Difference between revisions of "RFC8891"

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(Created page with " Independent Submission V. Dolmatov, Ed. Request for Comments: 8891 JSC "NPK Kryptonite" Updates: 5830...")
 
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Independent Submission                                  V. Dolmatov, Ed.
 
Independent Submission                                  V. Dolmatov, Ed.
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ISSN: 2070-1721                                          September 2020
 
ISSN: 2070-1721                                          September 2020
  
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+
            GOST R 34.12-2015: Block Cipher "Magma"
−
                GOST R 34.12-2015: Block Cipher "Magma"
 
  
 
Abstract
 
Abstract
  
−
  In addition to a new cipher with a block length of n=128 bits
+
In addition to a new cipher with a block length of n=128 bits
−
  (referred to as "Kuznyechik" and described in RFC 7801), Russian
+
(referred to as "Kuznyechik" and described in RFC 7801), Russian
−
  Federal standard GOST R 34.12-2015 includes an updated version of the
+
Federal standard GOST R 34.12-2015 includes an updated version of the
−
  block cipher with a block length of n=64 bits and key length of k=256
+
block cipher with a block length of n=64 bits and key length of k=256
−
  bits, which is also referred to as "Magma".  The algorithm is an
+
bits, which is also referred to as "Magma".  The algorithm is an
−
  updated version of an older block cipher with a block length of n=64
+
updated version of an older block cipher with a block length of n=64
−
  bits described in GOST 28147-89 (RFC 5830).  This document is
+
bits described in GOST 28147-89 (RFC 5830).  This document is
−
  intended to be a source of information about the updated version of
+
intended to be a source of information about the updated version of
−
  the 64-bit cipher.  It may facilitate the use of the block cipher in
+
the 64-bit cipher.  It may facilitate the use of the block cipher in
−
  Internet applications by providing information for developers and
+
Internet applications by providing information for developers and
−
  users of the GOST 64-bit cipher with the revised version of the
+
users of the GOST 64-bit cipher with the revised version of the
−
  cipher for encryption and decryption.
+
cipher for encryption and decryption.
  
 
Status of This Memo
 
Status of This Memo
  
−
  This document is not an Internet Standards Track specification; it is
+
This document is not an Internet Standards Track specification; it is
−
  published for informational purposes.
+
published for informational purposes.
  
−
  This is a contribution to the RFC Series, independently of any other
+
This is a contribution to the RFC Series, independently of any other
−
  RFC stream.  The RFC Editor has chosen to publish this document at
+
RFC stream.  The RFC Editor has chosen to publish this document at
−
  its discretion and makes no statement about its value for
+
its discretion and makes no statement about its value for
−
  implementation or deployment.  Documents approved for publication by
+
implementation or deployment.  Documents approved for publication by
−
  the RFC Editor are not candidates for any level of Internet Standard;
+
the RFC Editor are not candidates for any level of Internet Standard;
−
  see Section 2 of RFC 7841.
+
see Section 2 of RFC 7841.
  
−
  Information about the current status of this document, any errata,
+
Information about the current status of this document, any errata,
−
  and how to provide feedback on it may be obtained at
+
and how to provide feedback on it may be obtained at
−
  https://www.rfc-editor.org/info/rfc8891.
+
https://www.rfc-editor.org/info/rfc8891.
  
 
Copyright Notice
 
Copyright Notice
  
−
  Copyright (c) 2020 IETF Trust and the persons identified as the
+
Copyright (c) 2020 IETF Trust and the persons identified as the
−
  document authors.  All rights reserved.
+
document authors.  All rights reserved.
  
−
  This document is subject to BCP 78 and the IETF Trust's Legal
+
This document is subject to BCP 78 and the IETF Trust's Legal
−
  Provisions Relating to IETF Documents
+
Provisions Relating to IETF Documents
−
  (https://trustee.ietf.org/license-info) in effect on the date of
+
(https://trustee.ietf.org/license-info) in effect on the date of
−
  publication of this document.  Please review these documents
+
publication of this document.  Please review these documents
−
  carefully, as they describe your rights and restrictions with respect
+
carefully, as they describe your rights and restrictions with respect
−
  to this document.
+
to this document.
  
 
Table of Contents
 
Table of Contents
  
−
  1.  Introduction
+
1.  Introduction
−
  2.  General Information
+
2.  General Information
−
  3.  Definitions and Notation
+
3.  Definitions and Notation
−
    3.1.  Definitions
+
  3.1.  Definitions
−
    3.2.  Notation
+
  3.2.  Notation
−
  4.  Parameter Values
+
4.  Parameter Values
−
    4.1.  Nonlinear Bijection
+
  4.1.  Nonlinear Bijection
−
    4.2.  Transformations
+
  4.2.  Transformations
−
    4.3.  Key Schedule
+
  4.3.  Key Schedule
−
  5.  Basic Encryption Algorithm
+
5.  Basic Encryption Algorithm
−
    5.1.  Encryption
+
  5.1.  Encryption
−
    5.2.  Decryption
+
  5.2.  Decryption
−
  6.  IANA Considerations
+
6.  IANA Considerations
−
  7.  Security Considerations
+
7.  Security Considerations
−
  8.  References
+
8.  References
−
    8.1.  Normative References
+
  8.1.  Normative References
−
    8.2.  Informative References
+
  8.2.  Informative References
−
  Appendix A.  Test Examples
+
Appendix A.  Test Examples
−
    A.1.  Transformation t
+
  A.1.  Transformation t
−
    A.2.  Transformation g
+
  A.2.  Transformation g
−
    A.3.  Key Schedule
+
  A.3.  Key Schedule
−
    A.4.  Test Encryption
+
  A.4.  Test Encryption
−
    A.5.  Test Decryption
+
  A.5.  Test Decryption
−
  Appendix B.  Background
+
Appendix B.  Background
−
  Authors' Addresses
+
Authors' Addresses
  
−
1.  Introduction
+
== Introduction ==
  
−
  The Russian Federal standard [GOSTR3412-2015] specifies basic block
+
The Russian Federal standard [GOSTR3412-2015] specifies basic block
−
  ciphers used as cryptographic techniques for information processing
+
ciphers used as cryptographic techniques for information processing
−
  and information protection, including the provision of
+
and information protection, including the provision of
−
  confidentiality, authenticity, and integrity of information during
+
confidentiality, authenticity, and integrity of information during
−
  information transmission, processing, and storage in computer-aided
+
information transmission, processing, and storage in computer-aided
−
  systems.
+
systems.
  
−
  The cryptographic algorithms defined in this specification are
+
The cryptographic algorithms defined in this specification are
−
  designed both for hardware and software implementation.  They comply
+
designed both for hardware and software implementation.  They comply
−
  with modern cryptographic requirements and put no restrictions on the
+
with modern cryptographic requirements and put no restrictions on the
−
  confidentiality level of the protected information.
+
confidentiality level of the protected information.
  
−
  This document is intended to be a source of information about the
+
This document is intended to be a source of information about the
−
  updated version of the 64-bit cipher.  It may facilitate the use of
+
updated version of the 64-bit cipher.  It may facilitate the use of
−
  the block cipher in Internet applications by providing information
+
the block cipher in Internet applications by providing information
−
  for developers and users of a GOST 64-bit cipher with the revised
+
for developers and users of a GOST 64-bit cipher with the revised
−
  version of the cipher for encryption and decryption.
+
version of the cipher for encryption and decryption.
  
−
2.  General Information
+
== General Information ==
  
−
  The Russian Federal standard [GOSTR3412-2015] was developed by the
+
The Russian Federal standard [GOSTR3412-2015] was developed by the
−
  Center for Information Protection and Special Communications of the
+
Center for Information Protection and Special Communications of the
−
  Federal Security Service of the Russian Federation, with
+
Federal Security Service of the Russian Federation, with
−
  participation of the open joint-stock company "Information
+
participation of the open joint-stock company "Information
−
  Technologies and Communication Systems" (InfoTeCS JSC).  GOST R
+
Technologies and Communication Systems" (InfoTeCS JSC).  GOST R
−
  34.12-2015 was approved and introduced by Decree #749 of the Federal
+
34.12-2015 was approved and introduced by Decree #749 of the Federal
−
  Agency on Technical Regulating and Metrology on June 19, 2015.
+
Agency on Technical Regulating and Metrology on June 19, 2015.
  
