Independent Submission V. Dolmatov, Ed.
Request for Comments: 5830 Cryptocom, Ltd.
Category: Informational March 2010
ISSN: 2070-1721
GOST 28147-89: Encryption, Decryption,
and Message Authentication Code (MAC) Algorithms
Abstract
This document is intended to be a source of information about the
Russian Federal standard for electronic encryption, decryption, and
message authentication algorithms (GOST 28147-89), which is one of
the Russian cryptographic standard algorithms called GOST
algorithms. Recently, Russian cryptography is being used in
EID 2134 (Verified) is as follows:Section: Abstract
Original Text:
This document is intended to be a source of information about the
Russian Federal standard for electronic encryption, decryption, and
message authentication algorithms (GOST 28147-89), which is one of
the Russian cryptographic standard algorithms called GOST
algorithms).
Corrected Text:
This document is intended to be a source of information about the
Russian Federal standard for electronic encryption, decryption, and
message authentication algorithms (GOST 28147-89), which is one of
the Russian cryptographic standard algorithms called GOST
algorithms.
Notes:
None
Internet applications, and this document has been created as
information for developers and users of GOST 28147-89 for encryption,
decryption, and message authentication.
Status of This Memo
This document is not an Internet Standards Track specification; it is
published for informational purposes.
This is a contribution to the RFC Series, independently of any other
RFC stream. The RFC Editor has chosen to publish this document at
its discretion and makes no statement about its value for
implementation or deployment. Documents approved for publication by
the RFC Editor are not a candidate for any level of Internet
Standard; see Section 2 of RFC 5741.
Information about the current status of this document, any errata,
and how to provide feedback on it may be obtained at
http://www.rfc-editor.org/info/rfc5830.
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Table of Contents
1. Introduction ....................................................3
1.1. General Information ........................................3
2. Applicability ...................................................3
3. Definitions and Notations .......................................3
3.1. Definitions ................................................3
3.2. Notation ...................................................4
4. General Statements ..............................................4
5. The Electronic Codebook Mode ....................................6
5.1. Encryption of Plain Text in the Electronic Codebook Mode ...6
5.2. Decryption of the Ciphertext in the Electronic
Codebook Mode ..............................................9
6. The Counter Encryption Mode ....................................10
6.1. Encryption of Plain Text in the Counter Encryption Mode ...10
6.2. Decryption of Ciphertext in the Counter Encryption Mode ...13
7. The Cipher Feedback Mode .......................................13
7.1. Encryption of Plain Text in the Cipher Feedback Mode ......13
7.2. Decryption of Ciphertext in the Cipher Feedback Mode ......14
8. Message Authentication Code (MAC) Generation Mode ..............15
9. Security Considerations ........................................17
10. Normative References ..........................................17
Appendix A. Values of the Constants C1 and C2 .....................18
Appendix B. Contributors ..........................................19
1. Introduction
1.1. General Information
[GOST28147-89] is the unified cryptographic transformation algorithm
for information processing systems of different purposes, defining
the encryption/decryption rules and the message authentication code
(MAC) generation rules.
This cryptographic transformation algorithm is intended for hardware
or software implementation and corresponds to the cryptographic
requirements. It puts no limitations on the encrypted information
secrecy level.
2. Applicability
GOST 28147-89 defines the encryption/decryption model and MAC
generation for a given message (document) that is meant for
transmission via insecure public telecommunication channels between
data processing systems of different purposes.
GOST 28147-89 is obligatory to use in the Russian Federation in all
data processing systems providing public services.
3. Definitions and Notations
3.1. Definitions
The following terms are used in the standard:
Running key: a pseudo-random bit sequence generated by a given
algorithm for encrypting plain texts and decrypting encrypted texts.
Encryption: the process of transforming plain text to encrypted data
using a cipher.
MAC: an information string of fixed length that is generated from
plain text and a key according to some rule and added to the
encrypted data for protection against data falsification.
Key: a defined secret state of some parameters of a cryptographic
transformation algorithm, that provides a choice of one
transformation out of all the possible transformations.
Cryptographic protection: data protection using the data
cryptographic transformations.
Cryptographic transformation: data transformation using encryption
and (or) MAC.
Decryption: the process of transforming encrypted data to plain text
using a cipher.
Initialization vector: initial values of plain parameters of a
cryptographic transformation algorithm.
EID 2136 (Verified) is as follows:Section: 3.1
Original Text:
Initialisation vector: initial values of plain parameters of a
cryptographic transformation algorithm.
Corrected Text:
Initialization vector: initial values of plain parameters of a
cryptographic transformation algorithm.
Notes:
None
Encryption equation: a correlation showing the process of generating
encrypted data out of plain text as a result of transformations
defined by the cryptographic transformation algorithm.
Decryption equation: a correlation showing the process of generating
plain text out of encrypted data as a result of transformations
defined by the cryptographic transformation algorithm.
Cipher: a set of reversible transformations of the set of possible
plain texts onto the set of encrypted data carried out by specified
rules with the use of keys.
EID 2137 (Verified) is as follows:Section: 3.1
Original Text:
Cipher: a set of reversible transformations of the set of possible
plain texts onto the set of encrypted data, made after certain rules
and using keys.
Corrected Text:
Cipher: a set of reversible transformations of the set of possible
plain texts onto the set of encrypted data carried out by specified
rules with the use of keys.
Notes:
"After" does not mean "as a result."
3.2. Notation
In this document, the following notations are used:
^ is a power operator.
(+) is a bitwise addition of the words of the same length modulo 2.
[+] is an addition of 32-bit vectors modulo 2^32.
[+]' is an addition of the 32-bit vectors modulo 2^32-1.
1..N is all values from 1 to N.
