Independent Submission E. Karelina, Ed. Request for Comments: 9337 InfoTeCS Category: Informational December 2022 ISSN: 20701721
Generating PasswordBased Keys Using the GOST Algorithms
Abstract

This document specifies how to use "PKCS #5: PasswordBased 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 HashBased 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.rfceditor.org/info/rfc9337.
Copyright Notice

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Table of Contents

1. Introduction 2. Conventions Used in This Document 3. Basic Terms and Definitions 4. Algorithm for Generating a Key from a Password 5. Data Encryption 5.1. GOST R 34.122015 Data Encryption 5.1.1. Encryption 5.1.2. Decryption 6. Message Authentication 6.1. MAC Generation 6.2. MAC Verification 7. Identifiers and Parameters 7.1. PBKDF2 7.2. PBES2 7.3. Identifier and Parameters of Gost34.122015 Encryption Scheme 7.4. PBMAC1 8. Security Considerations 9. IANA Considerations 10. References 10.1. Normative References 10.2. Informative References Appendix A. PBKDF2 HMAC_GOSTR3411 Test Vectors Acknowledgments Author's Address
1. Introduction

This document provides a specification of usage of GOST R 34.122015 encryption algorithms and the GOST R 34.112012 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:
+==========+====================================================+  Notation  Definition  +==========+====================================================+  P  a password encoded as a Unicode UTF8 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  +++  B_n  a set of all octet strings of length n, n >= 0; if    n = 0, then the set B_n consists of an empty    string of length 0  +++  AC  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 = (a_(n_1),...,a_1) in B_(n_1) and C =    (c_(n_2),..., c_1) in B_(n_2), res =    (a_(n_1),...,a_1,c_(n_2),..., c_1) in B_(n_1+n_2))  +++  \xor  a bitwise exclusiveor of two octet strings of    the same length  +++  MSB^n_r:  a truncating of an octet string to size r by   B_n >  removing the least significant nr octets:   B_r  MSB^n_r(a_n,...,a_(nr+1),a_(nr),...,a_1)    =(a_n,...,a_(nr+1))  +++  LSB^n_r:  a truncating of an octet string to size r by   B_n >  removing the most significant nr octets:   B_r  LSB^n_r(a_n,...,a_(nr+1),a_(nr),...,a_1)    =(a_r,...,a_1)  +++  Int(i)  a fouroctet encoding of the integer i =< 2^32:    (i_1, i_2, i_3, i_4) in B_4, i = i_1 + 2^8 * i_2 +    2^16 * i_3 + 2^24 * i_4  +++  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  +++
Table 1: Terms and Definitions

This document uses the following abbreviations and symbols:
+================+===============================================+  Abbreviations  Definition   and Symbols   +================+===============================================+  HMAC_GOSTR3411  HashedBased Message Authentication Code. A    function for calculating a Message    Authentication Code (MAC) based on the GOST R    34.112012 hash function (see [RFC6986]) with    512bit output in accordance with [RFC2104].  +++
Table 2: Abbreviations and Symbols
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:
 If dkLen > (2^32  1) * 64, output "derived key too long" and stop.
 Calculate n = CEIL (dkLen / 64).
 Calculate a set of values for each i from 1 to n:
U_1(i) = HMAC_GOSTR3411 (P, S  INT (i)), U_2(i) = HMAC_GOSTR3411 (P, U_1(i)),


...

U_c(i) = HMAC_GOSTR3411 (P, U_(c1)(i)),

T(i) = U_1(i) \xor U_2(i) \xor ... \xor U_c(i).

 Concatenate the octet strings T(i) and extract the first dkLen octets to produce a derived key DK:
* DK = MSB^(n * 64)_dkLen(T(1)T(2)...T(n))
5. Data Encryption
5.1. GOST R 34.122015 Data Encryption

Data encryption using the DK is carried out in accordance with the PBES2 scheme (see [RFC8018], Section 6.2) using GOST R 34.122015 in CTR_ACPKM mode (see [RFC8645]).
5.1.1. Encryption

The encryption process for PBES2 consists of the following steps:
 Select the random value S of a length from 8 to 32 octets.
 Select the iteration count c depending on the conditions of use (see [GostPkcs5]). The minimum allowable value for the parameter is 1000.
 Set the value dkLen = 32.
 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) = MSB^64_32(T(1)).