−
  Terms and concepts in the specification comply with the following
+
Terms and concepts in the specification comply with the following
−
  international standards:
+
international standards:
  
−
  *  ISO/IEC 10116 [ISO-IEC10116]
+
*  ISO/IEC 10116 [ISO-IEC10116]
  
−
  *  series of standards ISO/IEC 18033 [ISO-IEC18033-1][ISO-IEC18033-3]
+
*  series of standards ISO/IEC 18033 [ISO-IEC18033-1][ISO-IEC18033-3]
  
−
3.  Definitions and Notation
+
== Definitions and Notation ==
  
−
  The following terms and their corresponding definitions are used in
+
The following terms and their corresponding definitions are used in
−
  the specification.
+
the specification.
  
−
3.1.  Definitions
+
=== Definitions ===
  
−
  encryption algorithm:  process that transforms plaintext into
+
encryption algorithm:  process that transforms plaintext into
−
      ciphertext (Clause 2.19 of [ISO-IEC18033-1])
+
  ciphertext (Clause 2.19 of [ISO-IEC18033-1])
  
−
  decryption algorithm:  process that transforms ciphertext into
+
decryption algorithm:  process that transforms ciphertext into
−
      plaintext (Clause 2.14 of [ISO-IEC18033-1])
+
  plaintext (Clause 2.14 of [ISO-IEC18033-1])
  
−
  basic block cipher:  block cipher that, for a given key, provides a
+
basic block cipher:  block cipher that, for a given key, provides a
−
      single invertible mapping of the set of fixed-length plaintext
+
  single invertible mapping of the set of fixed-length plaintext
−
      blocks into ciphertext blocks of the same length
+
  blocks into ciphertext blocks of the same length
  
−
  block:  string of bits of a defined length (Clause 2.6 of
+
block:  string of bits of a defined length (Clause 2.6 of
−
      [ISO-IEC18033-1])
+
  [ISO-IEC18033-1])
  
−
  block cipher:  symmetric encipherment system with the property that
+
block cipher:  symmetric encipherment system with the property that
−
      the encryption algorithm operates on a block of plaintext -- i.e.,
+
  the encryption algorithm operates on a block of plaintext -- i.e.,
−
      a string of bits of a defined length -- to yield a block of
+
  a string of bits of a defined length -- to yield a block of
−
      ciphertext (Clause 2.7 of [ISO-IEC18033-1])
+
  ciphertext (Clause 2.7 of [ISO-IEC18033-1])
  
−
      Note: In GOST R 34.12-2015, it is established that the terms
+
  Note: In GOST R 34.12-2015, it is established that the terms
−
      "block cipher" and "block encryption algorithm" are synonyms.
+
  "block cipher" and "block encryption algorithm" are synonyms.
  
−
  encryption:  reversible transformation of data by a cryptographic
+
encryption:  reversible transformation of data by a cryptographic
−
      algorithm to produce ciphertext -- i.e., to hide the information
+
  algorithm to produce ciphertext -- i.e., to hide the information
−
      content of the data (Clause 2.18 of [ISO-IEC18033-1])
+
  content of the data (Clause 2.18 of [ISO-IEC18033-1])
  
−
  round key:  sequence of symbols that is calculated from the key and
+
round key:  sequence of symbols that is calculated from the key and
−
      controls a transformation for one round of a block cipher
+
  controls a transformation for one round of a block cipher
  
−
  key:  sequence of symbols that controls the operation of a
+
key:  sequence of symbols that controls the operation of a
−
      cryptographic transformation (e.g., encipherment, decipherment)
+
  cryptographic transformation (e.g., encipherment, decipherment)
−
      (Clause 2.21 of [ISO-IEC18033-1])
+
  (Clause 2.21 of [ISO-IEC18033-1])
  
−
      Note: In GOST R 34.12-2015, the key must be a binary sequence.
+
  Note: In GOST R 34.12-2015, the key must be a binary sequence.
  
−
  plaintext:  unencrypted information (Clause 3.11 of [ISO-IEC10116])
+
plaintext:  unencrypted information (Clause 3.11 of [ISO-IEC10116])
  
−
  key schedule:  calculation of round keys from the key,
+
key schedule:  calculation of round keys from the key,
  
−
  decryption:  reversal of a corresponding encipherment (Clause 2.13 of
+
decryption:  reversal of a corresponding encipherment (Clause 2.13 of
−
      [ISO-IEC18033-1])
+
  [ISO-IEC18033-1])
  
−
  symmetric cryptographic technique:  cryptographic technique that uses
+
symmetric cryptographic technique:  cryptographic technique that uses
−
      the same secret key for both the originator's and the recipient's
+
  the same secret key for both the originator's and the recipient's
−
      transformation (Clause 2.32 of [ISO-IEC18033-1])
+
  transformation (Clause 2.32 of [ISO-IEC18033-1])
  
−
  cipher:  alternative term for encipherment system (Clause 2.20 of
+
cipher:  alternative term for encipherment system (Clause 2.20 of
−
      [ISO-IEC18033-1])
+
  [ISO-IEC18033-1])
  
−
  ciphertext:  data that has been transformed to hide its information
+
ciphertext:  data that has been transformed to hide its information
−
      content (Clause 3.3 of [ISO-IEC10116])
+
  content (Clause 3.3 of [ISO-IEC10116])
  
−
3.2.  Notation
+
=== Notation ===
  
−
  The following notation is used in the specification:
+
The following notation is used in the specification:
  
−
  V*  the set of all binary vector strings of a finite length
+
V*  the set of all binary vector strings of a finite length
−
      (hereinafter referred to as the strings), including the empty
+
  (hereinafter referred to as the strings), including the empty
−
      string
+
  string
  
−
  V_s  the set of all binary strings of length s, where s is a
+
V_s  the set of all binary strings of length s, where s is a
−
      nonnegative integer; substrings and string components are
+
  nonnegative integer; substrings and string components are
−
      enumerated from right to left, starting from zero
+
  enumerated from right to left, starting from zero
  
−
  U[*]W  direct (Cartesian) product of two sets U and W
+
U[*]W  direct (Cartesian) product of two sets U and W
  
−
  |A|  the number of components (the length) of a string A belonging to
+
|A|  the number of components (the length) of a string A belonging to
−
      V* (if A is an empty string, then |A| = 0)
+
  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||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
+
  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
+
  equal to A and the right substring from V_|B| is equal to B
  
−
  A<<<_11  cyclic rotation of string A belonging to V_32 by 11
+
A<<<_11  cyclic rotation of string A belonging to V_32 by 11
−
      components in the direction of components having greater indices
+
  components in the direction of components having greater indices
  
−
  Z_(2^n)  ring of residues modulo 2^n
+
Z_(2^n)  ring of residues modulo 2^n
  
−
  (xor)  exclusive-or of two binary strings of the same length
+
(xor)  exclusive-or of two binary strings of the same length
  
−
  [+]  addition in the ring Z_(2^32)
+
[+]  addition in the ring Z_(2^32)
  
−
  Vec_s: Z_(2^s) -> V_s  bijective mapping that maps an element from
+
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
+
  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) +
+
  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
+
  ... + (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
+
  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,
+
Int_s: V_s -> Z_(2^s)  the mapping inverse to the mapping Vec_s,
−
      i.e., Int_s = Vec_s^(-1)
+
  i.e., Int_s = Vec_s^(-1)
  
−
  PS  composition of mappings, where the mapping S applies first
+
PS  composition of mappings, where the mapping S applies first
  
−
  P^s  composition of mappings P^(s-1) and P, where P^1=P
+
P^s  composition of mappings P^(s-1) and P, where P^1=P
  
−
4.  Parameter Values
+
== Parameter Values ==
  
−
4.1.  Nonlinear Bijection
+
=== Nonlinear Bijection ===
  
−
  The bijective nonlinear mapping is a set of substitutions:
+
The bijective nonlinear mapping is a set of substitutions:
  
−
  Pi_i = Vec_4 Pi'_i Int_4: V_4 -> V_4,
+
Pi_i = Vec_4 Pi'_i Int_4: V_4 -> V_4,
  
−
  where
+
where
  
−
  Pi'_i: Z_(2^4) -> Z_(2^4), i = 0, 1, ..., 7.
+
Pi'_i: Z_(2^4) -> Z_(2^4), i = 0, 1, ..., 7.
  
−
  The values of the substitution Pi' are specified below as arrays.
+
The values of the substitution Pi' are specified below as arrays.
  