4. General Statements
The structure model of the cryptographic transformation algorithm (a
cryptographic model) contains:
- a 256-bit key data store (KDS) consisting of eight 32-bit registers
(X0, X1, X2, X3, X4, X5, X6, X7);
- four 32-bit registers (N1, N2, N3, N4);
- two 32-bit registers (N5 and N6) containing constants C1 and C2;
- two 32-bit adders modulo 2^32 (CM1, CM3);
- a 32-bit adder of bitwise sums modulo 2 (CM2);
- a 32-bit adder modulo (2^32-1) (CM4);
- an adder modulo 2 (CM5), with no limitation to its width;
- a substitution box (K);
- a register for a cyclic shift of 11 steps to the top digit (R).
A substitution box (S-box) K consists of eight substitution points
K1, K2, K3, K4, K5, K6, K7, K8, with 64-bit memory. A 32-bit vector
coming to the substitution box is divided into eight successive 4-bit
vectors, and each of them is transformed into a 4-bit vector by a
corresponding substitution point. A substitution point is a table
consisting of 16 lines, each containing four bits. The incoming
vector defines the line address in the table, and the contents of
that line is the outgoing vector. Then, these 4-bit outgoing vectors
are successively combined into a 32-bit vector.
Remark: the standard doesn't define any S-boxes. Some of them are
defined in [RFC4357].
When adding and cyclically shifting binary vectors, the registers
with larger numbers are considered the top digits.
When writing a key (W1, W2, ..., W256), Wq = 0..1, q = 1..256, in the
KDS:
- the value W1 is written into the 1st bit of the register X0;
- the value W2 is written into the 2nd bit of the register X0 (etc.);
- the value W32 is written into the 32nd bit of the register X0;
- the value W33 is written into the 1st bit of the register X1;
- the value W34 is written into the 2nd bit of the register X1
(etc.);
- the value W64 is written into the 32nd bit of the register X1;
- the value W65 is written into the 1st bit of the register X2
(etc.);
- the value W256 is written into the 32nd bit of the register X7.
EID 2138 (Verified) is as follows:Section: 4
Original Text:
When writing a key (W1, W2, ..., W256), Wq = 0..1, q = 1..256, in the
KDS the value:
- W1 is written into the 1st bit of the register X0;
- the value W2 is written into the 2nd bit of the register X0 (etc.);
- the value W32 is written into the 32nd bit of the register X0;
- the value W33 is written into the 1st bit of the register X1;
- the value W34 is written into the 2nd bit of the register X1
(etc.);
- the value W64 is written into the 32nd bit of the register X1;
- the value W65 is written into the 1st bit of the register X2
(etc.);
- the value W256 is written into the 32nd bit of the register X7.
Corrected Text:
When writing a key (W1, W2, ..., W256), Wq = 0..1, q = 1..256, in the
KDS:
- the value W1 is written into the 1st bit of the register X0;
- the value W2 is written into the 2nd bit of the register X0 (etc.);
- the value W32 is written into the 32nd bit of the register X0;
- the value W33 is written into the 1st bit of the register X1;
- the value W34 is written into the 2nd bit of the register X1
(etc.);
- the value W64 is written into the 32nd bit of the register X1;
- the value W65 is written into the 1st bit of the register X2
(etc.);
- the value W256 is written into the 32nd bit of the register X7.
Notes:
None
When rewriting the information, the value of the p-th bit of one
register (adder) is written into the p-th bit of another register
(adder).
The values of the constants C1 and C2 in the registers N5 and N6 are
in the Appendix 1.
The keys defining fillings of KDS and the substitution box K tables
are secret elements and are provided in accordance with the
established procedure.
The filling of the substitution box K is described in GOST 28147-89
as a long-term key element common for a whole computer network.
Usually, K is used as a parameter of algorithm, some possible sets of
K are described in [RFC4357].
The cryptographic model contemplates four working modes:
- data encryption (decryption) in the electronic codebook (ECB) mode,
- data encryption (decryption) in the counter (CNT) mode,
- data encryption (decryption) in the cipher feedback (CFB) mode, and
- the MAC generation mode.
[RFC4357] also describes the CBC mode of GOST 28147-89, but this mode
is not a part of the standard.
5. The Electronic Codebook Mode
5.1. Encryption of Plain Text in the Electronic Codebook Mode
The plain text to be encrypted is split into 64-bit blocks. Input of
any binary data block Tp = (a1(0), a2(0), ... , a31(0), a32(0), b1(0),
b2(0), ..., b32(0)) into the registers N1 and N2 is done so that the
value of a1(0) is put into the first bit of N1, the value of a2(0) is
put into the second bit of N1, etc., and the value of a32(0) is put
into the 32nd bit of N1. The value of b1(0) is put into the first
bit of N2, the value of b2(0) is put into the 2nd bit of N2, etc.,
and the value of b32(0) is input into the 32nd bit of N2.
EID 2139 (Verified) is as follows:Section: 5.1
Original Text:
The plain text to be encrypted is split into 64-bit blocks. Input of
a binary data block Tp = (a1(0), a2(0), ... , a31(0), a32(0), b1(0),
b2(0), ..., b32(0)) into the registers N1 and N2 is done so that the
value of a1(0) is put into the first bit of N1, the value of a2(0) is
put into the second bit of N1, etc., and the value of a32(0) is put
into the 32nd bit of N1. The value of b1(0) is put into the first
bit of N2, the value of b2(0) is put into the 2nd bit of N2, etc.,
and the value of b32(0) is input into the 32nd bit of N2.
Corrected Text:
The plain text to be encrypted is split into 64-bit blocks. Input of
any binary data block Tp = (a1(0), a2(0), ... , a31(0), a32(0), b1(0),
b2(0), ..., b32(0)) into the registers N1 and N2 is done so that the
value of a1(0) is put into the first bit of N1, the value of a2(0) is
put into the second bit of N1, etc., and the value of a32(0) is put
into the 32nd bit of N1. The value of b1(0) is put into the first
bit of N2, the value of b2(0) is put into the 2nd bit of N2, etc.,
and the value of b32(0) is input into the 32nd bit of N2.
Notes:
None
The result is the state (a32(0), a31(0), ..., a2(0), a1(0)) of the
register N1 and the state (b32(0), b31(0), ..., b1(0)) of the
register N2.
