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.
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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
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.
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.
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 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]
3. Definitions and Notation
The following terms and their corresponding definitions are used in
the specification.
3.1. 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])
3.2. 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
4. Parameter Values
4.1. 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);
4.2. 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.
4.3. 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.
5. Basic Encryption Algorithm
5.1. 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.
5.2. 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.
6. IANA Considerations
This document has no IANA actions.
7. 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.
8. References
8.1. 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,
<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>.
8.2. 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, 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: vdolmatov@gmail.com
Dmitry Baryshkov
Auriga, Inc.
office 1410
Torfyanaya Doroga, 7F
Saint-Petersburg
197374
Russian Federation
Email: dbaryshkov@gmail.com
