k](a_1)(xor)a_0,a_1), where k, a_0, a_1 belong
      to V_128.

4.4.  Key Schedule

   Key schedule uses round constants C_i belonging to V_128, i=1, 2,
   ..., 32, defined as

   C_i=L(Vec_128(i)), i=1,2,...,32.

   Round keys K_i, i=1, 2, ..., 10 are derived from key
   K=k_255||...||k_0 belonging to V_256, k_i belongs to V_1, i=0, 1,
   ..., 255, as follows:

   K_1=k_255||...||k_128;
   K_2=k_127||...||k_0;
   (K_(2i+1),K_(2i+2))=F[C_(8(i-1)+8)]...
    F[C_(8(i-1)+1)](K_(2i-1),K_(2i)), i=1,2,3,4.

4.5.  Basic Encryption Algorithm

4.5.1.  Encryption

   Depending on the values of round keys K_1,...,K_10, the encryption
   algorithm is a substitution E_(K_1,...,K_10) defined as follows:

   E_(K_1,...,K_10)(a)=X[K_10]LSX[K_9]...LSX[K_2]LSX[K_1](a),

   where a belongs to V_128.

4.5.2.  Decryption

   Depending on the values of round keys K_1,...,K_10, the decryption
   algorithm is a substitution D_(K_1,...,K_10) defined as follows:

   D_(K_1,...,K_10)(a)=X[K_1]L^(-1)S^(-1)X[K_2]...
    L^(-1)S^(-1)X[K_9] L^(-1)S^(-1)X[K_10](a),

   where a belongs to V_128.

5.  Examples (Informative)

   This section is for information only and is not a normative part of
   the standard.

5.1.  Transformation S

   S(ffeeddccbbaa99881122334455667700) =
    b66cd8887d38e8d77765aeea0c9a7efc,
   S(b66cd8887d38e8d77765aeea0c9a7efc) =
    559d8dd7bd06cbfe7e7b262523280d39,
   S(559d8dd7bd06cbfe7e7b262523280d39) =
    0c3322fed531e4630d80ef5c5a81c50b,
   S(0c3322fed531e4630d80ef5c5a81c50b) =
    23ae65633f842d29c5df529c13f5acda.

5.2.  Transformation R

   R(00000000000000000000000000000100) =
    94000000000000000000000000000001,
   R(94000000000000000000000000000001) =
    a5940000000000000000000000000000,
   R(a5940000000000000000000000000000) =
    64a59400000000000000000000000000,
   R(64a59400000000000000000000000000) =
    0d64a594000000000000000000000000.

5.3.  Transformation L

   L(64a59400000000000000000000000000) =
    d456584dd0e3e84cc3166e4b7fa2890d,
   L(d456584dd0e3e84cc3166e4b7fa2890d) =
    79d26221b87b584cd42fbc4ffea5de9a,
   L(79d26221b87b584cd42fbc4ffea5de9a) =
    0e93691a0cfc60408b7b68f66b513c13,
   L(0e93691a0cfc60408b7b68f66b513c13) =
    e6a8094fee0aa204fd97bcb0b44b8580.

5.4.  Key Schedule

   In this test example, the key is equal to:

   K = 8899aabbccddeeff0011223344556677fedcba9876543210012345678
        9abcdef.

   K_1 = 8899aabbccddeeff0011223344556677,
   K_2 = fedcba98765432100123456789abcdef.

   C_1 = 6ea276726c487ab85d27bd10dd849401,
   X[C_1](K_1) = e63bdcc9a09594475d369f2399d1f276,
   SX[C_1](K_1) = 0998ca37a7947aabb78f4a5ae81b748a,
   LSX[C_1](K_1) = 3d0940999db75d6a9257071d5e6144a6,
   F[C_1](K_1, K_2) = = (c3d5fa01ebe36f7a9374427ad7ca8949,
          8899aabbccddeeff0011223344556677).

   C_2 = dc87ece4d890f4b3ba4eb92079cbeb02,
   F [C_2]F [C_1](K_1, K_2) = (37777748e56453377d5e262d90903f87,
          c3d5fa01ebe36f7a9374427ad7ca8949).

   C_3 = b2259a96b4d88e0be7690430a44f7f03,
   F[C_3]...F[C_1](K_1, K_2) = (f9eae5f29b2815e31f11ac5d9c29fb01,
          37777748e56453377d5e262d90903f87).

   C_4 = 7bcd1b0b73e32ba5b79cb140f2551504,
   F[C_4]...F[C_1](K_1, K_2) = (e980089683d00d4be37dd3434699b98f,
          f9eae5f29b2815e31f11ac5d9c29fb01).

   C_5 = 156f6d791fab511deabb0c502fd18105,
   F[C_5]...F[C_1](K_1, K_2) = (b7bd70acea4460714f4ebe13835cf004,
          e980089683d00d4be37dd3434699b98f).

   C_6 = a74af7efab73df160dd208608b9efe06,
   F[C_6]...F[C_1](K_1, K_2) = (1a46ea1cf6ccd236467287df93fdf974,
          b7bd70acea4460714f4ebe13835cf004).

   C_7 = c9e8819dc73ba5ae50f5b570561a6a07,
   F[C_7]...F [C_1](K_1, K_2) = (3d4553d8e9cfec6815ebadc40a9ffd04,
          1a46ea1cf6ccd236467287df93fdf974).