−
  Pi'_i = (Pi'_i(0), Pi'_i(1), ... , Pi'_i(15)), i = 0, 1, ..., 7:
+
Pi'_i = (Pi'_i(0), Pi'_i(1), ... , Pi'_i(15)), i = 0, 1, ..., 7:
  
−
  Pi'_0 = (12, 4, 6, 2, 10, 5, 11, 9, 14, 8, 13, 7, 0, 3, 15, 1);
+
Pi'_0 = (12, 4, 6, 2, 10, 5, 11, 9, 14, 8, 13, 7, 0, 3, 15, 1);
−
  Pi'_1 = (6, 8, 2, 3, 9, 10, 5, 12, 1, 14, 4, 7, 11, 13, 0, 15);
+
Pi'_1 = (6, 8, 2, 3, 9, 10, 5, 12, 1, 14, 4, 7, 11, 13, 0, 15);
−
  Pi'_2 = (11, 3, 5, 8, 2, 15, 10, 13, 14, 1, 7, 4, 12, 9, 6, 0);
+
Pi'_2 = (11, 3, 5, 8, 2, 15, 10, 13, 14, 1, 7, 4, 12, 9, 6, 0);
−
  Pi'_3 = (12, 8, 2, 1, 13, 4, 15, 6, 7, 0, 10, 5, 3, 14, 9, 11);
+
Pi'_3 = (12, 8, 2, 1, 13, 4, 15, 6, 7, 0, 10, 5, 3, 14, 9, 11);
−
  Pi'_4 = (7, 15, 5, 10, 8, 1, 6, 13, 0, 9, 3, 14, 11, 4, 2, 12);
+
Pi'_4 = (7, 15, 5, 10, 8, 1, 6, 13, 0, 9, 3, 14, 11, 4, 2, 12);
−
  Pi'_5 = (5, 13, 15, 6, 9, 2, 12, 10, 11, 7, 8, 1, 4, 3, 14, 0);
+
Pi'_5 = (5, 13, 15, 6, 9, 2, 12, 10, 11, 7, 8, 1, 4, 3, 14, 0);
−
  Pi'_6 = (8, 14, 2, 5, 6, 9, 1, 12, 15, 4, 11, 0, 13, 10, 3, 7);
+
Pi'_6 = (8, 14, 2, 5, 6, 9, 1, 12, 15, 4, 11, 0, 13, 10, 3, 7);
−
  Pi'_7 = (1, 7, 14, 13, 0, 5, 8, 3, 4, 15, 10, 6, 9, 12, 11, 2);
+
Pi'_7 = (1, 7, 14, 13, 0, 5, 8, 3, 4, 15, 10, 6, 9, 12, 11, 2);
  
−
4.2.  Transformations
+
=== Transformations ===
  
−
  The following transformations are applicable for encryption and
+
The following transformations are applicable for encryption and
−
  decryption algorithms:
+
decryption algorithms:
  
−
  t: V_32 -> V_32
+
t: V_32 -> V_32
−
      t(a) = t(a_7||...||a_0) = Pi_7(a_7)||...||Pi_0(a_0), where
+
  t(a) = t(a_7||...||a_0) = Pi_7(a_7)||...||Pi_0(a_0), where
−
      a=a_7||...||a_0 belongs to V_32, a_i belongs to V_4, i=0, 1, ...,
+
  a=a_7||...||a_0 belongs to V_32, a_i belongs to V_4, i=0, 1, ...,
−
      7.
+
  7.
  
−
  g[k]: V_32 -> V_32
+
g[k]: V_32 -> V_32
−
      g[k](a) = (t(Vec_32(Int_32(a) [+] Int_32(k)))) <<<_11, where k, a
+
  g[k](a) = (t(Vec_32(Int_32(a) [+] Int_32(k)))) <<<_11, where k, a
−
      belong to V_32
+
  belong to V_32
  
−
  G[k]: V_32[*]V_32 -> V_32[*]V_32
+
G[k]: V_32[*]V_32 -> V_32[*]V_32
−
      G[k](a_1, a_0) = (a_0, g[k](a_0) (xor) a_1), where k, a_0, a_1
+
  G[k](a_1, a_0) = (a_0, g[k](a_0) (xor) a_1), where k, a_0, a_1
−
      belong to V_32
+
  belong to V_32
  
−
  G^*[k]: V_32[*]V_32 -> V_64
+
G^*[k]: V_32[*]V_32 -> V_64
−
      G^*[k](a_1, a_0) = (g[k](a_0) (xor) a_1) || a_0, where k, a_0, a_1
+
  G^*[k](a_1, a_0) = (g[k](a_0) (xor) a_1) || a_0, where k, a_0, a_1
−
      belong to V_32.
+
  belong to V_32.
  
−
4.3.  Key Schedule
+
=== Key Schedule ===
  
−
  Round keys K_i belonging to V_32, i=1, 2, ..., 32 are derived from
+
Round keys K_i belonging to V_32, i=1, 2, ..., 32 are derived from
−
  key K = k_255||...||k_0 belonging to V_256, k_i belongs to V_1, i=0,
+
key K = k_255||...||k_0 belonging to V_256, k_i belongs to V_1, i=0,
−
  1, ..., 255, as follows:
+
1, ..., 255, as follows:
  
−
  K_1 = k_255||...||k_224;
+
K_1 = k_255||...||k_224;
−
  K_2 = k_223||...||k_192;
+
K_2 = k_223||...||k_192;
−
  K_3 = k_191||...||k_160;
+
K_3 = k_191||...||k_160;
−
  K_4 = k_159||...||k_128;
+
K_4 = k_159||...||k_128;
−
  K_5 = k_127||...||k_96;
+
K_5 = k_127||...||k_96;
−
  K_6 = k_95||...||k_64;
+
K_6 = k_95||...||k_64;
−
  K_7 = k_63||...||k_32;
+
K_7 = k_63||...||k_32;
−
  K_8 = k_31||...||k_0;
+
K_8 = k_31||...||k_0;
−
  K_(i+8) = K_i, i = 1, 2, ..., 8;
+
K_(i+8) = K_i, i = 1, 2, ..., 8;
−
  K_(i+16) = K_i, i = 1, 2, ..., 8;
+
K_(i+16) = K_i, i = 1, 2, ..., 8;
−
  K_(i+24) = K_(9-i), i = 1, 2, ..., 8.
+
K_(i+24) = K_(9-i), i = 1, 2, ..., 8.
  
−
5.  Basic Encryption Algorithm
+
== Basic Encryption Algorithm ==
  
−
5.1.  Encryption
+
=== Encryption ===
  
−
  Depending on the values of round keys K_1,...,K_32, the encryption
+
Depending on the values of round keys K_1,...,K_32, the encryption
−
  algorithm is a substitution E_(K_1,...,K_32) defined as follows:
+
algorithm is a substitution E_(K_1,...,K_32) defined as follows:
  
−
  E_(K_1,...,K_32)(a)=G^*[K_32]G[K_31]...G[K_2]G[K_1](a_1, a_0),
+
E_(K_1,...,K_32)(a)=G^*[K_32]G[K_31]...G[K_2]G[K_1](a_1, a_0),
  
−
  where a=(a_1, a_0) belongs to V_64, and a_0, a_1 belong to V_32.
+
where a=(a_1, a_0) belongs to V_64, and a_0, a_1 belong to V_32.
  
−
5.2.  Decryption
+
=== Decryption ===
  
−
  Depending on the values of round keys K_1,...,K_32, the decryption
+
Depending on the values of round keys K_1,...,K_32, the decryption
−
  algorithm is a substitution D_(K_1,...,K_32) defined as follows:
+
algorithm is a substitution D_(K_1,...,K_32) defined as follows:
  
−
  D_(K_1,...,K_32)(a)=G^*[K_1]G[K_2]...G[K_31]G[K_32](a_1, a_0),
+
D_(K_1,...,K_32)(a)=G^*[K_1]G[K_2]...G[K_31]G[K_32](a_1, a_0),
  
−
  where a=(a_1, a_0) belongs to V_64, and a_0, a_1 belong to V_32.
+
where a=(a_1, a_0) belongs to V_64, and a_0, a_1 belong to V_32.
  
−
6.  IANA Considerations
+
== IANA Considerations ==
  
−
  This document has no IANA actions.
+
This document has no IANA actions.
  
−
7.  Security Considerations
+
== Security Considerations ==
  
−
  This entire document is about security considerations.
+
This entire document is about security considerations.
  
−
  Unlike [RFC5830] (GOST 28147-89), but like [RFC7801], this
+
Unlike [RFC5830] (GOST 28147-89), but like [RFC7801], this
−
  specification does not define exact block modes that should be used
+
specification does not define exact block modes that should be used
−
  together with the updated Magma cipher.  One is free to select block
+
together with the updated Magma cipher.  One is free to select block
−
  modes depending on the protocol and necessity.
+
modes depending on the protocol and necessity.
  
