





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
   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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Copyright Notice

   Copyright (c) 2010 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
   (http://trustee.ietf.org/license-info) in effect on the date of
   publication of this document.  Please review these documents
   carefully, as they describe your rights and restrictions with respect
   to this document.

   This document may not be modified, and derivative works of it may not
   be created, except to format it for publication as an RFC or to
   translate it into languages other than English.

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











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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.





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   Cryptographic transformation: data transformation using encryption
   and (or) MAC.

   Decryption: the process of transforming encrypted data to plain text
   using a cipher.

   Initialisation vector: initial values of plain parameters of a
   cryptographic transformation algorithm.

   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, made after certain rules
   and using keys.

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);



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   - 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.





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   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
   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.

   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:



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      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




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   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)).



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   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




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   The fillings of the adders N1 and N2 after 32 working rounds are a
   plain text block.

      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) is A(a(0), b(0)) = (a(32), b(32)) = Tc.

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.








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   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 33th bit of N2 (etc.);

   - the value of S64 is written into the 32nd bit of N2.

   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)).






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   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 first 64-bit block of the plain text Tp(2).  The
   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).





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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.

   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 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)).

   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;



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   - 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 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).

   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 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).






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   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).

   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])

     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.



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   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).

   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]).

   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:




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      (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).

   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.

   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.






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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 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




























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Appendix B.  Contributors

   Dmitry Kabelev
   Cryptocom, Ltd.
   14 Kedrova St., Bldg. 2
   Moscow, 117218
   Russian Federation

   EMail: kdb@cryptocom.ru


   Igor Ustinov
   Cryptocom, Ltd.
   14 Kedrova St., Bldg. 2
   Moscow, 117218
   Russian Federation

   EMail: igus@cryptocom.ru


   Irene Emelianova
   Cryptocom Ltd.
   14 Kedrova St., Bldg. 2
   Moscow, 117218
   Russian Federation

   EMail: irene@cryptocom.ru

Author's Address

   Vasily Dolmatov, Ed.
   Cryptocom, Ltd.
   14 Kedrova St., Bldg. 2
   Moscow, 117218
   Russian Federation

   EMail: dol@cryptocom.ru














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