RFC 9337 GOST Password-Based Keys December 2022
Karelina Informational [Page]
Stream:
Independent Submission
RFC:
9337
Category:
Informational
Published:
ISSN:
2070-1721
Author:
E. Karelina, Ed.
InfoTeCS

RFC 9337

Generating Password-Based Keys Using the GOST Algorithms

Abstract

This document specifies how to use "PKCS #5: Password-Based Cryptography Specification Version 2.1" (RFC 8018) to generate a symmetric key from a password in conjunction with the Russian national standard GOST algorithms.

PKCS #5 applies a Pseudorandom Function (PRF) -- a cryptographic hash, cipher, or Hash-Based Message Authentication Code (HMAC) -- to the input password along with a salt value and repeats the process many times to produce a derived key.

This specification has been developed outside the IETF. The purpose of publication being to facilitate interoperable implementations that wish to support the GOST algorithms. This document does not imply IETF endorsement of the cryptographic algorithms used here.

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/rfc9337.

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Table of Contents

1. Introduction

This document provides a specification of usage of GOST R 34.12-2015 encryption algorithms and the GOST R 34.11-2012 hashing functions with PKCS #5. The methods described in this document are designed to generate key information using the user's password and to protect information using the generated keys.

2. Conventions Used in This Document

The key words "MUST", "MUST NOT", "REQUIRED", "SHALL", "SHALL NOT", "SHOULD", "SHOULD NOT", "RECOMMENDED", "NOT RECOMMENDED", "MAY", and "OPTIONAL" in this document are to be interpreted as described in BCP 14 [RFC2119] [RFC8174] when, and only when, they appear in all capitals, as shown here.

3. Basic Terms and Definitions

Throughout this document, the following notation is used:

Table 1: Terms and Definitions
Notation Definition
P a password encoded as a Unicode UTF-8 string
S a random initializing value
c a number of iterations of algorithm, a positive integer
dkLen a length in octets of derived key, a positive integer
DK a derived key of length dkLen
Bn a set of all octet strings of length n, n >= 0; if n = 0, then the set Bn consists of an empty string of length 0
A||C a concatenation of two octet strings A, C, i.e., a vector from B|A|+|C|, where the left subvector from B|A| is equal to the vector A and the right subvector from B|C| is equal to the vector C: A = (an1,...,a1) in Bn1 and C = (cn2,..., c1) in Bn2, res = (an1,...,a1,cn2,..., c1) in Bn1+n2)
\xor a bit-wise exclusive-or of two octet strings of the same length
MSBnr: Bn -> Br a truncating of an octet string to size r by removing the least significant n-r octets: MSBnr(an,...,an-r+1,an-r,...,a1) =(an,...,an-r+1)
LSBnr: Bn -> Br a truncating of an octet string to size r by removing the most significant n-r octets: LSBnr(an,...,an-r+1,an-r,...,a1) =(ar,...,a1)
Int(i) a four-octet encoding of the integer i =< 232: (i1, i2, i3, i4) in B4, i = i1 + 28 * i2 + 216 * i3 + 224 * i4
b[i, j] a substring extraction operator, extracts octets i through j, 0 =< i =< j
CEIL(x) the smallest integer greater than or equal to x

This document uses the following abbreviations and symbols:

Table 2: Abbreviations and Symbols
Abbreviations and Symbols Definition
HMAC_GOSTR3411 Hashed-Based Message Authentication Code. A function for calculating a Message Authentication Code (MAC) based on the GOST R 34.11-2012 hash function (see [RFC6986]) with 512-bit output in accordance with [RFC2104].

4. Algorithm for Generating a Key from a Password

The DK is calculated by means of a key derivation function PBKDF2 (P, S, c, dkLen) (see [RFC8018], Section 5.2) using the HMAC_GOSTR3411 function as the PRF:

DK = PBKDF2 (P, S, c, dkLen).

The PBKDF2 function is defined as the following algorithm:

  1. If dkLen > (232 - 1) * 64, output "derived key too long" and stop.
  2. Calculate n = CEIL (dkLen / 64).

  3. Calculate a set of values for each i from 1 to n:

    • U1(i) = HMAC_GOSTR3411 (P, S || INT (i)),
    • U2(i) = HMAC_GOSTR3411 (P, U1(i)),
    • ...
    • Uc(i) = HMAC_GOSTR3411 (P, Uc-1(i)),
    • T(i) = U1(i) \xor U2(i) \xor ... \xor Uc(i).