−
8.  References
+
== References ==
  
−
8.1.  Normative References
+
=== Normative References ===
  
−
  [GOSTR3412-2015]
+
[GOSTR3412-2015]
−
              Federal Agency on Technical Regulating and Metrology,
+
          Federal Agency on Technical Regulating and Metrology,
−
              "Information technology. Cryptographic data security.
+
          "Information technology. Cryptographic data security.
−
              Block ciphers.", GOST R 34.12-2015, 2015.
+
          Block ciphers.", GOST R 34.12-2015, 2015.
  
−
  [RFC5830]  Dolmatov, V., Ed., "GOST 28147-89: Encryption, Decryption,
+
[RFC5830]  Dolmatov, V., Ed., "GOST 28147-89: Encryption, Decryption,
−
              and Message Authentication Code (MAC) Algorithms",
+
          and Message Authentication Code (MAC) Algorithms",
−
              RFC 5830, DOI 10.17487/RFC5830, March 2010,
+
          RFC 5830, DOI 10.17487/RFC5830, March 2010,
−
              <https://www.rfc-editor.org/info/rfc5830>.
+
          <https://www.rfc-editor.org/info/rfc5830>.
  
−
  [RFC7801]  Dolmatov, V., Ed., "GOST R 34.12-2015: Block Cipher
+
[RFC7801]  Dolmatov, V., Ed., "GOST R 34.12-2015: Block Cipher
−
              "Kuznyechik"", RFC 7801, DOI 10.17487/RFC7801, March 2016,
+
          "Kuznyechik"", RFC 7801, DOI 10.17487/RFC7801, March 2016,
−
              <https://www.rfc-editor.org/info/rfc7801>.
+
          <https://www.rfc-editor.org/info/rfc7801>.
  
−
8.2.  Informative References
+
=== Informative References ===
  
−
  [GOST28147-89]
+
[GOST28147-89]
−
              Government Committee of the USSR for Standards,
+
          Government Committee of the USSR for Standards,
−
              "Cryptographic Protection for Data Processing System, GOST
+
          "Cryptographic Protection for Data Processing System, GOST
−
              28147-89, Gosudarstvennyi Standard of USSR", 1989.
+
          28147-89, Gosudarstvennyi Standard of USSR", 1989.
  
−
  [ISO-IEC10116]
+
[ISO-IEC10116]
−
              ISO/IEC, "Information technology -- Security techniques --
+
          ISO/IEC, "Information technology -- Security techniques --
−
              Modes of operation for an n-bit block cipher", ISO/
+
          Modes of operation for an n-bit block cipher", ISO/
−
              IEC 10116, 2017.
+
          IEC 10116, 2017.
  
−
  [ISO-IEC18033-1]
+
[ISO-IEC18033-1]
−
              ISO/IEC, "Information technology -- Security techniques --
+
          ISO/IEC, "Information technology -- Security techniques --
−
              Encryption algorithms -- Part 1: General", ISO/
+
          Encryption algorithms -- Part 1: General", ISO/
−
              IEC 18033-1:2015, 2015.
+
          IEC 18033-1:2015, 2015.
  
−
  [ISO-IEC18033-3]
+
[ISO-IEC18033-3]
−
              ISO/IEC, "Information technology -- Security techniques --
+
          ISO/IEC, "Information technology -- Security techniques --
−
              Encryption algorithms -- Part 3: Block ciphers", ISO/
+
          Encryption algorithms -- Part 3: Block ciphers", ISO/
−
              IEC 18033-3:2010, 2010.
+
          IEC 18033-3:2010, 2010.
  
−
  [RFC7836]  Smyshlyaev, S., Ed., Alekseev, E., Oshkin, I., Popov, V.,
+
[RFC7836]  Smyshlyaev, S., Ed., Alekseev, E., Oshkin, I., Popov, V.,
−
              Leontiev, S., Podobaev, V., and D. Belyavsky, "Guidelines
+
          Leontiev, S., Podobaev, V., and D. Belyavsky, "Guidelines
−
              on the Cryptographic Algorithms to Accompany the Usage of
+
          on the Cryptographic Algorithms to Accompany the Usage of
−
              Standards GOST R 34.10-2012 and GOST R 34.11-2012",
+
          Standards GOST R 34.10-2012 and GOST R 34.11-2012",
−
              RFC 7836, DOI 10.17487/RFC7836, March 2016,
+
          RFC 7836, DOI 10.17487/RFC7836, March 2016,
−
              <https://www.rfc-editor.org/info/rfc7836>.
+
          <https://www.rfc-editor.org/info/rfc7836>.
  
 
Appendix A.  Test Examples
 
Appendix A.  Test Examples
  
−
  This section is for information only and is not a normative part of
+
This section is for information only and is not a normative part of
−
  the specification.
+
the specification.
  
 
A.1.  Transformation t
 
A.1.  Transformation t
  
−
  t(fdb97531) = 2a196f34,
+
t(fdb97531) = 2a196f34,
−
  t(2a196f34) = ebd9f03a,
+
t(2a196f34) = ebd9f03a,
−
  t(ebd9f03a) = b039bb3d,
+
t(ebd9f03a) = b039bb3d,
−
  t(b039bb3d) = 68695433.
+
t(b039bb3d) = 68695433.
  
 
A.2.  Transformation g
 
A.2.  Transformation g
  
−
  g[87654321](fedcba98) = fdcbc20c,
+
g[87654321](fedcba98) = fdcbc20c,
−
  g[fdcbc20c](87654321) = 7e791a4b,
+
g[fdcbc20c](87654321) = 7e791a4b,
−
  g[7e791a4b](fdcbc20c) = c76549ec,
+
g[7e791a4b](fdcbc20c) = c76549ec,
−
  g[c76549ec](7e791a4b) = 9791c849.
+
g[c76549ec](7e791a4b) = 9791c849.
  
 
A.3.  Key Schedule
 
A.3.  Key Schedule
  
−
  With key set to
+
With key set to
  
−
  K = ffeeddccbbaa99887766554433221100f0f1f2f3f4f5f6f7f8f9fafbfcfdfeff,
+
K = ffeeddccbbaa99887766554433221100f0f1f2f3f4f5f6f7f8f9fafbfcfdfeff,
  
−
  the following round keys are generated:
+
the following round keys are generated:
  
−
  K_1 = ffeeddcc,
+
K_1 = ffeeddcc,
−
  K_2 = bbaa9988,
+
K_2 = bbaa9988,
−
  K_3 = 77665544,
+
K_3 = 77665544,
−
  K_4 = 33221100,
+
K_4 = 33221100,
−
  K_5 = f0f1f2f3,
+
K_5 = f0f1f2f3,
−
  K_6 = f4f5f6f7,
+
K_6 = f4f5f6f7,
−
  K_7 = f8f9fafb,
+
K_7 = f8f9fafb,
−
  K_8 = fcfdfeff,
+
K_8 = fcfdfeff,
  
−
  K_9 = ffeeddcc,
+
K_9 = ffeeddcc,
−
  K_10 = bbaa9988,
+
K_10 = bbaa9988,
−
  K_11 = 77665544,
+
K_11 = 77665544,
−
  K_12 = 33221100,
+
K_12 = 33221100,
−
  K_13 = f0f1f2f3,
+
K_13 = f0f1f2f3,
−
  K_14 = f4f5f6f7,
+
K_14 = f4f5f6f7,
−
  K_15 = f8f9fafb,
+
K_15 = f8f9fafb,
−
  K_16 = fcfdfeff,
+
K_16 = fcfdfeff,
  
−
  K_17 = ffeeddcc,
+
K_17 = ffeeddcc,
−
  K_18 = bbaa9988,
+
K_18 = bbaa9988,
−
  K_19 = 77665544,
+
K_19 = 77665544,
−
  K_20 = 33221100,
+
K_20 = 33221100,
−
  K_21 = f0f1f2f3,
+
K_21 = f0f1f2f3,
−
  K_22 = f4f5f6f7,
+
K_22 = f4f5f6f7,
−
  K_23 = f8f9fafb,
+
K_23 = f8f9fafb,
−
  K_24 = fcfdfeff,
+
K_24 = fcfdfeff,
  
−
  K_25 = fcfdfeff,
+
K_25 = fcfdfeff,
−
  K_26 = f8f9fafb,
+
K_26 = f8f9fafb,
−
  K_27 = f4f5f6f7,
+
K_27 = f4f5f6f7,
−
  K_28 = f0f1f2f3,
+
K_28 = f0f1f2f3,
−
  K_29 = 33221100,
+
K_29 = 33221100,
−
  K_30 = 77665544,
+
K_30 = 77665544,
−
  K_31 = bbaa9988,
+
K_31 = bbaa9988,
−
  K_32 = ffeeddcc.
+
K_32 = ffeeddcc.
  