The 256 bits of the key are entered into the KDS. The contents of
eight 32-bit registers X0, X1, ..., X7 are:
X0 = W32, W31, ..., W2, W1
X1 = W64, W63, ..., W34, W33
. . . . . . . . . . . . . . .
X7 = W256, W255, ..., W226, W225
The algorithm for enciphering 64-bit blocks of plain text in the
electronic codebook mode consists of 32 rounds.
In the first round, the initial value of register N1 is added modulo
2^32 in the adder CM1 to the contents of the register X0. Note: the
value of register N1 is unchanged.
The result of the addition is transformed in the substitution block
K, and the resulting vector is put into the register R, where it is
cyclically shifted by 11 steps towards the top digit. The result of
this shift is added bitwise modulo 2 in the adder CM2 to the 32-bit
contents of the register N2. The result produced in CM2 is then
written into N1, and the old contents of N1 are written in N2. Thus,
the first round ends.
The subsequent rounds are similar to the first one:
- in the second round, the contents of X1 are read from the KDS;
- in the third round, the contents of X2 are read from the KDS, etc.;
- in the 8th round, the contents of X7 are read from the KDS.
- in rounds 9 through 16 and 17 through 24, the contents of the KDS
are read in the same order:
X0, X1, X2, X3, X4, X5, X6, X7.
- in the last eight rounds from the 25th to the 32nd, the contents of
the KDS are read backwards:
X7, X6, X5, X4, X3, X2, X1, X0.
Thus, during the 32 rounds of encryption, the following order of
choosing the registers' contents is implemented:
X0, X1, X2, X3, X4, X5, X6, X7, X0, X1, X2, X3, X4, X5, X6, X7,
X0, X1, X2, X3, X4, X5, X6, X7, X7, X6, X5, X4, X3, X2, X1, X0
In the 32nd round, the result in the adder CM2 is written into the
register N2, and the old contents of register N1 are unchanged.
After the 32nd round, the contents of the registers N1 and N2 are an
encrypted data block corresponding to a block of plain text.
The equations for enciphering in the electronic codebook mode are:
|a(j) = (a(j-1) [+] X(j-1)(mod 8))*K*R (+) b (j-1)
| j = 1..24;
|b(j) = a(j-1)
|a(j) = (a(j-1) [+] X(32-j))*K*R (+) b(j-1)
| j = 25..31; a32 = a31;
|b(j) = a(j-1)
b(32) = (a(31) [+] X0)*K*R (+) b(31) j=32,
where:
a(0) = (a32(0), a31(0), ..., a1(0)) constitutes the initial contents
of N1 before the first round of encryption;
b(0) = (b32(0), b31(0), ..., b1(0)) constitutes the initial contents
of N2 before the first round of encryption;
a(j) = (a32(j), a31(j), ..., a1(j)) constitutes the contents of N1
after the j-th round of encryption;
b(j) = (b32(j), b31(j), ..., b1(j)) constitutes the contents of N2
after the j-th round of encryption, j = 1..32.
R is the operation of cyclic shift towards the top digit by 11 steps,
as follows:
R(r32, r31, r30, r29, r28, r27, r26, r25, r24, r23, r22, r21,
r20, ..., r2, r1) =
(r21, r20, ..., r2, r1, r32, r31, r30, r29, r28, r27, r26, r25,
r24, r23, r22)
The 64-bit block of ciphertext Tc is taken out of the registers N1,
N2 in the following order:
the first, second, ..., 32nd bit of the register N1, then the first,
second, ..., 32nd bit of the register N2, i.e.,
Tc = a1(32), a2(32), ..., a32(32), b1(32), b2(32), ..., b32(32)).
The remaining blocks of the plain text in electronic codebook mode
are encrypted in the same fashion.
5.2. Decryption of the Ciphertext in the Electronic Codebook Mode
The same 256-bit key that was used for encryption is loaded into the
KDS, the encrypted data to be deciphered is divided into 64-bit
blocks. The loading of any binary information block
Tc = (a1(32), a2(32), ..., a32(32), b1(32), b2(32), ..., b32(32))
into the registers N1 and N2 is done in such a way that:
- the contents of a1(32) are written into the first bit of N1;
- the contents of a2(32) are written into the second bit of N1 (and
so on);
- the contents of a32(32) are written into the 32nd bit of N1;
- the contents of b1(32) are written into the first bit of N2 (and so
on);
- and the contents of b32(32) are written into the 32nd bit of N2.
The decryption procedure uses the same algorithm as the encryption of
plain text, with one exception: the contents of the registers X0, X1,
..., X7 are read from the KDS in the decryption rounds in the
following order:
X0,X1,X2,X3,X4,X5,X6,X7, X7,X6,X5,X4,X3,X2,X1,X0,
X7,X6,X5,X4,X3,X2,X1,X0, X7,X6,X5,X4,X3,X2,X1,X0.
The decryption equations are:
|a(32-j) = (a(32-j+1) [+] X(j-1))*K*R (+) b(32-j+1)
| j = 1..8;
|b(32-1) = a(32-j+1)
|a(32-j) = (a(32-j+1) [+] X(j-1)(mod 8))*K*R (+) b(32-j+1)
| j = 9..31;
|b(32-1) = a(32-j+1)
|a(0) = a(1)
| j=32.
|b(0) = (a(1) [+] X0)*K*R (+) b1
After 32 working rounds contents of registers N1 and N2 are a plain text block.
EID 2140 (Verified) is as follows:Section: 5.2
Original Text:
The fillings of the adders N1 and N2 after 32 working rounds are a
plain text block.
Corrected Text:
After 32 working rounds contents of registers N1 and N2 are a plain text block.
Notes:
N1 and N2 aren't adders.