  4. Concatenate the octet strings T(i) and extract the first dkLen octets to produce a derived key DK:

    • DK = MSBn * 64dkLen(T(1)||T(2)||...||T(n))

5. Data Encryption

5.1. GOST R 34.12-2015 Data Encryption

Data encryption using the DK is carried out in accordance with the PBES2 scheme (see [RFC8018], Section 6.2) using GOST R 34.12-2015 in CTR_ACPKM mode (see [RFC8645]).

5.1.1. Encryption

The encryption process for PBES2 consists of the following steps:

  1. Select the random value S of a length from 8 to 32 octets.
  2. Select the iteration count c depending on the conditions of use (see [GostPkcs5]). The minimum allowable value for the parameter is 1000.
  3. Set the value dkLen = 32.

  4. Apply the key derivation function to the password P, the random value S, and the iteration count c to produce a derived key DK of length dkLen octets in accordance with the algorithm from Section 4. Generate the sequence T(1) and truncate it to 32 octets, i.e.,

    • DK = PBKDF2 (P, S, c, 32) = MSB6432(T(1)).

  5. Generate the random value ukm of size n, where n takes a value of 12 or 16 octets depending on the selected encryption algorithm:

    • GOST R 34.12-2015 "Kuznyechik" n = 16 (see [RFC7801])
    • GOST R 34.12-2015 "Magma" n = 12 (see [RFC8891])
  6. Set the value S' = ukm[1..n-8].
  7. For the id-gostr3412-2015-magma-ctracpkm and id-gostr3412-2015-kuznyechik-ctracpkm algorithms (see Section 7.3), encrypt the message M with the GOST R 34.12-2015 algorithm with the derived key DK and the random value S' to produce a ciphertext C.

  8. For the id-gostr3412-2015-magma-ctracpkm-omac and id-gostr3412-2015-kuznyechik-ctracpkm-omac algorithms (see Section 7.3), encrypt the message M with the GOST R 34.12-2015 algorithm with the derived key DK and the ukm in accordance with the following steps:

    • Generate two keys from the derived key DK using the KDF_TREE_GOSTR3411_2012_256 algorithm (see [RFC7836]):

      encryption key K(1)

      MAC key K(2)

      Input parameters for the KDF_TREE_GOSTR3411_2012_256 algorithm take the following values:

      Kin = DK

      label = "kdf tree" (8 octets)

      seed = ukm[n-7..n]

      R = 1

      The input string label above is encoded using ASCII (see [RFC0020]).

    • Compute the MAC for the message M using the K(2) key in accordance with the GOST R 34.12-2015 algorithm. Append the computed MAC value to the message M: M||MAC.
    • Encrypt the resulting octet string with MAC with the GOST R 34.12-2015 algorithm with the derived key K(1) and the random value S' to produce a ciphertext C.
  9. Serialize the parameters S, c, and ukm as algorithm parameters in accordance with Section 7.2.

5.1.2. Decryption

The decryption process for PBES2 consists of the following steps:

  1. Set the value dkLen = 32.
  2. Apply the key derivation function PBKDF2 to the password P, the random value S, and the iteration count c to produce a derived key DK of length dkLen octets in accordance with the algorithm from Section 4. Generate the sequence T(1) and truncate it to 32 octets, i.e., DK = PBKFD2 (P, S, c, 32) = MSB6432(T(1)).
  3. Set the value S' = ukm[1..n-8], where n is the size of ukm in octets.
  4. For the id-gostr3412-2015-magma-ctracpkm and id-gostr3412-2015-kuznyechik-ctracpkm algorithms (see Section 7.3), decrypt the ciphertext C with the GOST R 34.12-2015 algorithm with the derived key DK and the random value S' to produce the message M.