 
A.4.  Test Encryption
 
A.4.  Test Encryption
  
−
  In this test example, encryption is performed on the round keys
+
In this test example, encryption is performed on the round keys
−
  specified in Appendix A.3.  Let the plaintext be
+
specified in Appendix A.3.  Let the plaintext be
  
−
  a = fedcba9876543210,
+
a = fedcba9876543210,
  
−
  then
+
then
  
−
  (a_1, a_0) = (fedcba98, 76543210),
+
(a_1, a_0) = (fedcba98, 76543210),
−
  G[K_1](a_1, a_0) = (76543210, 28da3b14),
+
G[K_1](a_1, a_0) = (76543210, 28da3b14),
−
  G[K_2]G[K_1](a_1, a_0) = (28da3b14, b14337a5),
+
G[K_2]G[K_1](a_1, a_0) = (28da3b14, b14337a5),
−
  G[K_3]...G[K_1](a_1, a_0) = (b14337a5, 633a7c68),
+
G[K_3]...G[K_1](a_1, a_0) = (b14337a5, 633a7c68),
−
  G[K_4]...G[K_1](a_1, a_0) = (633a7c68, ea89c02c),
+
G[K_4]...G[K_1](a_1, a_0) = (633a7c68, ea89c02c),
−
  G[K_5]...G[K_1](a_1, a_0) = (ea89c02c, 11fe726d),
+
G[K_5]...G[K_1](a_1, a_0) = (ea89c02c, 11fe726d),
−
  G[K_6]...G[K_1](a_1, a_0) = (11fe726d, ad0310a4),
+
G[K_6]...G[K_1](a_1, a_0) = (11fe726d, ad0310a4),
−
  G[K_7]...G[K_1](a_1, a_0) = (ad0310a4, 37d97f25),
+
G[K_7]...G[K_1](a_1, a_0) = (ad0310a4, 37d97f25),
−
  G[K_8]...G[K_1](a_1, a_0) = (37d97f25, 46324615),
+
G[K_8]...G[K_1](a_1, a_0) = (37d97f25, 46324615),
−
  G[K_9]...G[K_1](a_1, a_0) = (46324615, ce995f2a),
+
G[K_9]...G[K_1](a_1, a_0) = (46324615, ce995f2a),
−
  G[K_10]...G[K_1](a_1, a_0) = (ce995f2a, 93c1f449),
+
G[K_10]...G[K_1](a_1, a_0) = (ce995f2a, 93c1f449),
−
  G[K_11]...G[K_1](a_1, a_0) = (93c1f449, 4811c7ad),
+
G[K_11]...G[K_1](a_1, a_0) = (93c1f449, 4811c7ad),
−
  G[K_12]...G[K_1](a_1, a_0) = (4811c7ad, c4b3edca),
+
G[K_12]...G[K_1](a_1, a_0) = (4811c7ad, c4b3edca),
−
  G[K_13]...G[K_1](a_1, a_0) = (c4b3edca, 44ca5ce1),
+
G[K_13]...G[K_1](a_1, a_0) = (c4b3edca, 44ca5ce1),
−
  G[K_14]...G[K_1](a_1, a_0) = (44ca5ce1, fef51b68),
+
G[K_14]...G[K_1](a_1, a_0) = (44ca5ce1, fef51b68),
−
  G[K_15]...G[K_1](a_1, a_0) = (fef51b68, 2098cd86)
+
G[K_15]...G[K_1](a_1, a_0) = (fef51b68, 2098cd86)
−
  G[K_16]...G[K_1](a_1, a_0) = (2098cd86, 4f15b0bb),
+
G[K_16]...G[K_1](a_1, a_0) = (2098cd86, 4f15b0bb),
−
  G[K_17]...G[K_1](a_1, a_0) = (4f15b0bb, e32805bc),
+
G[K_17]...G[K_1](a_1, a_0) = (4f15b0bb, e32805bc),
−
  G[K_18]...G[K_1](a_1, a_0) = (e32805bc, e7116722),
+
G[K_18]...G[K_1](a_1, a_0) = (e32805bc, e7116722),
−
  G[K_19]...G[K_1](a_1, a_0) = (e7116722, 89cadf21),
+
G[K_19]...G[K_1](a_1, a_0) = (e7116722, 89cadf21),
−
  G[K_20]...G[K_1](a_1, a_0) = (89cadf21, bac8444d),
+
G[K_20]...G[K_1](a_1, a_0) = (89cadf21, bac8444d),
−
  G[K_21]...G[K_1](a_1, a_0) = (bac8444d, 11263a21),
+
G[K_21]...G[K_1](a_1, a_0) = (bac8444d, 11263a21),
−
  G[K_22]...G[K_1](a_1, a_0) = (11263a21, 625434c3),
+
G[K_22]...G[K_1](a_1, a_0) = (11263a21, 625434c3),
−
  G[K_23]...G[K_1](a_1, a_0) = (625434c3, 8025c0a5),
+
G[K_23]...G[K_1](a_1, a_0) = (625434c3, 8025c0a5),
−
  G[K_24]...G[K_1](a_1, a_0) = (8025c0a5, b0d66514),
+
G[K_24]...G[K_1](a_1, a_0) = (8025c0a5, b0d66514),
−
  G[K_25]...G[K_1](a_1, a_0) = (b0d66514, 47b1d5f4),
+
G[K_25]...G[K_1](a_1, a_0) = (b0d66514, 47b1d5f4),
−
  G[K_26]...G[K_1](a_1, a_0) = (47b1d5f4, c78e6d50),
+
G[K_26]...G[K_1](a_1, a_0) = (47b1d5f4, c78e6d50),
−
  G[K_27]...G[K_1](a_1, a_0) = (c78e6d50, 80251e99),
+
G[K_27]...G[K_1](a_1, a_0) = (c78e6d50, 80251e99),
−
  G[K_28]...G[K_1](a_1, a_0) = (80251e99, 2b96eca6),
+
G[K_28]...G[K_1](a_1, a_0) = (80251e99, 2b96eca6),
−
  G[K_29]...G[K_1](a_1, a_0) = (2b96eca6, 05ef4401),
+
G[K_29]...G[K_1](a_1, a_0) = (2b96eca6, 05ef4401),
−
  G[K_30]...G[K_1](a_1, a_0) = (05ef4401, 239a4577),
+
G[K_30]...G[K_1](a_1, a_0) = (05ef4401, 239a4577),
−
  G[K_31]...G[K_1](a_1, a_0) = (239a4577, c2d8ca3d).
+
G[K_31]...G[K_1](a_1, a_0) = (239a4577, c2d8ca3d).
  
−
  Then the ciphertext is
+
Then the ciphertext is
  
−
  b = G^*[K_32]G[K_31]...G[K_1](a_1, a_0) = 4ee901e5c2d8ca3d.
+
b = G^*[K_32]G[K_31]...G[K_1](a_1, a_0) = 4ee901e5c2d8ca3d.
  
 
A.5.  Test Decryption
 
A.5.  Test Decryption
  
−
  In this test example, decryption is performed on the round keys
+
In this test example, decryption is performed on the round keys
−
  specified in Appendix A.3.  Let the ciphertext be
+
specified in Appendix A.3.  Let the ciphertext be
  