Tp = (a1(0), a2(0), ... , a32(0), b1(0), b2(0), ..., b32(0))
corresponding to the encrypted data block:
- the value of a1(0) of the block Tp corresponds to the contents of
the first bit of N1;
- the value of a2(0) corresponds to the contents of the second bit of
N1 (etc.);
- the value of b1(0) corresponds to the contents of the first bit of
N2;
- the value of b2(0) corresponds to the contents of the second bit of
N2 (etc.);
- the value of b32(0) corresponds to the contents of 32nd bit of N2;
- the remaining blocks of encrypted data are decrypted similarly.
The encryption algorithm in the electronic codebook mode of a 64-bit
block Tp is denoted by A, that is:
A(Tp) = A(a(0), b(0)) = (a(32), b(32)) = Tc.
EID 2141 (Verified) is as follows:Section: 5.2
Original Text:
A(Tp) is A(a(0), b(0)) = (a(32), b(32)) = Tc.
Corrected Text:
A(Tp) = A(a(0), b(0)) = (a(32), b(32)) = Tc.
Notes:
None
6. The Counter Encryption Mode
6.1. Encryption of Plain Text in the Counter Encryption Mode
The plain text divided into 64-bit blocks Tp(1), Tp(2), ..., Tp(M-1),
Tp(M) is encrypted in the counter encryption mode by bitwise addition
modulo 2 in the adder CM5 with the running key Gc produced in 64-bit
blocks, that is:
Gc = (Gc(1), Gc(2), ..., Gc(M-1), Gc(M))
where M is defined by the size of the plain text being encrypted.
Gc(i) is the i-th 64-bit block where i=1..M, the number of bits in a
block Tp(M) can be less than 64. In this case, the unused part of
the running key block Gc(M) is discarded.
256 bits of the key are put into the KDS. The registers N1 and N2
accept a 64-bit binary sequence (an initialisation vector) S = (S1,
S2, ..., S64), that is, the initial filling of these registers for
subsequent generation of M blocks of the running key. The
initialisation vector is put into the registers N1 and N2 so:
- the value of S1 is written into the first bit of N1;
- the value of S2 is written into the second bit of N1 (etc.);
- the value of S32 is written into the 32nd bit of N1;
- the value of S33 is written into the first bit of N2;
- the value of S34 is written into the second bit of N2 (etc.);
- the value of S64 is written into the 32nd bit of N2.
EID 2094 (Verified) is as follows:Section: 6.1
Original Text:
- the value of S1 is written into the first bit of N1;
- the value of S2 is written into the second bit of N1 (etc.);
- the value of S32 is written into the 32nd bit of N1;
- the value of S33 is written into the first bit of N2;
- the value of S34 is written into the 33th bit of N2 (etc.);
- the value of S64 is written into the 32nd bit of N2.
Corrected Text:
- the value of S1 is written into the first bit of N1;
- the value of S2 is written into the second bit of N1 (etc.);
- the value of S32 is written into the 32nd bit of N1;
- the value of S33 is written into the first bit of N2;
- the value of S34 is written into the second bit of N2 (etc.);
- the value of S64 is written into the 32nd bit of N2.
Notes:
The initial filling of the registers N1 and N2 (the initialisation
vector S) is encrypted in the electronic codebook mode in accordance
with the requirements from section 5.1. The result of that
encryption A(S) = (Y0, Z0) is rewritten into the 32-bit registers N3
and N4 so as the contents of N1 are written into N3, and the contents
of N2 are written into N4.
The filling of the register N4 is added modulo (2^32-1) in the adder
CM4 to the 32-bit constant C1 from the register N6; the result is
written into N4. The filling of the register N3 is added modulo 2^32
in the adder CM3 with the 32-bit constant C2 from the register N5;
the result is written into N3.
The filling of N3 is copied into N1, and the filling of N4 is copied
into N2, while the fillings of N3 and N4 are kept.
The filling of N1 and N2 is encrypted in the electronic codebook mode
according to the requirements of section 5.1. The resulting
encrypted filling of N1 and N2 is the first 64-bit block of the
running key Gc(1), this block is bitwise added modulo 2 in the adder
CM5 with the first 64-bit block of the plain text:
Tp(1) = (t1(1), t2(1), ..., t63(1), t64(1)).
The result of this addition is a 64-bit block of the encrypted data:
Tc(1) = (tau1(1), tau2(1), ..., tau63(1), tau64(1)).
The value of tau1(1) of the block Tc(1) is the result of the addition
of modulo 2 in the CM5 the value t1(1) of the block Tp(1) to the
value of the first bit of N1; the value of tau2(1) of the block Tc(1)
is the result of addition modulo 2 in the CM5 the value of t2(1) from
the block Tp(1) to the value of the second bit of N1, etc.; the value
of tau64(1) of the block Tc(1) is the result of addition modulo 2 in
the CM5 of the value t64(1) of the block Tp(1) to the value of the
32nd bit of N2.
To get the next 64-bit block of the running key Gc(2), the filling of
N4 is added modulo (2^32-1) in the adder CM4 with the constant C1
from N6; the filling of N3 is added modulo 2^32 in the adder CM3 with
the constant C2 from N5. The new filling of N3 is copied into N1;
the new filling of N4 is copied into N2; the fillings of N3 and N4
are kept.
The filling of N1 and N2 is encrypted in the electronic codebook mode
according to the requirements of section 5.1. The resulting
encrypted filling of N1 and N2 is the second 64-bit block of the
running key Gc(2); this block is bitwise added modulo 2 in the adder
CM5 with the second 64-bit block of the plain text Tp(2). The
EID 2144 (Verified) is as follows:Section: 6.1
Original Text:
The filling of N1 and N2 is encrypted in the electronic codebook mode
according to the requirements of section 5.1. The resulting
encrypted filling of N1 and N2 is the second 64-bit block of the
running key Gc(2); this block is bitwise added modulo 2 in the adder
CM5 with the first 64-bit block of the plain text Tp(2).
Corrected Text:
The filling of N1 and N2 is encrypted in the electronic codebook mode
according to the requirements of section 5.1. The resulting
encrypted filling of N1 and N2 is the second 64-bit block of the
running key Gc(2); this block is bitwise added modulo 2 in the adder
CM5 with the second 64-bit block of the plain text Tp(2).