  5. For id-gostr3412-2015-magma-ctracpkm-omac and id-gostr3412-2015-kuznyechik-ctracpkm-omac algorithms (see Section 7.3), decrypt the ciphertext C with the GOST R 34.12-2015 algorithm with the derived key DK and the ukm in accordance with the following steps:

    • Generate two keys from the derived key DK using the KDF_TREE_GOSTR3411_2012_256 algorithm:

      encryption key K(1)

      MAC key K(2)

      Input parameters for the KDF_TREE_GOSTR3411_2012_256 algorithm take the following values:

      Kin = DK

      label = "kdf tree" (8 octets)

      seed = ukm[n-7..n]

      R = 1

      The input string label above is encoded using ASCII (see [RFC0020]).

    • Decrypt the ciphertext C with the GOST R 34.12-2015 algorithm with the derived key K(1) and the random value S' to produce the plaintext. The last k octets of the text are the MAC, where k depends on the selected encryption algorithm.
    • Compute the MAC for the text[1..m - k] using the K(2) key in accordance with GOST R 34.12-2015 algorithm, where m is the size of text.
    • Compare the computing MAC and the receiving MAC. If the sizes or values do not match, the message is distorted.

6. Message Authentication

The PBMAC1 scheme is used for message authentication (see [RFC8018], Section 7.1). This scheme is based on the HMAC_GOSTR3411 function.

6.1. MAC Generation

The MAC generation operation for PBMAC1 consists of the following steps:

  1. Select the random value S of a length from 8 to 32 octets.
  2. Select the iteration count c depending on the conditions of use (see [GostPkcs5]). The minimum allowable value for the parameter is 1000.
  3. Set the dkLen to at least 32 octets. The number of octets depends on previous parameter values.
  4. Apply the key derivation function to the password P, the random value S, and the iteration count c to generate a sequence K of length dkLen octets in accordance with the algorithm from Section 4.
  5. Truncate the sequence K to 32 octets to get the derived key DK, i.e., DK = LSBdkLen32(K).
  6. Process the message M with the underlying message authentication scheme with the derived key DK to generate a message authentication code T.
  7. Save the parameters S and c as algorithm parameters in accordance with Section 7.4.

6.2. MAC Verification

The MAC verification operation for PBMAC1 consists of the following steps:

  1. Set the dkLen to at least 32 octets. The number of octets depends on previous parameter values.
  2. Apply the key derivation function to the password P, the random value S, and the iteration count c to generate a sequence K of length dkLen octets in accordance with the algorithm from Section 4.
  3. Truncate the sequence K to 32 octets to get the derived key DK, i.e., DK = LSBdkLen32(K).
  4. Process the message M with the underlying message authentication scheme with the derived key DK to generate a MAC.
  5. Compare the computing MAC and the receiving MAC. If the sizes or values do not match, the message is distorted.

7. Identifiers and Parameters

This section defines the ASN.1 syntax for the key derivation functions, the encryption schemes, the message authentication scheme, and supporting techniques (see [RFC8018]).

rsadsi OBJECT IDENTIFIER ::= { iso(1) member-body(2) us(840) 113549 }
pkcs OBJECT IDENTIFIER ::= { rsadsi 1 }
pkcs-5 OBJECT IDENTIFIER ::= { pkcs 5 }

7.1. PBKDF2

The Object Identifier (OID) id-PBKDF2 identifies the PBKDF2 key derivation function:

id-PBKDF2 OBJECT IDENTIFIER ::= { pkcs-5 12 }

The parameters field associated with this OID in an AlgorithmIdentifier SHALL have type PBKDF2-params:

PBKDF2-params ::= SEQUENCE
{
    salt            CHOICE
    {
        specified       OCTET STRING,
        otherSource     AlgorithmIdentifier {{PBKDF2-SaltSources}}
    },
    iterationCount  INTEGER (1000..MAX),
    keyLength       INTEGER (32..MAX) OPTIONAL,
    prf             AlgorithmIdentifier {{PBKDF2-PRFs}}
}

The fields of type PBKDF2-params have the following meanings:

  • salt contains the random value S in OCTET STRING.
  • iterationCount specifies the iteration count c.
  • keyLength is the length of the derived key in octets. It is an optional field for the PBES2 scheme since it is always 32 octets. It MUST be present for the PBMAC1 scheme and MUST be at least 32 octets since the HMAC_GOSTR3411 function has a variable key size.
  • prf identifies the pseudorandom function. The identifier value MUST be id-tc26-hmac-gost-3411-12-512 and the parameters value must be NULL: 
id-tc26-hmac-gost-3411-12-512 OBJECT IDENTIFIER ::=
{
    iso(1) member-body(2) ru(643) reg7(7)
    tk26(1) algorithms(1) hmac(4) 512(2)
}