−
  b = 4ee901e5c2d8ca3d,
+
b = 4ee901e5c2d8ca3d,
  
−
  then
+
then
  
−
  (b_1, b_0) = (4ee901e5, c2d8ca3d),
+
(b_1, b_0) = (4ee901e5, c2d8ca3d),
−
  G[K_32](b_1, b_0) = (c2d8ca3d, 239a4577),
+
G[K_32](b_1, b_0) = (c2d8ca3d, 239a4577),
−
  G[K_31]G[K_32](b_1, b_0) = (239a4577, 05ef4401),
+
G[K_31]G[K_32](b_1, b_0) = (239a4577, 05ef4401),
−
  G[K_30]...G[K_32](b_1, b_0) = (05ef4401, 2b96eca6),
+
G[K_30]...G[K_32](b_1, b_0) = (05ef4401, 2b96eca6),
−
  G[K_29]...G[K_32](b_1, b_0) = (2b96eca6, 80251e99),
+
G[K_29]...G[K_32](b_1, b_0) = (2b96eca6, 80251e99),
−
  G[K_28]...G[K_32](b_1, b_0) = (80251e99, c78e6d50),
+
G[K_28]...G[K_32](b_1, b_0) = (80251e99, c78e6d50),
−
  G[K_27]...G[K_32](b_1, b_0) = (c78e6d50, 47b1d5f4),
+
G[K_27]...G[K_32](b_1, b_0) = (c78e6d50, 47b1d5f4),
−
  G[K_26]...G[K_32](b_1, b_0) = (47b1d5f4, b0d66514),
+
G[K_26]...G[K_32](b_1, b_0) = (47b1d5f4, b0d66514),
−
  G[K_25]...G[K_32](b_1, b_0) = (b0d66514, 8025c0a5),
+
G[K_25]...G[K_32](b_1, b_0) = (b0d66514, 8025c0a5),
−
  G[K_24]...G[K_32](b_1, b_0) = (8025c0a5, 625434c3),
+
G[K_24]...G[K_32](b_1, b_0) = (8025c0a5, 625434c3),
−
  G[K_23]...G[K_32](b_1, b_0) = (625434c3, 11263a21),
+
G[K_23]...G[K_32](b_1, b_0) = (625434c3, 11263a21),
−
  G[K_22]...G[K_32](b_1, b_0) = (11263a21, bac8444d),
+
G[K_22]...G[K_32](b_1, b_0) = (11263a21, bac8444d),
−
  G[K_21]...G[K_32](b_1, b_0) = (bac8444d, 89cadf21),
+
G[K_21]...G[K_32](b_1, b_0) = (bac8444d, 89cadf21),
−
  G[K_20]...G[K_32](b_1, b_0) = (89cadf21, e7116722),
+
G[K_20]...G[K_32](b_1, b_0) = (89cadf21, e7116722),
−
  G[K_19]...G[K_32](b_1, b_0) = (e7116722, e32805bc),
+
G[K_19]...G[K_32](b_1, b_0) = (e7116722, e32805bc),
−
  G[K_18]...G[K_32](b_1, b_0) = (e32805bc, 4f15b0bb),
+
G[K_18]...G[K_32](b_1, b_0) = (e32805bc, 4f15b0bb),
−
  G[K_17]...G[K_32](b_1, b_0) = (4f15b0bb, 2098cd86),
+
G[K_17]...G[K_32](b_1, b_0) = (4f15b0bb, 2098cd86),
−
  G[K_16]...G[K_32](b_1, b_0) = (2098cd86, fef51b68),
+
G[K_16]...G[K_32](b_1, b_0) = (2098cd86, fef51b68),
−
  G[K_15]...G[K_32](b_1, b_0) = (fef51b68, 44ca5ce1),
+
G[K_15]...G[K_32](b_1, b_0) = (fef51b68, 44ca5ce1),
−
  G[K_14]...G[K_32](b_1, b_0) = (44ca5ce1, c4b3edca),
+
G[K_14]...G[K_32](b_1, b_0) = (44ca5ce1, c4b3edca),
−
  G[K_13]...G[K_32](b_1, b_0) = (c4b3edca, 4811c7ad),
+
G[K_13]...G[K_32](b_1, b_0) = (c4b3edca, 4811c7ad),
−
  G[K_12]...G[K_32](b_1, b_0) = (4811c7ad, 93c1f449),
+
G[K_12]...G[K_32](b_1, b_0) = (4811c7ad, 93c1f449),
−
  G[K_11]...G[K_32](b_1, b_0) = (93c1f449, ce995f2a),
+
G[K_11]...G[K_32](b_1, b_0) = (93c1f449, ce995f2a),
−
  G[K_10]...G[K_32](b_1, b_0) = (ce995f2a, 46324615),
+
G[K_10]...G[K_32](b_1, b_0) = (ce995f2a, 46324615),
−
  G[K_9]...G[K_32](b_1, b_0) = (46324615, 37d97f25),
+
G[K_9]...G[K_32](b_1, b_0) = (46324615, 37d97f25),
−
  G[K_8]...G[K_32](b_1, b_0) = (37d97f25, ad0310a4),
+
G[K_8]...G[K_32](b_1, b_0) = (37d97f25, ad0310a4),
−
  G[K_7]...G[K_32](b_1, b_0) = (ad0310a4, 11fe726d),
+
G[K_7]...G[K_32](b_1, b_0) = (ad0310a4, 11fe726d),
−
  G[K_6]...G[K_32](b_1, b_0) = (11fe726d, ea89c02c),
+
G[K_6]...G[K_32](b_1, b_0) = (11fe726d, ea89c02c),
−
  G[K_5]...G[K_32](b_1, b_0) = (ea89c02c, 633a7c68),
+
G[K_5]...G[K_32](b_1, b_0) = (ea89c02c, 633a7c68),
−
  G[K_4]...G[K_32](b_1, b_0) = (633a7c68, b14337a5),
+
G[K_4]...G[K_32](b_1, b_0) = (633a7c68, b14337a5),
−
  G[K_3]...G[K_32](b_1, b_0) = (b14337a5, 28da3b14),
+
G[K_3]...G[K_32](b_1, b_0) = (b14337a5, 28da3b14),
−
  G[K_2]...G[K_32](b_1, b_0) = (28da3b14, 76543210).
+
G[K_2]...G[K_32](b_1, b_0) = (28da3b14, 76543210).
  
−
  Then the plaintext is
+
Then the plaintext is
  
−
  a = G^*[K_1]G[K_2]...G[K_32](b_1, b_0) = fedcba9876543210.
+
a = G^*[K_1]G[K_2]...G[K_32](b_1, b_0) = fedcba9876543210.
  
 
Appendix B.  Background
 
Appendix B.  Background
  
−
  This specification is a translation of relevant parts of the
+
This specification is a translation of relevant parts of the
−
  [GOSTR3412-2015] standard.  The order of terms in both parts of
+
[GOSTR3412-2015] standard.  The order of terms in both parts of
−
  Section 3 comes from the original text.  Combining [RFC7801] with
+
Section 3 comes from the original text.  Combining [RFC7801] with
−
  this document will create a complete translation of [GOSTR3412-2015]
+
this document will create a complete translation of [GOSTR3412-2015]
−
  into English.
+
into English.
  
−
  Algorithmically, Magma is a variation of the block cipher defined in
+
Algorithmically, Magma is a variation of the block cipher defined in
−
  [RFC5830] ([GOST28147-89]) with the following clarifications and
+
[RFC5830] ([GOST28147-89]) with the following clarifications and
−
  minor modifications:
+
minor modifications:
  
−
  1.  S-BOX set is fixed at id-tc26-gost-28147-param-Z (see Appendix C
+
1.  S-BOX set is fixed at id-tc26-gost-28147-param-Z (see Appendix C
−
      of [RFC7836]);
+
    of [RFC7836]);
  
−
  2.  key is parsed as a single big-endian integer (compared to the
+
2.  key is parsed as a single big-endian integer (compared to the
−
      little-endian approach used in [GOST28147-89]), which results in
+
    little-endian approach used in [GOST28147-89]), which results in
−
      different subkey values being used;
+
    different subkey values being used;
  
−
  3.  data bytes are also parsed as a single big-endian integer
+
3.  data bytes are also parsed as a single big-endian integer
−
      (instead of being parsed as little-endian integer).
+
    (instead of being parsed as little-endian integer).
  
 
Authors' Addresses
 
Authors' Addresses
  
−
  Vasily Dolmatov (editor)
+
Vasily Dolmatov (editor)
−
  JSC "NPK Kryptonite"
+
JSC "NPK Kryptonite"
−
  Spartakovskaya sq., 14, bld 2, JSC "NPK Kryptonite"
+
Spartakovskaya sq., 14, bld 2, JSC "NPK Kryptonite"
−
  Moscow
+
Moscow
−
  105082
+
105082
−
  Russian Federation
+
Russian Federation
−
 
 
− 
  
 +
  
−
  Dmitry Baryshkov
+
Dmitry Baryshkov
−
  Auriga, Inc.
+
Auriga, Inc.
−
  office 1410
+
office 1410
−
  Torfyanaya Doroga, 7F
+
Torfyanaya Doroga, 7F
−
  Saint-Petersburg
+
Saint-Petersburg
−
  197374
+
197374
−
  Russian Federation
+
Russian Federation
  
−+

Revision as of 00:01, 28 September 2020



Independent Submission V. Dolmatov, Ed. Request for Comments: 8891 JSC "NPK Kryptonite" Updates: 5830 D. Baryshkov Category: Informational Auriga, Inc. ISSN: 2070-1721 September 2020 

            GOST R 34.12-2015: Block Cipher "Magma"

Abstract

In addition to a new cipher with a block length of n=128 bits (referred to as "Kuznyechik" and described in RFC 7801), Russian Federal standard GOST R 34.12-2015 includes an updated version of the block cipher with a block length of n=64 bits and key length of k=256 bits, which is also referred to as "Magma". The algorithm is an updated version of an older block cipher with a block length of n=64 bits described in GOST 28147-89 (RFC 5830). This document is intended to be a source of information about the updated version of the 64-bit cipher. It may facilitate the use of the block cipher in Internet applications by providing information for developers and users of the GOST 64-bit cipher with the revised version of the cipher for encryption and decryption.