Notes:
None
remaining running key blocks Gc(3), Gc(4), ..., Gc(M) are generated
and the plain text blocks Tp(3), Tp(4), ..., Tp(M) are encrypted
similarly. If the length of the last M-th block of the plain text is
less than 64 bits, then only the corresponding number of bits from
the last M-th block of the running key is used; remaining bits are
discarded.
The initialisation vector S and the blocks of encrypted data Tc(1),
Tc(2), ..., Tc(M) are transmitted to the telecommunication channel or
to the computer memory.
The encryption equation is:
Tc(i) = A(Y[i-1] [+] C2, Z[i-1]) [+]' C1) (+) Tp(i)
= Gc(i) (+) Tp(i) i=1..M
where:
Y[i] is the contents of the register N3 after encrypting the
i-th block of the plain text Tp(i);
Z(i) is the contents of the register N4 after encrypting the
i-th block of the plain text Tp(i);
(Y[0], Z[0]) = A(S).
6.2. Decryption of Ciphertext in the Counter Encryption Mode
256 bits of the key that was used for encrypting the data Tp(1),
Tp(2), ..., Tp(M) are put into the KDS. The initialisation vector S
is put into the registers N1 and N2 and, like in the section 6.1 M
blocks of the running key, Gc(1), Gc(2), ..., Gc(M) are generated.
The encrypted data blocks Tc(1), Tc(2), ..., Tc(M) are added bitwise
modulo 2 in the adder CM5 with the blocks of the running key, and
this results in the blocks of plain text Tp(1), Tp(2), ..., Tp(M),
and Tp(M) may contain less than 64 bit.
The decryption equation is:
Tp(i) = A (Y[i-1] [+] C2, Z[i-1] [+]' C1) (+) Tc(i)
= Gc(i) (+) Tc(i) i = 1..M
7. The Cipher Feedback Mode
7.1. Encryption of Plain Text in the Cipher Feedback Mode
The plain text is divided into 64-bit blocks Tp(1), Tp(2), ..., Tp(M)
and encrypted in the cipher feedback mode by bitwise addition modulo
2 in the adder CM5 with the running key Gc generated in 64-bit
blocks, i.e., Gc(i)=(Gc(1), Gc(2), ..., Gc(M)), where M is defined by
the length of the plain text, Gc(i) is the i-th 64-bit block, i=1,M.
The number of bits in the block Tp(M) may be less than 64.
EID 2135 (Verified) is as follows:Section: 7.1
Original Text:
The plain text is divided into 64-bit blocks Tp(1), Tp(2), ..., Tp(M)
and encrypted in the cipher feedback mode by bitwise addition modulo
2 in the adder CM5 with the running key Gc generated in 64-bit
blocks, i.e., Gc(i)=(Gc(1), Gc(2), ..., Gc(M)), where M is defined by
___
the length of the plain text, Gc(i) is the i-th 64-bit block, i=1,M.
The number of bits in the block Tp(M) may be less than 64.
Corrected Text:
The plain text is divided into 64-bit blocks Tp(1), Tp(2), ..., Tp(M)
and encrypted in the cipher feedback mode by bitwise addition modulo
2 in the adder CM5 with the running key Gc generated in 64-bit
blocks, i.e., Gc(i)=(Gc(1), Gc(2), ..., Gc(M)), where M is defined by
the length of the plain text, Gc(i) is the i-th 64-bit block, i=1,M.
The number of bits in the block Tp(M) may be less than 64.
Notes:
None
EID 2145 (Verified) is as follows:Section: 7.1
Original Text:
The plain text is divided into 64-bit blocks Tp(1), Tp(2), ..., Tp(M)
and encrypted in the cipher feedback mode by bitwise addition modulo
2 in the adder CM5 with the running key Gc generated in 64-bit
blocks, i.e., Gc(i)=(Gc(1), Gc(2), ..., Gc(M)), where M is defined by
___
the length of the plain text, Gc(i) is the i-th 64-bit block, i=1,M.
The number of bits in the block Tp(M) may be less than 64.
Corrected Text:
The plain text is divided into 64-bit blocks Tp(1), Tp(2), ..., Tp(M)
and encrypted in the cipher feedback mode by bitwise addition modulo
2 in the adder CM5 with the running key Gc generated in 64-bit
blocks, i.e., Gc(i)=(Gc(1), Gc(2), ..., Gc(M)), where M is defined by
the length of the plain text, Gc(i) is the i-th 64-bit block, i=1..M.
The number of bits in the block Tp(M) may be less than 64.
Notes:
None
256 bits of the key are put into the KDS. The 64-bit initialisation
vector S = (S1, S2, ..., S64) is put into N1 and N2 as described in
section 6.1.
The initial filling of N1 and N2 is encrypted in the electronic
codebook mode in accordance with the requirements in section 5.1. If
resulting encrypted filling N1 and N2 is the first 64-bit block of
the running key Gc(1)=A(S), then this block is added bitwise modulo 2
with the first 64-bit block of plain text Tp(1) = (t1(1), t2(1), ...,
t64(1)).
EID 2146 (Verified) is as follows:Section: 7.1
Original Text:
The initial filling of N1 and N2 is encrypted in the electronic
codebook mode in accordance with the requirements in section 6.1. If
resulting encrypted filling N1 and N2 is the first 64-bit block of
the running key Gc(1)=A(S), then this block is added bitwise modulo 2
with the first 64-bit block of plain text Tp(1) = (t1(1), t2(1), ...,
t64(1)).
Corrected Text:
The initial filling of N1 and N2 is encrypted in the electronic
codebook mode in accordance with the requirements in section 5.1. If
resulting encrypted filling N1 and N2 is the first 64-bit block of
the running key Gc(1)=A(S), then this block is added bitwise modulo 2
with the first 64-bit block of plain text Tp(1) = (t1(1), t2(1), ...,
t64(1)).