7.2. PBES2

The OID id-PBES2 identifies the PBES2 encryption scheme:

id-PBES2 OBJECT IDENTIFIER ::= { pkcs-5 13 }

The parameters field associated with this OID in an AlgorithmIdentifier SHALL have type PBES2-params:

PBES2-params ::= SEQUENCE
{
    keyDerivationFunc   AlgorithmIdentifier { { PBES2-KDFs } },
    encryptionScheme    AlgorithmIdentifier { { PBES2-Encs } }
}

The fields of type PBES2-params have the following meanings:

  • keyDerivationFunc identifies the key derivation function in accordance with Section 7.1.
  • encryptionScheme identifies the encryption scheme in accordance with Section 7.3.

7.3. Identifier and Parameters of Gost34.12-2015 Encryption Scheme

The Gost34.12-2015 encryption algorithm identifier SHALL take one of the following values:

id-gostr3412-2015-magma-ctracpkm OBJECT IDENTIFIER ::=
{
    iso(1) member-body(2) ru(643) rosstandart(7)
    tc26(1) algorithms(1) cipher(5)
    gostr3412-2015-magma(1) mode-ctracpkm(1)
}

When the id-gostr3412-2015-magma-ctracpkm identifier is used, the data is encrypted by the GOST R 34.12-2015 Magma cipher in CTR_ACPKM mode in accordance with [RFC8645]. The block size is 64 bits and the section size is fixed within a specific protocol based on the requirements of the system capacity and the key lifetime.

id-gostr3412-2015-magma-ctracpkm-omac OBJECT IDENTIFIER ::=
{
    iso(1) member-body(2) ru(643) rosstandart(7)
    tc26(1) algorithms(1) cipher(5)
    gostr3412-2015-magma(1) mode-ctracpkm-omac(2)
}

When the id-gostr3412-2015-magma-ctracpkm-omac identifier is used, the data is encrypted by the GOST R 34.12-2015 Magma cipher in CTR_ACPKM mode in accordance with [RFC8645] and the MAC is computed by the GOST R 34.12-2015 Magma cipher in MAC mode (MAC size is 64 bits). The block size is 64 bits and the section size is fixed within a specific protocol based on the requirements of the system capacity and the key lifetime.

id-gostr3412-2015-kuznyechik-ctracpkm OBJECT IDENTIFIER ::=
{
    iso(1) member-body(2) ru(643) rosstandart(7)
    tc26(1) algorithms(1) cipher(5)
    gostr3412-2015-kuznyechik(2) mode-ctracpkm(1)
}

When the id-gostr3412-2015-kuznyechik-ctracpkm identifier is used, the data is encrypted by the GOST R 34.12-2015 Kuznyechik cipher in CTR_ACPKM mode in accordance with [RFC8645]. The block size is 128 bits and the section size is fixed within a specific protocol based on the requirements of the system capacity and the key lifetime.

id-gostr3412-2015-kuznyechik-ctracpkm-omac OBJECT IDENTIFIER ::=
{
    iso(1) member-body(2) ru(643) rosstandart(7)
    tc26(1) algorithms(1) cipher(5)
    gostr3412-2015-kuznyechik(2) mode-ctracpkm-omac(2)
}

When the id-gostr3412-2015-kuznyechik-ctracpkm-omac identifier is used, the data is encrypted by the GOST R 34.12-2015 Kuznyechik cipher in CTR_ACPKM mode in accordance with [RFC8645] and MAC is computed by the GOST R 34.12-2015 Kuznyechik cipher in MAC mode (MAC size is 128 bits). The block size is 128 bits and the section size is fixed within a specific protocol based on the requirements of the system capacity and the key lifetime.

