Internet Engineering Task Force V. Dolmatov, Ed.
Internet-Draft JSC "NPK Kryptonite"
Updates: 5830 (if approved) D. Eremin-Solenikov
Intended status: Informational Auriga, Inc
Expires: March 26, 2020 September 23, 2019
GOST R 34.12-2015: Block Cipher "Magma"
draft-dolmatov-magma-02
Abstract
The Russian Federal standard for electronic encryption, decryption,
and message authentication algorithms (GOST 28147-89), which is one
of the Russian cryptographic standard algorithms is described in RFC
5830. Since its publication, an update to the Russian Federal
standard was published as GOST R 34.12-2015 that includes the
specification of the block cipher known as "Kuznyechik" which has
been described in RFC7801.
GOST R 34.12-2015 also includes an updated version of the block
cipher with block length of n=64 bits and key length k=256 bits,
which is also referred as "Magma". This document is intended to be a
source of information about the updated version of 64-bit cipher. It
may facilitate the use of the block cipher in Internet applications
by providing information for developers and users of GOST 64-bit
cipherwith the revised version of the cipherfor encryption and
decryption.
Unlike RFC 5830 (GOST 28147-89) and like RFC 7801 this specification
does not define exact block modes which should be used together with
updated Magma cipher. One is free to select block modes depending on
the protocol and necessity.
Status of This Memo
This Internet-Draft is submitted in full conformance with the
provisions of BCP 78 and BCP 79.
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This Internet-Draft will expire on March 26, 2020.
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Table of Contents
1. Introduction . . . . . . . . . . . . . . . . . . . . . . . . 3
2. General Information . . . . . . . . . . . . . . . . . . . . . 3
3. Definitions and Notations . . . . . . . . . . . . . . . . . . 3
3.1. Definitions . . . . . . . . . . . . . . . . . . . . . . . 3
3.2. Notations . . . . . . . . . . . . . . . . . . . . . . . . 5
4. Description of Kuznyechik cipher . . . . . . . . . . . . . . 6
5. Parameter Values . . . . . . . . . . . . . . . . . . . . . . 6
5.1. Nonlinear Bijection . . . . . . . . . . . . . . . . . . . 6
5.2. Transformations . . . . . . . . . . . . . . . . . . . . . 6
5.3. Key schedule . . . . . . . . . . . . . . . . . . . . . . 7
6. Basic encryption algorithm . . . . . . . . . . . . . . . . . 7
6.1. Encryption . . . . . . . . . . . . . . . . . . . . . . . 7
6.2. Decryption . . . . . . . . . . . . . . . . . . . . . . . 7
7. IANA Considerations . . . . . . . . . . . . . . . . . . . . . 7
8. Security Considerations . . . . . . . . . . . . . . . . . . . 8
9. References . . . . . . . . . . . . . . . . . . . . . . . . . 8
9.1. Normative References . . . . . . . . . . . . . . . . . . 8
9.2. Informative References . . . . . . . . . . . . . . . . . 8
Appendix A. Test Examples . . . . . . . . . . . . . . . . . . . 9
A.1. Transformation t . . . . . . . . . . . . . . . . . . . . 9
A.2. Transformation g . . . . . . . . . . . . . . . . . . . . 9
A.3. Key schedule . . . . . . . . . . . . . . . . . . . . . . 9
A.4. Test Encryption . . . . . . . . . . . . . . . . . . . . . 10
A.5. Test Decryption . . . . . . . . . . . . . . . . . . . . . 11
Appendix B. Background . . . . . . . . . . . . . . . . . . . . . 12
Authors' Addresses . . . . . . . . . . . . . . . . . . . . . . . 13
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1. 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.
2. 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 19.06.2015.
Terms and concepts in the specification comply with the following
international standards:
o ISO/IEC 10116 [ISO-IEC10116],
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 specification.
3.1. Definitions
Definitions
encryption algorithm: process which transforms plaintext into
ciphertext (Clause 2.19 of [ISO-IEC18033-1]),
decryption algorithm: process which transforms ciphertext into
plaintext (Clause 2.14 of [ISO-IEC18033-1]),
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basic block cipher: block cipher which 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 which 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 which has been transformed to hide its
information content (Clause 3.3 of [ISO-IEC10116]).
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3.2. Notations
The following notations are 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
non-negative integer; substrings and string components are
enumerated from right to left starting from zero,
U[*]W direct (Cartesian) product of two set 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 the two binary strings of the same length,
[+] addition in the ring Z_(2^32)
Vec_s: Z_(2^s) -> V_s bijective mapping which 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,
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4. Description of Kuznyechik cipher
This section corresponds to a section in [GOSTR3412-2015] which
describes "Kuznyechik" cipher (a cipher with 128-bit block length an
256 bytes key length). Translation of that section is provided as a
part of [RFC7801].
5. Parameter Values
5.1. 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);
5.2. 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;
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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.
5.3. 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.
6. Basic encryption algorithm
6.1. 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.
6.2. 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.
7. IANA Considerations
This memo includes no request to IANA.
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8. Security Considerations
This entire document is about security considerations.
9. References
9.1. 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,
.
[RFC7801] Dolmatov, V., Ed., "GOST R 34.12-2015: Block Cipher
"Kuznyechik"", RFC 7801, DOI 10.17487/RFC7801, March 2016,
.
9.2. 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", 2006.
[ISO-IEC18033-1]
ISO-IEC, "Information technology - Security techniques -
Encryption algorithms - Part 1: General, ISO-IEC 18033-1",
2013.
[ISO-IEC18033-3]
ISO-IEC, "Information technology - Security techniques -
Encryption algorithms - Part 3: Block ciphers, ISO-IEC
18033-3", 2010.
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[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,
.
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,
following round keys are generated:
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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 clause A.3. Let the plaintext be
a = fedcba9876543210,
then
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(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 clause A.3. Let the ciphertext be
b = 4ee901e5c2d8ca3d,
then
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(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
[GOSTR3412-2015] standard. The order of terms in both parts of
Section 3 comes from original text. Empty section Section 4 is a
placeholder for a section from original standard describing
Kuznyechik. If one combines [RFC7801] with this document, he will
have complete translation of [GOSTR3412-2015] into English.
Dolmatov & Eremin-SolenikExpires March 26, 2020 [Page 12]
Internet-Draft Abbreviated Title September 2019
Algoritmically Magma is a variation of 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 little-
endian approach used in [GOST28147-89]), which results in
different subkey values being used;
3. data bytes are also parsed as 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: vdolmatov@gmail.com
Dmitry Eremin-Solenikov
Auriga, Inc
Torfyanaya Doroga, 7F, office 1410
Saint-Petersburg 197374
Russian Federation
Email: dbaryshkov@gmail.com
Dolmatov & Eremin-SolenikExpires March 26, 2020 [Page 13]