Notes:
None
EID 2148 (Verified) is as follows:Section: 7.1
Original Text:
The initial filling of N1 and N2 is encrypted in the electronic
codebook mode in accordance with the requirements in section 6.1. If
resulting encrypted filling N1 and N2 is the first 64-bit block of
the running key Gc(1)=A(S), then this block is added bitwise modulo 2
with the first 64-bit block of plain text Tp(1) = (t1(1), t2(1), ...,
t64(1)).
Corrected Text:
The initial filling of N1 and N2 is encrypted in the electronic
codebook mode in accordance with the requirements in section 6.1. The
resulting encrypted filling N1 and N2 is the first 64-bit block of
the running key Gc(1)=A(S), then this block is added bitwise modulo 2
in the adder CM5 with the first 64-bit block of plain text Tp(1) =
(t1(1), t2(1), ..., t64(1)).
Notes:
None
The result is a 64-bit block of encrypted data
Tc(1) = (tau1(1), tau2(1), ..., tau64(1)).
The block of encrypted data Tc(1) is simultaneously the initial state
of N1 and N2 for generating the second block of the running key Gc(2)
and is written on feedback in these registers. Here:
- the value of tau1(1) is written into the first bit of N1;
- the value of tau2(1) is written into the second bit of N1, etc.;
- the value of tau32(1) is written into the 32nd bit of N1;
- the value of tau33(1) is written into the first bit of N2;
- the value of tau34(1) is written into the second bit of N2, etc.;
- the value of tau64(1) is written into the 32nd bit of N2.
The filling of N1 and N2 is encrypted in the electronic codebook mode
in accordance with the requirements in the section 5.1. The
encrypted filling of N1 and N2 makes the second 64-bit block of the
running key Gc(2), this block is added bitwise modulo 2 in the adder
CM5 to the second block of the plain text Tp(2).
EID 2147 (Verified) is as follows:Section: 7.1
Original Text:
The filling of N1 and N2 is encrypted in the electronic codebook mode
in accordance with the requirements in the section 6.1. The
encrypted filling of N1 and N2 makes the second 64-bit block of the
running key Gc(2), this block is added bitwise modulo 2 in the adder
CM5 to the second block of the plain text Tp(2).
Corrected Text:
The filling of N1 and N2 is encrypted in the electronic codebook mode
in accordance with the requirements in the section 5.1. The
encrypted filling of N1 and N2 makes the second 64-bit block of the
running key Gc(2), this block is added bitwise modulo 2 in the adder
CM5 to the second block of the plain text Tp(2).
Notes:
None
The generation of subsequent blocks of the running key Gc(i) and the
encryption of the corresponding blocks of the plain text Tp(i) (i =
3..M) are performed similarly. If the length of the last M-th block
of the plain text is less than 64 bits, only the corresponding number
of bits of the M-th block of the running key Gc(M) is used; remaining
bits are discarded.
The encryption equations in the cipher feedback mode are:
|Tc(1) = A(S) (+) Tp(1) = Gc(1) (+) Tp(1)
|
|Tc(i) = A(Tc(i-1)) (+) Tp(i) = Gc(i) + Tp(i), i = 2..M.
The initialisation vector S and the blocks of encrypted data Tc(1),
Tc(2), ..., Tc(M) are transmitted into the telecommunication channel
or to the computer memory.
7.2. Decryption of Ciphertext in the Cipher Feedback Mode
256 bits of the key used for the encryption of Tp(1), Tp(2), ...,
Tp(M) are put into the KDS. The initialisation vector S is put into
N1 and N2 similar to 6.1.
The initial filling of N1 and N2 (the initialisation vector S) is
encrypted in the electronic codebook mode in accordance with the
subsection 5.1. The encrypted filling of N1, N2 is the first block
of the running key Gc(1) = A(S), this block is added bitwise modulo 2
in the adder CM5 with the encrypted data block Tc(1). This results
in the first block of plain text Tp(1).
EID 2149 (Verified) is as follows:Section: 7.2
Original Text:
The initial filling of N1 and N2 (the initialisation vector S) is
encrypted in the electronic codebook mode in accordance with the
subsection 6.1. The encrypted filling of N1, N2 is the first block
of the running key Gc(1) = A(S), this block is added bitwise modulo 2
in the adder CM5 with the encrypted data block Tc(1). This results
in the first block of plain text Tp(1).
Corrected Text:
The initial filling of N1 and N2 (the initialisation vector S) is
encrypted in the electronic codebook mode in accordance with the
subsection 5.1. The encrypted filling of N1, N2 is the first block
of the running key Gc(1) = A(S), this block is added bitwise modulo 2
in the adder CM5 with the encrypted data block Tc(1). This results
in the first block of plain text Tp(1).
Notes:
None
The block of encrypted data Tc(1) makes the initial filling of N1, N2
for generating the second block of the running key Gc(2). The block
Tc(1) is written in N1 and N2 in accordance with the requirements in
the subsection 6.1. The filling of N1 and N2 is encrypted in the electronic
codebook mode according to the requirements of section 5.1. The encrypted
filling of N1 and N2 makes the second 64-bit block Gc(2) which is added
bitwise modulo 2 in the adder CM5 to the second block of the encrypted data
Tc(2). This results in the block of plain text Tc(2).
EID 2152 (Verified) is as follows:Section: 7.2
Original Text:
The block of encrypted data Tc(1) makes the initial filling of N1, N2
for generating the second block of the running key Gc(2). The block
Tc(1) is written in N1 and N2 in accordance with the requirements in
the subsection 6.1, the resulted block Gc(2) is added bitwise modulo
2 in the adder CM5 to the second block of the encrypted data Tc(2).
This results in the block of plain text Tc(2).
Corrected Text:
The block of encrypted data Tc(1) makes the initial filling of N1, N2
for generating the second block of the running key Gc(2). The block
Tc(1) is written in N1 and N2 in accordance with the requirements in
the subsection 6.1. The filling of N1 and N2 is encrypted in the electronic
codebook mode according to the requirements of section 5.1. The encrypted
filling of N1 and N2 makes the second 64-bit block Gc(2) which is added
bitwise modulo 2 in the adder CM5 to the second block of the encrypted data
Tc(2). This results in the block of plain text Tc(2).