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 candidates for any level of Internet Standard; see Section 2 of RFC 7841.

Information about the current status of this document, any errata, and how to provide feedback on it may be obtained at https://www.rfc-editor.org/info/rfc8891.

Copyright Notice

Copyright (c) 2020 IETF Trust and the persons identified as the document authors. All rights reserved.

This document is subject to BCP 78 and the IETF Trust's Legal Provisions Relating to IETF Documents (https://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.

Table of Contents

1. Introduction 2. General Information 3. Definitions and Notation 

 3.1.  Definitions
 3.2.  Notation

4. Parameter Values 

 4.1.  Nonlinear Bijection
 4.2.  Transformations
 4.3.  Key Schedule

5. Basic Encryption Algorithm 

 5.1.  Encryption
 5.2.  Decryption

6. IANA Considerations 7. Security Considerations 8. References 

 8.1.  Normative References
 8.2.  Informative References

Appendix A. Test Examples 

 A.1.  Transformation t
 A.2.  Transformation g
 A.3.  Key Schedule
 A.4.  Test Encryption
 A.5.  Test Decryption

Appendix B. Background Authors' Addresses

Introduction

The Russian Federal standard [GOSTR3412-2015] 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 defined in this specification 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.

This document is intended to be a source of information about the updated version of the 64-bit cipher. It may facilitate the use of the block cipher in Internet applications by providing information for developers and users of a GOST 64-bit cipher with the revised version of the cipher for encryption and decryption.

General Information

The Russian Federal standard [GOSTR3412-2015] 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 specification comply with the following international standards:

  • ISO/IEC 10116 [ISO-IEC10116]
  • series of standards ISO/IEC 18033 [ISO-IEC18033-1][ISO-IEC18033-3]

Definitions and Notation

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

Definitions

encryption algorithm: process that transforms plaintext into 

  ciphertext (Clause 2.19 of [ISO-IEC18033-1])

decryption algorithm: process that transforms ciphertext into 

  plaintext (Clause 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 (Clause 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 (Clause 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 (Clause 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, decipherment)
  (Clause 2.21 of [ISO-IEC18033-1])

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

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

key schedule: calculation of round keys from the key,

decryption: reversal of a corresponding encipherment (Clause 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 (Clause 2.32 of [ISO-IEC18033-1])

cipher: alternative term for encipherment system (Clause 2.20 of 

  [ISO-IEC18033-1])

ciphertext: data that has been transformed to hide its information 

  content (Clause 3.3 of [ISO-IEC10116])

Notation

The following notation is used in the specification:

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 

  nonnegative 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

A<<<_11 cyclic rotation of string A belonging to V_32 by 11 

  components in the direction of components having greater indices

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

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

[+] addition in the ring Z_(2^32)

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)

PS composition of mappings, where the mapping S applies first

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

Parameter Values

Nonlinear Bijection

The bijective nonlinear mapping is a set of substitutions:

Pi_i = Vec_4 Pi'_i Int_4: V_4 -> V_4,

where

Pi'_i: Z_(2^4) -> Z_(2^4), i = 0, 1, ..., 7.

The values of the substitution Pi' are specified below as arrays.

Pi'_i = (Pi'_i(0), Pi'_i(1), ... , Pi'_i(15)), i = 0, 1, ..., 7:

Pi'_0 = (12, 4, 6, 2, 10, 5, 11, 9, 14, 8, 13, 7, 0, 3, 15, 1); Pi'_1 = (6, 8, 2, 3, 9, 10, 5, 12, 1, 14, 4, 7, 11, 13, 0, 15); Pi'_2 = (11, 3, 5, 8, 2, 15, 10, 13, 14, 1, 7, 4, 12, 9, 6, 0); Pi'_3 = (12, 8, 2, 1, 13, 4, 15, 6, 7, 0, 10, 5, 3, 14, 9, 11); Pi'_4 = (7, 15, 5, 10, 8, 1, 6, 13, 0, 9, 3, 14, 11, 4, 2, 12); Pi'_5 = (5, 13, 15, 6, 9, 2, 12, 10, 11, 7, 8, 1, 4, 3, 14, 0); Pi'_6 = (8, 14, 2, 5, 6, 9, 1, 12, 15, 4, 11, 0, 13, 10, 3, 7); Pi'_7 = (1, 7, 14, 13, 0, 5, 8, 3, 4, 15, 10, 6, 9, 12, 11, 2);

Transformations

The following transformations are applicable for encryption and decryption algorithms:

t: V_32 -> V_32 

  t(a) = t(a_7||...||a_0) = Pi_7(a_7)||...||Pi_0(a_0), where
  a=a_7||...||a_0 belongs to V_32, a_i belongs to V_4, i=0, 1, ...,
  7.

g[k]: V_32 -> V_32 

  g[k](a) = (t(Vec_32(Int_32(a) [+] Int_32(k)))) <<<_11, where k, a
  belong to V_32

G[k]: V_32[*]V_32 -> V_32[*]V_32 

  G[k](a_1, a_0) = (a_0, g[k](a_0) (xor) a_1), where k, a_0, a_1
  belong to V_32

G^*[k]: V_32[*]V_32 -> V_64 

  G^*[k](a_1, a_0) = (g[k](a_0) (xor) a_1) || a_0, where k, a_0, a_1
  belong to V_32.

Key Schedule

Round keys K_i belonging to V_32, i=1, 2, ..., 32 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_224; K_2 = k_223||...||k_192; K_3 = k_191||...||k_160; K_4 = k_159||...||k_128; K_5 = k_127||...||k_96; K_6 = k_95||...||k_64; K_7 = k_63||...||k_32; K_8 = k_31||...||k_0; K_(i+8) = K_i, i = 1, 2, ..., 8; K_(i+16) = K_i, i = 1, 2, ..., 8; K_(i+24) = K_(9-i), i = 1, 2, ..., 8.

Basic Encryption Algorithm

Encryption

Depending on the values of round keys K_1,...,K_32, the encryption algorithm is a substitution E_(K_1,...,K_32) defined as follows:

E_(K_1,...,K_32)(a)=G^*[K_32]G[K_31]...G[K_2]G[K_1](a_1, a_0),

where a=(a_1, a_0) belongs to V_64, and a_0, a_1 belong to V_32.

Decryption

Depending on the values of round keys K_1,...,K_32, the decryption algorithm is a substitution D_(K_1,...,K_32) defined as follows:

D_(K_1,...,K_32)(a)=G^*[K_1]G[K_2]...G[K_31]G[K_32](a_1, a_0),

where a=(a_1, a_0) belongs to V_64, and a_0, a_1 belong to V_32.

IANA Considerations

This document has no IANA actions.

Security Considerations

This entire document is about security considerations.

Unlike [RFC5830] (GOST 28147-89), but like [RFC7801], this specification does not define exact block modes that should be used together with the updated Magma cipher. One is free to select block modes depending on the protocol and necessity.

References

Normative References

[GOSTR3412-2015] 

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

[RFC5830] Dolmatov, V., Ed., "GOST 28147-89: Encryption, Decryption, 

          and Message Authentication Code (MAC) Algorithms",
          RFC 5830, DOI 10.17487/RFC5830, March 2010,
          <https://www.rfc-editor.org/info/rfc5830>.

[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>.

Informative References

[GOST28147-89] 

          Government Committee of the USSR for Standards,
          "Cryptographic Protection for Data Processing System, GOST
          28147-89, Gosudarstvennyi Standard of USSR", 1989.

[ISO-IEC10116] 

          ISO/IEC, "Information technology -- Security techniques --
          Modes of operation for an n-bit block cipher", ISO/
          IEC 10116, 2017.

[ISO-IEC18033-1] 

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

[ISO-IEC18033-3] 

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

[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>.

Appendix A. Test Examples

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

A.1. Transformation t

t(fdb97531) = 2a196f34, t(2a196f34) = ebd9f03a, t(ebd9f03a) = b039bb3d, t(b039bb3d) = 68695433.

A.2. Transformation g

g[87654321](fedcba98) = fdcbc20c, g[fdcbc20c](87654321) = 7e791a4b, g[7e791a4b](fdcbc20c) = c76549ec, g[c76549ec](7e791a4b) = 9791c849.