 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 34.122015 "Kuznyechik" n = 16 (see [RFC7801]) * GOST R 34.122015 "Magma" n = 12 (see [RFC8891])
 Set the value S' = ukm[1..n8].
7. For the idgostr34122015magmactracpkm and idgostr34122015 kuznyechikctracpkm algorithms (see Section 7.3), encrypt the message M with the GOST R 34.122015 algorithm with the derived key DK and the random value S' to produce a ciphertext C. 8. For the idgostr34122015magmactracpkmomac and id gostr34122015kuznyechikctracpkmomac algorithms (see Section 7.3), encrypt the message M with the GOST R 34.122015 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:

K_in = DK



label = "kdf tree" (8 octets)


seed = ukm[n7..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 34.122015 algorithm. Append the computed MAC value to the message M: MMAC.
 Encrypt the resulting octet string with MAC with the GOST R 34.122015 algorithm with the derived key K(1) and the random value S' to produce a ciphertext C.

 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:
 Set the value dkLen = 32.
 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) = MSB^64_32(T(1)).
3. Set the value S' = ukm[1..n8], where n is the size of ukm in octets. 4. For the idgostr34122015magmactracpkm and idgostr34122015 kuznyechikctracpkm algorithms (see Section 7.3), decrypt the ciphertext C with the GOST R 34.122015 algorithm with the derived key DK and the random value S' to produce the message M. 5. For idgostr34122015magmactracpkmomac and idgostr34122015 kuznyechikctracpkmomac algorithms (see Section 7.3), decrypt the ciphertext C with the GOST R 34.122015 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:

K_in = DK



label = "kdf tree" (8 octets)


seed = ukm[n7..n] R = 1


The input string label above is encoded using ASCII (see [RFC0020]).
 Decrypt the ciphertext C with the GOST R 34.122015 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 34.122015 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:
 Select the random value S of a length from 8 to 32 octets.
 Select the iteration count c depending on the conditions of use (see [GostPkcs5]). The minimum allowable value for the parameter is 1000.
 Set the dkLen to at least 32 octets. The number of octets depends on previous parameter values.
 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.
 Truncate the sequence K to 32 octets to get the derived key DK, i.e., DK = LSB^dkLen_32(K).
 Process the message M with the underlying message authentication scheme with the derived key DK to generate a message authentication code T.
 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:
 Set the dkLen to at least 32 octets. The number of octets depends on previous parameter values.
 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.
 Truncate the sequence K to 32 octets to get the derived key DK, i.e., DK = LSB^dkLen_32(K).
 Process the message M with the underlying message authentication scheme with the derived key DK to generate a MAC.
 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) memberbody(2) us(840) 113549 } pkcs OBJECT IDENTIFIER ::= { rsadsi 1 } pkcs5 OBJECT IDENTIFIER ::= { pkcs 5 }
7.1. PBKDF2

The Object Identifier (OID) idPBKDF2 identifies the PBKDF2 key derivation function:
idPBKDF2 OBJECT IDENTIFIER ::= { pkcs5 12 }
The parameters field associated with this OID in an AlgorithmIdentifier SHALL have type PBKDF2params:
PBKDF2params ::= SEQUENCE { salt CHOICE { specified OCTET STRING, otherSource AlgorithmIdentifier {{PBKDF2SaltSources}} }, iterationCount INTEGER (1000..MAX), keyLength INTEGER (32..MAX) OPTIONAL, prf AlgorithmIdentifier {{PBKDF2PRFs}} }
The fields of type PBKDF2params 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 idtc26hmacgost341112512 and the parameters value must be NULL:
idtc26hmacgost341112512 OBJECT IDENTIFIER ::= { iso(1) memberbody(2) ru(643) reg7(7) tk26(1) algorithms(1) hmac(4) 512(2) }
7.2. PBES2

The OID idPBES2 identifies the PBES2 encryption scheme:
idPBES2 OBJECT IDENTIFIER ::= { pkcs5 13 }
The parameters field associated with this OID in an AlgorithmIdentifier SHALL have type PBES2params:
PBES2params ::= SEQUENCE { keyDerivationFunc AlgorithmIdentifier { { PBES2KDFs } }, encryptionScheme AlgorithmIdentifier { { PBES2Encs } } }
The fields of type PBES2params 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 Gost34.122015 Encryption Scheme