Notes:
One necessary statement was missed in the text.
Similarly, the blocks of encrypted data Tc(2), Tc(3), ..., Tc(M-1)
are written in N1, N2 successively, and the blocks of the running key
Gc(3), Gc(4), ..., Gc(M) are generated out of them in the electronic
codebook mode. The blocks of the running key are added bitwise
modulo 2 in the adder CM5 to the blocks of the encrypted data Tc(3),
Tc(4), ..., Tc(M), this results in the blocks of plain text Tp(3),
Tp(4), ..., Tp(M); here, the number of bits in the last block of the
plain text Tp(M) can be less than 64 bit.
The decryption equations in the cipher feedback mode are:
|Tp(1) = A(S) (+) Tc(1) = Gc(1) (+) Tc(1)
|
|Tp(1) = A(Tc(i-1)) (+) Tc(i) = Gc(i) (+) Tc(i), i=2..M
8. Message Authentication Code (MAC) Generation Mode
To provide the protection from falsification of plain text consisting
of M 64-bit blocks Tp(1), Tp(2), ..., Tp(M), M >= 2, an additional
l-bit block is generated (the message authentication code I(l)). The
process of MAC generation is the same for all the
encryption/decryption modes.
The first block of plain text:
Tp(1) = (t1(1), t1(2), ..., t64(1)) = (a1(1)[0], a2(1)[0], ...,
a32(1)[0], b1(1)[0], b2(1)[0], ..., b32(1)[0])
EID 2150 (Verified) is as follows:Section: 8
Original Text:
- The first block of plain text:
Tp(1) = (t1(1), t1(2), ..., t64(1)) = (a1(1)[0], a2(1)[0], ...,
a32(1)[0], b1(1)[0], b2(1)[0], ..., b32(1)[0])
Corrected Text:
The first block of plain text:
Tp(1) = (t1(1), t1(2), ..., t64(1)) = (a1(1)[0], a2(1)[0], ...,
a32(1)[0], b1(1)[0], b2(1)[0], ..., b32(1)[0])
Notes:
None
is written to the registers N1 and N2;
- the value of t1(1) = a1(1)[0] is written into the first bit of N1;
- the value of t2(1) = a2(1)[0] is written into the second bit of N1,
etc.;
- the value of t32(1) = a32(1)[0] is written into the 32nd bit of N1;
- the value of t33(1) = b1(1)[0] is written into the first bit of N2,
etc.;
- the value of t64(1) = b32(1)[0] is written into the 32nd bit of N2.
The filling of N1 and N2 is transformed in accordance with the first
16 rounds of the encryption algorithm in the electronic codebook mode
(see the subsection 5.1). In the KDS, there exists the same key that
is used for encrypting the blocks of plain text Tp(1), Tp(2), ...,
Tp(M) in the corresponding blocks of encrypted data Tc(1), Tc(2),
..., Tc(M).
EID 2151 (Verified) is as follows:Section: 8
Original Text:
The filling of N1 and N2 is transformed in accordance with the first
16 rounds of the encryption algorithm in the electronic codebook mode
(see the subsection 6.1). In the KDS, there exists the same key that
is used for encrypting the blocks of plain text Tp(1), Tp(2), ...,
Tp(M) in the corresponding blocks of encrypted data Tc(1), Tc(2),
..., Tc(M).
Corrected Text:
The filling of N1 and N2 is transformed in accordance with the first
16 rounds of the encryption algorithm in the electronic codebook mode
(see the subsection 5.1). In the KDS, there exists the same key that
is used for encrypting the blocks of plain text Tp(1), Tp(2), ...,
Tp(M) in the corresponding blocks of encrypted data Tc(1), Tc(2),
..., Tc(M).
Notes:
None
The filling of N1 and N2 after the 16 working rounds, looking like
(a1(1)[16], a2(1)[16], ..., a32(1)[16], b1(1)[16], b2(1)[16], ...,
b32(1)[16]), is added in CM5 modulo 2 to the second block Tp(2) =
(t1(2), t2(2), ..., t64(2)).
The result of this addition
(a1(1)[16](+)t1(2), a2(1)[16](+)t2(2), ..., a32(1)[16](+)t32(2),
b1(1)[16](+)t33(2), b2(1)[16](+)t34(2), ..., b32(1)[16](+)t64(2))
=
(a1(2)[0], a2(2)[0] ..., a32(2)[0], b1(2)[0], b2(2)[0], ...,
b32(2)[0])
is written into N1 and N2 and is transformed in accordance with the
first 16 rounds of the encryption algorithm in the electronic
codebook mode.
The resulting filling of N1 and N2 is added in the CM5 modulo 2 with
the third block Tp(3), etc., the last block Tp(M) = (t1(M), t2(M),
..., t64(M)), padded if necessary to a complete 64-bit block by
zeros, is added in CM5 modulo 2 with the filling N1, N2
(a1(M-1)[16], a2(M-1)[16], ..., a32(M-1)[16], b1(M-1)[16],
b2(M-1)[16], ..., b32(M-1)[16]).
EID 2153 (Verified) is as follows:Section: 8
Original Text:
The resulting filling of N1 and N2 is added in the CM5 modulo 2 with
the third block Tp(3), etc., the last block Tp(M) = (t1(M), t2(M),
..., t64(M)), padded if necessary to a complete 64-bit block by
zeros, is added in CM5 modulo 2 with the filling N1, N2 (a1(M-1)[16],
a2(M-1)[16], ..., a32(M-1)[16], b1(M-1)[16], b2(M-1)[16], ...,
b32(M-1)[16]).