A.3. Key Schedule

With key set to

K = ffeeddccbbaa99887766554433221100f0f1f2f3f4f5f6f7f8f9fafbfcfdfeff,

the following round keys are generated:

K_1 = ffeeddcc, K_2 = bbaa9988, K_3 = 77665544, K_4 = 33221100, K_5 = f0f1f2f3, K_6 = f4f5f6f7, K_7 = f8f9fafb, K_8 = fcfdfeff,

K_9 = ffeeddcc, K_10 = bbaa9988, K_11 = 77665544, K_12 = 33221100, K_13 = f0f1f2f3, K_14 = f4f5f6f7, K_15 = f8f9fafb, K_16 = fcfdfeff,

K_17 = ffeeddcc, K_18 = bbaa9988, K_19 = 77665544, K_20 = 33221100, K_21 = f0f1f2f3, K_22 = f4f5f6f7, K_23 = f8f9fafb, K_24 = fcfdfeff,

K_25 = fcfdfeff, K_26 = f8f9fafb, K_27 = f4f5f6f7, K_28 = f0f1f2f3, K_29 = 33221100, K_30 = 77665544, K_31 = bbaa9988, K_32 = ffeeddcc.

A.4. Test Encryption

In this test example, encryption is performed on the round keys specified in Appendix A.3. Let the plaintext be

a = fedcba9876543210,

then

(a_1, a_0) = (fedcba98, 76543210), G[K_1](a_1, a_0) = (76543210, 28da3b14), G[K_2]G[K_1](a_1, a_0) = (28da3b14, b14337a5), G[K_3]...G[K_1](a_1, a_0) = (b14337a5, 633a7c68), G[K_4]...G[K_1](a_1, a_0) = (633a7c68, ea89c02c), G[K_5]...G[K_1](a_1, a_0) = (ea89c02c, 11fe726d), G[K_6]...G[K_1](a_1, a_0) = (11fe726d, ad0310a4), G[K_7]...G[K_1](a_1, a_0) = (ad0310a4, 37d97f25), G[K_8]...G[K_1](a_1, a_0) = (37d97f25, 46324615), G[K_9]...G[K_1](a_1, a_0) = (46324615, ce995f2a), G[K_10]...G[K_1](a_1, a_0) = (ce995f2a, 93c1f449), G[K_11]...G[K_1](a_1, a_0) = (93c1f449, 4811c7ad), G[K_12]...G[K_1](a_1, a_0) = (4811c7ad, c4b3edca), G[K_13]...G[K_1](a_1, a_0) = (c4b3edca, 44ca5ce1), G[K_14]...G[K_1](a_1, a_0) = (44ca5ce1, fef51b68), G[K_15]...G[K_1](a_1, a_0) = (fef51b68, 2098cd86) G[K_16]...G[K_1](a_1, a_0) = (2098cd86, 4f15b0bb), G[K_17]...G[K_1](a_1, a_0) = (4f15b0bb, e32805bc), G[K_18]...G[K_1](a_1, a_0) = (e32805bc, e7116722), G[K_19]...G[K_1](a_1, a_0) = (e7116722, 89cadf21), G[K_20]...G[K_1](a_1, a_0) = (89cadf21, bac8444d), G[K_21]...G[K_1](a_1, a_0) = (bac8444d, 11263a21), G[K_22]...G[K_1](a_1, a_0) = (11263a21, 625434c3), G[K_23]...G[K_1](a_1, a_0) = (625434c3, 8025c0a5), G[K_24]...G[K_1](a_1, a_0) = (8025c0a5, b0d66514), G[K_25]...G[K_1](a_1, a_0) = (b0d66514, 47b1d5f4), G[K_26]...G[K_1](a_1, a_0) = (47b1d5f4, c78e6d50), G[K_27]...G[K_1](a_1, a_0) = (c78e6d50, 80251e99), G[K_28]...G[K_1](a_1, a_0) = (80251e99, 2b96eca6), G[K_29]...G[K_1](a_1, a_0) = (2b96eca6, 05ef4401), G[K_30]...G[K_1](a_1, a_0) = (05ef4401, 239a4577), G[K_31]...G[K_1](a_1, a_0) = (239a4577, c2d8ca3d).

Then the ciphertext is

b = G^*[K_32]G[K_31]...G[K_1](a_1, a_0) = 4ee901e5c2d8ca3d.

A.5. Test Decryption

In this test example, decryption is performed on the round keys specified in Appendix A.3. Let the ciphertext be

b = 4ee901e5c2d8ca3d,

then

(b_1, b_0) = (4ee901e5, c2d8ca3d), G[K_32](b_1, b_0) = (c2d8ca3d, 239a4577), G[K_31]G[K_32](b_1, b_0) = (239a4577, 05ef4401), G[K_30]...G[K_32](b_1, b_0) = (05ef4401, 2b96eca6), G[K_29]...G[K_32](b_1, b_0) = (2b96eca6, 80251e99), G[K_28]...G[K_32](b_1, b_0) = (80251e99, c78e6d50), G[K_27]...G[K_32](b_1, b_0) = (c78e6d50, 47b1d5f4), G[K_26]...G[K_32](b_1, b_0) = (47b1d5f4, b0d66514), G[K_25]...G[K_32](b_1, b_0) = (b0d66514, 8025c0a5), G[K_24]...G[K_32](b_1, b_0) = (8025c0a5, 625434c3), G[K_23]...G[K_32](b_1, b_0) = (625434c3, 11263a21), G[K_22]...G[K_32](b_1, b_0) = (11263a21, bac8444d), G[K_21]...G[K_32](b_1, b_0) = (bac8444d, 89cadf21), G[K_20]...G[K_32](b_1, b_0) = (89cadf21, e7116722), G[K_19]...G[K_32](b_1, b_0) = (e7116722, e32805bc), G[K_18]...G[K_32](b_1, b_0) = (e32805bc, 4f15b0bb), G[K_17]...G[K_32](b_1, b_0) = (4f15b0bb, 2098cd86), G[K_16]...G[K_32](b_1, b_0) = (2098cd86, fef51b68), G[K_15]...G[K_32](b_1, b_0) = (fef51b68, 44ca5ce1), G[K_14]...G[K_32](b_1, b_0) = (44ca5ce1, c4b3edca), G[K_13]...G[K_32](b_1, b_0) = (c4b3edca, 4811c7ad), G[K_12]...G[K_32](b_1, b_0) = (4811c7ad, 93c1f449), G[K_11]...G[K_32](b_1, b_0) = (93c1f449, ce995f2a), G[K_10]...G[K_32](b_1, b_0) = (ce995f2a, 46324615), G[K_9]...G[K_32](b_1, b_0) = (46324615, 37d97f25), G[K_8]...G[K_32](b_1, b_0) = (37d97f25, ad0310a4), G[K_7]...G[K_32](b_1, b_0) = (ad0310a4, 11fe726d), G[K_6]...G[K_32](b_1, b_0) = (11fe726d, ea89c02c), G[K_5]...G[K_32](b_1, b_0) = (ea89c02c, 633a7c68), G[K_4]...G[K_32](b_1, b_0) = (633a7c68, b14337a5), G[K_3]...G[K_32](b_1, b_0) = (b14337a5, 28da3b14), G[K_2]...G[K_32](b_1, b_0) = (28da3b14, 76543210).

Then the plaintext is

a = G^*[K_1]G[K_2]...G[K_32](b_1, b_0) = fedcba9876543210.

Appendix B. Background

This specification is a translation of relevant parts of the [GOSTR3412-2015] standard. The order of terms in both parts of Section 3 comes from the original text. Combining [RFC7801] with this document will create a complete translation of [GOSTR3412-2015] into English.

Algorithmically, Magma is a variation of the block cipher defined in [RFC5830] ([GOST28147-89]) with the following clarifications and minor modifications:

1. S-BOX set is fixed at id-tc26-gost-28147-param-Z (see Appendix C 

   of [RFC7836]);

2. key is parsed as a single big-endian integer (compared to the 

   little-endian approach used in [GOST28147-89]), which results in
   different subkey values being used;

3. data bytes are also parsed as a single big-endian integer 

   (instead of being parsed as little-endian integer).

Authors' Addresses

Vasily Dolmatov (editor) JSC "NPK Kryptonite" Spartakovskaya sq., 14, bld 2, JSC "NPK Kryptonite" Moscow 105082 Russian Federation

Email: [email protected]

Dmitry Baryshkov Auriga, Inc. office 1410 Torfyanaya Doroga, 7F Saint-Petersburg 197374 Russian Federation

Email: [email protected]

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