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INFORMATIONAL
Errata Exist
Independent Submission                                  V. Dolmatov, Ed.Request for Comments: 7801                  Research Computer Center MSUCategory: Informational                                       March 2016ISSN: 2070-1721GOST 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; seeSection 2 of RFC 5741.   Information about the current status of this document, any errata,   and how to provide feedback on it may be obtained athttp://www.rfc-editor.org/info/rfc7801.Copyright Notice   Copyright (c) 2016 IETF Trust and the persons identified as the   document authors.  All rights reserved.   This document is subject toBCP 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.Dolmatov                      Informational                     [Page 1]

RFC 7801                    GOST R 34.12-2015                 March 2016Table of Contents1.  Scope . . . . . . . . . . . . . . . . . . . . . . . . . . . .22.  General Information . . . . . . . . . . . . . . . . . . . . .33.  Definitions and Notations . . . . . . . . . . . . . . . . . .33.1.  Definitions . . . . . . . . . . . . . . . . . . . . . . .33.2.  Notations . . . . . . . . . . . . . . . . . . . . . . . .44.  Parameter Values  . . . . . . . . . . . . . . . . . . . . . .64.1.  Nonlinear Bijection . . . . . . . . . . . . . . . . . . .64.2.  Linear Transformation . . . . . . . . . . . . . . . . . .74.3.  Transformations . . . . . . . . . . . . . . . . . . . . .84.4.  Key Schedule  . . . . . . . . . . . . . . . . . . . . . .94.5.  Basic Encryption Algorithm  . . . . . . . . . . . . . . .94.5.1.  Encryption  . . . . . . . . . . . . . . . . . . . . .94.5.2.  Decryption  . . . . . . . . . . . . . . . . . . . . .95.  Examples (Informative)  . . . . . . . . . . . . . . . . . . .105.1.  Transformation S  . . . . . . . . . . . . . . . . . . . .105.2.  Transformation R  . . . . . . . . . . . . . . . . . . . .105.3.  Transformation L  . . . . . . . . . . . . . . . . . . . .105.4.  Key Schedule  . . . . . . . . . . . . . . . . . . . . . .115.5.  Test Encryption . . . . . . . . . . . . . . . . . . . . .125.6.  Test Decryption . . . . . . . . . . . . . . . . . . . . .136.  Security Considerations . . . . . . . . . . . . . . . . . . .137.  References  . . . . . . . . . . . . . . . . . . . . . . . . .147.1.  Normative References  . . . . . . . . . . . . . . . . . .147.2.  Informative References  . . . . . . . . . . . . . . . . .14   Author's Address  . . . . . . . . . . . . . . . . . . . . . . . .141.  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.Dolmatov                      Informational                     [Page 2]

RFC 7801                    GOST R 34.12-2015                 March 20162.  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.Dolmatov                      Informational                     [Page 3]

RFC 7801                    GOST R 34.12-2015                 March 2016      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),Dolmatov                      Informational                     [Page 4]

RFC 7801                    GOST R 34.12-2015                 March 2016   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.Dolmatov                      Informational                     [Page 5]

RFC 7801                    GOST R 34.12-2015                 March 20164.  Parameter Values4.1.  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).Dolmatov                      Informational                     [Page 6]

RFC 7801                    GOST R 34.12-2015                 March 2016   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.Dolmatov                      Informational                     [Page 7]

RFC 7801                    GOST R 34.12-2015                 March 20164.3.  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.Dolmatov                      Informational                     [Page 8]

RFC 7801                    GOST R 34.12-2015                 March 20164.4.  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 Algorithm4.5.1.  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.Dolmatov                      Informational                     [Page 9]

RFC 7801                    GOST R 34.12-2015                 March 20165.  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.Dolmatov                      Informational                    [Page 10]

RFC 7801                    GOST R 34.12-2015                 March 20165.4.  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).Dolmatov                      Informational                    [Page 11]

RFC 7801                    GOST R 34.12-2015                 March 2016   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 inSection 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.Dolmatov                      Informational                    [Page 12]

RFC 7801                    GOST R 34.12-2015                 March 20165.6.  Test Decryption   In this test example, decryption is performed on the round keys   specified inSection 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.Dolmatov                      Informational                    [Page 13]

RFC 7801                    GOST R 34.12-2015                 March 20167.  References7.1.  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.ruDolmatov                      Informational                    [Page 14]

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