Corrected Text:
The resulting filling of N1 and N2 is added in the CM5 modulo 2 with
the third block Tp(3), etc., the last block Tp(M) = (t1(M), t2(M),
..., t64(M)), padded if necessary to a complete 64-bit block by
zeros, is added in CM5 modulo 2 with the filling N1, N2
(a1(M-1)[16], a2(M-1)[16], ..., a32(M-1)[16], b1(M-1)[16],
b2(M-1)[16], ..., b32(M-1)[16]).
Notes:
None
The result of the addition
(a1(M-1)[16](+)t1(M), a2(M-1)[16](+)t2(M), ..., a32(M-1)[16](+)
t32(M), b1(M-1)[16](+)t33(M), b2(M-1)[16](+)t34(M), ...,
b32(M-1)[16](+)t64(M))
=
(a1(M)[0], a2(M)[0] ..., a32(M)[0], b1(M)[0], b2(M)[0], ...,
b32(M)[0])
is written into N1, N2 and encrypted in the electronic codebook mode
after the first 16 rounds of the algorithm's work. Out of the
resulting filling of the registers N1 and N2:
(a1(M)[16], a2(M)[16] ..., a32(M)[16], b1(M)[16], b2(M)[16], ...,
b32(M)[16])
an l-bit string I(l) (the MAC) is chosen:
I(l) = [a(32-l+1)(M)[16], a(32-l+2)(M)[16], ..., a32(M)[16]].
The MAC I(l) is transmitted through the telecommunication channel or
to the computer memory attached to the end of the encrypted data,
i.e., Tc(1), Tc(2), ..., Tc(M), I(l).
he encrypted data Tc(1), Tc(2), ..., Tc(M), when arriving, are
decrypted, out of the resulting plain text blocks Tp(1), Tp(2), ...,
Tp(M). The MAC I'(l) is generated as described above
and compared with the MAC I(l) received together with the encrypted
data from the telecommunication channel or from the computer memory.
If the MACs are not equal, the resulting plain text blocks Tp(1),
Tp(2), ..., Tp(M) are considered false.
EID 2154 (Verified) is as follows:Section: 8
Original Text:
The encrypted data Tc(1), Tc(2), ..., Tc(M), when arriving, are
decrypted, out of the resulting plain text blocks Tp(1), Tp(2), ...,
Tp(M). The MAC I'(l) is generated as described in the subsection 5.3
and compared with the MAC I(l) received together with the encrypted
data from the telecommunication channel or from the computer memory.
If the MACs are not equal, the resulting plain text blocks Tp(1),
Tp(2), ..., Tp(M) are considered false.
Corrected Text:
he encrypted data Tc(1), Tc(2), ..., Tc(M), when arriving, are
decrypted, out of the resulting plain text blocks Tp(1), Tp(2), ...,
Tp(M). The MAC I'(l) is generated as described above
and compared with the MAC I(l) received together with the encrypted
data from the telecommunication channel or from the computer memory.
If the MACs are not equal, the resulting plain text blocks Tp(1),
Tp(2), ..., Tp(M) are considered false.
Notes:
wrong reference to the original text sections
The MAC I(l) (I'(l)) can be generated either before encryption (after
decryption, respectively) of the whole message or simultaneously with
the encryption (decryption) in blocks. The first plain text blocks,
used in the MAC generation, can contain service information (the
address section, a time mark, the initialisation vector, etc.) and
they may be unencrypted.
The parameter l value (the bit length of the MAC) is defined by the
actual cryptographic requirements, while considering that the
possibility of imposing false data is 2^-l.
9. Security Considerations
This entire document is about security considerations.
10. Normative References
[GOST28147-89] "Cryptographic Protection for Data Processing System",
GOST 28147-89, Gosudarstvennyi Standard of USSR,
Government Committee of the USSR for Standards, 1989.
(In Russian)
[RFC4357] Popov, V., Kurepkin, I., and S. Leontiev, "Additional
Cryptographic Algorithms for Use with GOST 28147-89,
GOST R 34.10-94, GOST R 34.10-2001, and GOST R
34.11-94 Algorithms", RFC 4357, January 2006.
Appendix A. Values of the Constants C1 and C2
The constant C1 is:
The bit of N6 32 31 30 29 28 27 26 25 24 23 22 21 20 19 18
The bit value 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0
The bit of N6 17 16 15 14 13 12 11 10 9 8 7 6 5 4 3 2 1
The bit value 1 0 0 0 0 0 0 0 1 0 0 0 0 0 1 0 0
The constant C2 is:
The bit of N5 32 31 30 29 28 27 26 25 24 23 22 21 20 19 18
The bit value 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0
The bit of N5 17 16 15 14 13 12 11 10 9 8 7 6 5 4 3 2 1
The bit value 1 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 1
EID 2692 (Verified) is as follows:Section: Appendix A
Original Text:
The constant C1 is:
The bit of N6 32 31 30 29 28 27 26 25 24 23 22 21 20 19 18
The bit value 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0
The bit of N6 17 16 15 14 13 12 11 10 9 8 7 6 5 4 3 2 1
The bit value 1 0 0 0 0 0 0 0 1 0 0 0 0 0 1 0 0
The constant C2 is:
The bit of N6 32 31 30 29 28 27 26 25 24 23 22 21 20 19 18
The bit value 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0
The bit of N6 17 16 15 14 13 12 11 10 9 8 7 6 5 4 3 2 1
The bit value 1 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 1
Corrected Text:
The constant C1 is:
The bit of N6 32 31 30 29 28 27 26 25 24 23 22 21 20 19 18
The bit value 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0
The bit of N6 17 16 15 14 13 12 11 10 9 8 7 6 5 4 3 2 1
The bit value 1 0 0 0 0 0 0 0 1 0 0 0 0 0 1 0 0
The constant C2 is:
The bit of N5 32 31 30 29 28 27 26 25 24 23 22 21 20 19 18
The bit value 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0
The bit of N5 17 16 15 14 13 12 11 10 9 8 7 6 5 4 3 2 1
The bit value 1 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 1
Notes:
C1 is stored in N6 and C2 is stored in N5 (not both in N6)