   C_8 = f6593616e6055689adfba18027aa2a08,
   (K_3, K_4) = F [C_8]...F [C_1](K_1, K_2) =
          (db31485315694343228d6aef8cc78c44,
           3d4553d8e9cfec6815ebadc40a9ffd04).

   The round keys K_i, i = 1, 2, ..., 10, take the following values:

   K_1 = 8899aabbccddeeff0011223344556677,
   K_2 = fedcba98765432100123456789abcdef,
   K_3 = db31485315694343228d6aef8cc78c44,
   K_4 = 3d4553d8e9cfec6815ebadc40a9ffd04,
   K_5 = 57646468c44a5e28d3e59246f429f1ac,
   K_6 = bd079435165c6432b532e82834da581b,
   K_7 = 51e640757e8745de705727265a0098b1,
   K_8 = 5a7925017b9fdd3ed72a91a22286f984,
   K_9 = bb44e25378c73123a5f32f73cdb6e517,
   K_10 = 72e9dd7416bcf45b755dbaa88e4a4043.

5.5.  Test Encryption

   In this test example, encryption is performed on the round keys
   specified in Section 5.4.  Let the plaintext be

   a = 1122334455667700ffeeddccbbaa9988,

   then

   X[K_1](a) = 99bb99ff99bb99ffffffffffffffffff,
   SX[K_1](a) = e87de8b6e87de8b6b6b6b6b6b6b6b6b6,
   LSX[K_1](a) = e297b686e355b0a1cf4a2f9249140830,
   LSX[K_2]LSX[K_1](a) = 285e497a0862d596b36f4258a1c69072,
   LSX[K_3]...LSX[K_1](a) = 0187a3a429b567841ad50d29207cc34e,
   LSX[K_4]...LSX[K_1](a) = ec9bdba057d4f4d77c5d70619dcad206,
   LSX[K_5]...LSX[K_1](a) = 1357fd11de9257290c2a1473eb6bcde1,
   LSX[K_6]...LSX[K_1](a) = 28ae31e7d4c2354261027ef0b32897df,
   LSX[K_7]...LSX[K_1](a) = 07e223d56002c013d3f5e6f714b86d2d,
   LSX[K_8]...LSX[K_1](a) = cd8ef6cd97e0e092a8e4cca61b38bf65,
   LSX[K_9]...LSX[K_1](a) = 0d8e40e4a800d06b2f1b37ea379ead8e.

   Then the ciphertext is

   b = X[K_10]LSX[K_9]...LSX[K_1](a) = 7f679d90bebc24305a468d42b9d4edcd.

5.6.  Test Decryption

   In this test example, decryption is performed on the round keys
   specified in Section 5.4.  Let the ciphertext be

   b = 7f679d90bebc24305a468d42b9d4edcd,

   then

   X[K_10](b) = 0d8e40e4a800d06b2f1b37ea379ead8e,
   L^(-1)X[K_10](b) = 8a6b930a52211b45c5baa43ff8b91319,
   S^(-1)L^(-1)X[K_10](b) = 76ca149eef27d1b10d17e3d5d68e5a72,
   S^(-1)L^(-1)X[K_9]S^(-1)L^(-1)X[K_10](b) =
    5d9b06d41b9d1d2d04df7755363e94a9,
   S^(-1)L^(-1)X[K_8]...S^(-1)L^(-1)X[K_10](b) =
    79487192aa45709c115559d6e9280f6e,
   S^(-1)L^(-1)X[K_7]...S^(-1)L^(-1)X[K_10](b) =
    ae506924c8ce331bb918fc5bdfb195fa,
   S^(-1)L^(-1)X[K_6]...S^(-1)L^(-1)X[K_10](b) =
    bbffbfc8939eaaffafb8e22769e323aa,
   S^(-1)L^(-1)X[K_5]...S^(-1)L^(-1)X[K_10](b) =
    3cc2f07cc07a8bec0f3ea0ed2ae33e4a,
   S^(-1)L^(-1)X[K_4]...S^(-1)L^(-1)X[K_10](b) =
    f36f01291d0b96d591e228b72d011c36,
   S^(-1)L^(-1)X[K_3]...S^(-1)L^(-1)X[K_10](b) =
    1c4b0c1e950182b1ce696af5c0bfc5df,
   S^(-1)L^(-1)X[K_2]...S^(-1)L^(-1)X[K_10](b) =
    99bb99ff99bb99ffffffffffffffffff.

   Then the plaintext is

   a = X[K_1]S^(-1)L^(-1)X[K_2]...S^(-1)L^(-1)X[K_10](b) =
    1122334455667700ffeeddccbbaa9988.

6.  Security Considerations

   This entire document is about security considerations.

7.  References

7.1.  Normative References

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

7.2.  Informative References

   [ISO-IEC10116]
              ISO/IEC, "Information technology -- Security techniques --
              Modes of operation for an n-bit block cipher", ISO/
              IEC 10116, 2006.

   [ISO-IEC18033-1]
              ISO/IEC, "Information technology -- Security techniques --
              Encryption algorithms -- Part 1: General", ISO/
              IEC 18033-1, 2015.

   [ISO-IEC18033-3]
              ISO/IEC, "Information technology -- Security techniques --
              Encryption algorithms -- Part 3: Block ciphers", ISO/
              IEC 18033-3, 2010.

Author's Address

   Vasily Dolmatov (editor)
   Research Computer Center MSU
   Leninskiye Gory, 1, Building 4, MGU NIVC
   Moscow  119991
   Russian Federation

   Email: dol@srcc.msu.ru