The parameters field in an AlgorithmIdentifier SHALL have type Gost3412-15-Encryption-Parameters:

Gost3412-15-Encryption-Parameters ::= SEQUENCE
{
    ukm OCTET STRING
}

The field of type Gost3412-15-Encryption-Parameters have the following meanings:

  • ukm MUST be present and MUST contain n octets. Its value depends on the selected encryption algorithm:

    • GOST R 34.12-2015 "Kuznyechik" n = 16 (see [RFC7801])
    • GOST R 34.12-2015 "Magma" n = 12 (see [RFC8891])

7.4. PBMAC1

The OID id-PBMAC1 identifies the PBMAC1 message authentication scheme:

id-PBMAC1 OBJECT IDENTIFIER ::= { pkcs-5 14 }

The parameters field associated with this OID in an AlgorithmIdentifier SHALL have type PBMAC1-params:

PBMAC1-params ::=  SEQUENCE
{
    keyDerivationFunc AlgorithmIdentifier { { PBMAC1-KDFs } },
    messageAuthScheme AlgorithmIdentifier { { PBMAC1-MACs } }
}

The fields of type PBMAC1-params have the following meanings:

  • keyDerivationFunc is the identifier and parameters of key derivation function in accordance with Section 7.1.
  • messageAuthScheme is the identifier and parameters of the HMAC_GOSTR3411 algorithm.

8. Security Considerations

For information on security considerations for password-based cryptography, see [RFC8018].

Conforming applications MUST use unique values for ukm and S in order to avoid the encryption of different data on the same keys with the same initialization vector.

It is RECOMMENDED that parameter S consist of at least 32 octets of pseudorandom data in order to reduce the probability of collisions of keys generated from the same password.

9. IANA Considerations

This document has no IANA actions.

10. References

10.1. Normative References

[GostPkcs5]
Potashnikov, A., Karelina, E., Pianov, S., and A. Naumenko, "Information technology. Cryptographic Data Security. Password-based key security.", R 1323565.1.040-2022. Federal Agency on Technical Regulating and Metrology (In Russian).
[RFC0020]
Cerf, V., "ASCII format for network interchange", STD 80, RFC 20, DOI 10.17487/RFC0020, , <https://www.rfc-editor.org/info/rfc20>.
[RFC2104]
Krawczyk, H., Bellare, M., and R. Canetti, "HMAC: Keyed-Hashing for Message Authentication", RFC 2104, DOI 10.17487/RFC2104, , <https://www.rfc-editor.org/info/rfc2104>.
[RFC2119]
Bradner, S., "Key words for use in RFCs to Indicate Requirement Levels", BCP 14, RFC 2119, DOI 10.17487/RFC2119, , <https://www.rfc-editor.org/info/rfc2119>.
[RFC6986]
Dolmatov, V., Ed. and A. Degtyarev, "GOST R 34.11-2012: Hash Function", RFC 6986, DOI 10.17487/RFC6986, , <https://www.rfc-editor.org/info/rfc6986>.
[RFC7801]
Dolmatov, V., Ed., "GOST R 34.12-2015: Block Cipher "Kuznyechik"", RFC 7801, DOI 10.17487/RFC7801, , <https://www.rfc-editor.org/info/rfc7801>.
[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, , <https://www.rfc-editor.org/info/rfc7836>.
[RFC8018]
Moriarty, K., Ed., Kaliski, B., and A. Rusch, "PKCS #5: Password-Based Cryptography Specification Version 2.1", RFC 8018, DOI 10.17487/RFC8018, , <https://www.rfc-editor.org/info/rfc8018>.
[RFC8174]
Leiba, B., "Ambiguity of Uppercase vs Lowercase in RFC 2119 Key Words", BCP 14, RFC 8174, DOI 10.17487/RFC8174, , <https://www.rfc-editor.org/info/rfc8174>.
[RFC8645]
Smyshlyaev, S., Ed., "Re-keying Mechanisms for Symmetric Keys", RFC 8645, DOI 10.17487/RFC8645, , <https://www.rfc-editor.org/info/rfc8645>.
[RFC8891]
Dolmatov, V., Ed. and D. Baryshkov, "GOST R 34.12-2015: Block Cipher "Magma"", RFC 8891, DOI 10.17487/RFC8891, , <https://www.rfc-editor.org/info/rfc8891>.

10.2. Informative References

[RFC6070]
Josefsson, S., "PKCS #5: Password-Based Key Derivation Function 2 (PBKDF2) Test Vectors", RFC 6070, DOI 10.17487/RFC6070, , <https://www.rfc-editor.org/info/rfc6070>.