The Gost34.122015 encryption algorithm identifier SHALL take one of the following values:
idgostr34122015magmactracpkm OBJECT IDENTIFIER ::= { iso(1) memberbody(2) ru(643) rosstandart(7) tc26(1) algorithms(1) cipher(5) gostr34122015magma(1) modectracpkm(1) }
When the idgostr34122015magmactracpkm identifier is used, the data is encrypted by the GOST R 34.122015 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.
idgostr34122015magmactracpkmomac OBJECT IDENTIFIER ::= { iso(1) memberbody(2) ru(643) rosstandart(7) tc26(1) algorithms(1) cipher(5) gostr34122015magma(1) modectracpkmomac(2) }
When the idgostr34122015magmactracpkmomac identifier is used, the data is encrypted by the GOST R 34.122015 Magma cipher in CTR_ACPKM mode in accordance with [RFC8645] and the MAC is computed by the GOST R 34.122015 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.
idgostr34122015kuznyechikctracpkm OBJECT IDENTIFIER ::= { iso(1) memberbody(2) ru(643) rosstandart(7) tc26(1) algorithms(1) cipher(5) gostr34122015kuznyechik(2) modectracpkm(1) }
When the idgostr34122015kuznyechikctracpkm identifier is used, the data is encrypted by the GOST R 34.122015 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.
idgostr34122015kuznyechikctracpkmomac OBJECT IDENTIFIER ::= { iso(1) memberbody(2) ru(643) rosstandart(7) tc26(1) algorithms(1) cipher(5) gostr34122015kuznyechik(2) modectracpkmomac(2) }
When the idgostr34122015kuznyechikctracpkmomac identifier is used, the data is encrypted by the GOST R 34.122015 Kuznyechik cipher in CTR_ACPKM mode in accordance with [RFC8645] and MAC is computed by the GOST R 34.122015 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 Gost341215EncryptionParameters:
Gost341215EncryptionParameters ::= SEQUENCE { ukm OCTET STRING }
The field of type Gost341215EncryptionParameters have the following meanings:
 ukm MUST be present and MUST contain n octets. Its value depends on the selected encryption algorithm:
 GOST R 34.122015 "Kuznyechik" n = 16 (see [RFC7801])  GOST R 34.122015 "Magma" n = 12 (see [RFC8891])
7.4. PBMAC1

The OID idPBMAC1 identifies the PBMAC1 message authentication scheme:
idPBMAC1 OBJECT IDENTIFIER ::= { pkcs5 14 }
The parameters field associated with this OID in an AlgorithmIdentifier SHALL have type PBMAC1params:
PBMAC1params ::= SEQUENCE { keyDerivationFunc AlgorithmIdentifier { { PBMAC1KDFs } }, messageAuthScheme AlgorithmIdentifier { { PBMAC1MACs } } }
The fields of type PBMAC1params 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 passwordbased 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. Passwordbased key security.", R 1323565.1.0402022. 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, October 1969, <https://www.rfceditor.org/info/rfc20>. [RFC2104] Krawczyk, H., Bellare, M., and R. Canetti, "HMAC: Keyed Hashing for Message Authentication", RFC 2104, DOI 10.17487/RFC2104, February 1997, <https://www.rfceditor.org/info/rfc2104>. [RFC2119] Bradner, S., "Key words for use in RFCs to Indicate Requirement Levels", BCP 14, RFC 2119, DOI 10.17487/RFC2119, March 1997, <https://www.rfceditor.org/info/rfc2119>. [RFC6986] Dolmatov, V., Ed. and A. Degtyarev, "GOST R 34.112012: Hash Function", RFC 6986, DOI 10.17487/RFC6986, August 2013, <https://www.rfceditor.org/info/rfc6986>. [RFC7801] Dolmatov, V., Ed., "GOST R 34.122015: Block Cipher "Kuznyechik"", RFC 7801, DOI 10.17487/RFC7801, March 2016, <https://www.rfceditor.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 34.102012 and GOST R 34.112012", RFC 7836, DOI 10.17487/RFC7836, March 2016, <https://www.rfceditor.org/info/rfc7836>. [RFC8018] Moriarty, K., Ed., Kaliski, B., and A. Rusch, "PKCS #5: PasswordBased Cryptography Specification Version 2.1", RFC 8018, DOI 10.17487/RFC8018, January 2017, <https://www.rfceditor.org/info/rfc8018>. [RFC8174] Leiba, B., "Ambiguity of Uppercase vs Lowercase in RFC 2119 Key Words", BCP 14, RFC 8174, DOI 10.17487/RFC8174, May 2017, <https://www.rfceditor.org/info/rfc8174>. [RFC8645] Smyshlyaev, S., Ed., "Rekeying Mechanisms for Symmetric Keys", RFC 8645, DOI 10.17487/RFC8645, August 2019, <https://www.rfceditor.org/info/rfc8645>. [RFC8891] Dolmatov, V., Ed. and D. Baryshkov, "GOST R 34.122015: Block Cipher "Magma"", RFC 8891, DOI 10.17487/RFC8891, September 2020, <https://www.rfceditor.org/info/rfc8891>.
10.2. Informative References

[RFC6070] Josefsson, S., "PKCS #5: PasswordBased Key Derivation Function 2 (PBKDF2) Test Vectors", RFC 6070, DOI 10.17487/RFC6070, January 2011, <https://www.rfceditor.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 Email: Ekaterina.Karelina@infotecs.ru