Appendix A. PBKDF2 HMAC_GOSTR3411 Test Vectors

These test vectors are formed by analogy with test vectors from [RFC6070]. The input strings below are encoded using ASCII (see [RFC0020]). The sequence "\0" (without quotation marks) means a literal ASCII NULL value (1 octet). "DK" refers to the derived key.

Input:
    P = "password" (8 octets)
    S = "salt" (4 octets)
    c = 1
    dkLen = 64

Output:
    DK = 64 77 0a f7 f7 48 c3 b1 c9 ac 83 1d bc fd 85 c2
         61 11 b3 0a 8a 65 7d dc 30 56 b8 0c a7 3e 04 0d
         28 54 fd 36 81 1f 6d 82 5c c4 ab 66 ec 0a 68 a4
         90 a9 e5 cf 51 56 b3 a2 b7 ee cd db f9 a1 6b 47

Input:
    P = "password" (8 octets)
    S = "salt" (4 octets)
    c = 2
    dkLen = 64

Output:
    DK = 5a 58 5b af df bb 6e 88 30 d6 d6 8a a3 b4 3a c0
         0d 2e 4a eb ce 01 c9 b3 1c 2c ae d5 6f 02 36 d4
         d3 4b 2b 8f bd 2c 4e 89 d5 4d 46 f5 0e 47 d4 5b
         ba c3 01 57 17 43 11 9e 8d 3c 42 ba 66 d3 48 de

Input:
    P = "password" (8 octets)
    S = "salt" (4 octets)
    c = 4096
    dkLen = 64

Output:
    DK = e5 2d eb 9a 2d 2a af f4 e2 ac 9d 47 a4 1f 34 c2
         03 76 59 1c 67 80 7f 04 77 e3 25 49 dc 34 1b c7
         86 7c 09 84 1b 6d 58 e2 9d 03 47 c9 96 30 1d 55
         df 0d 34 e4 7c f6 8f 4e 3c 2c da f1 d9 ab 86 c3

Input:
    P = "password" (8 octets)
    S = "salt" (4 octets)
    c = 16777216
    dkLen = 64

Output:
    DK = 49 e4 84 3b ba 76 e3 00 af e2 4c 4d 23 dc 73 92
         de f1 2f 2c 0e 24 41 72 36 7c d7 0a 89 82 ac 36
         1a db 60 1c 7e 2a 31 4e 8c b7 b1 e9 df 84 0e 36
         ab 56 15 be 5d 74 2b 6c f2 03 fb 55 fd c4 80 71

Input:
    P = "passwordPASSWORDpassword" (24 octets)
    S = "saltSALTsaltSALTsaltSALTsaltSALTsalt" (36 octets)
    c = 4096
    dkLen = 100

Output:
    DK = b2 d8 f1 24 5f c4 d2 92 74 80 20 57 e4 b5 4e 0a
         07 53 aa 22 fc 53 76 0b 30 1c f0 08 67 9e 58 fe
         4b ee 9a dd ca e9 9b a2 b0 b2 0f 43 1a 9c 5e 50
         f3 95 c8 93 87 d0 94 5a ed ec a6 eb 40 15 df c2
         bd 24 21 ee 9b b7 11 83 ba 88 2c ee bf ef 25 9f
         33 f9 e2 7d c6 17 8c b8 9d c3 74 28 cf 9c c5 2a
         2b aa 2d 3a

Input:
    P = "pass\0word" (9 octets)
    S = "sa\0lt" (5 octets)
    c = 4096
    dkLen = 64

Output:
    DK = 50 df 06 28 85 b6 98 01 a3 c1 02 48 eb 0a 27 ab
         6e 52 2f fe b2 0c 99 1c 66 0f 00 14 75 d7 3a 4e
         16 7f 78 2c 18 e9 7e 92 97 6d 9c 1d 97 08 31 ea
         78 cc b8 79 f6 70 68 cd ac 19 10 74 08 44 e8 30

Acknowledgments

The author thanks Potashnikov Alexander, Pianov Semen, Davletshina Alexandra, Belyavsky Dmitry, and Smyslov Valery for their careful readings and useful comments.

Author's Address

Ekaterina Karelina (editor)
InfoTeCS
2B stroenie 1, ul. Otradnaya
Moscow
127273
Russian Federation