Internet-Draft Abbreviated Title April 2021
Karelina Expires 1 November 2021 [Page]
Workgroup:
Network Working Group
Internet-Draft:
draft-pkcs5-gost-00
Published:
Intended Status:
Informational
Expires:
Author:
E.K. Karelina, Ed.
InfoTeCS

Password-based key protection

Abstract

This document supplements [RFC8018]. It contains the specifications of the cryptographic algorithms defined by the Russian national standards for their implementation of generating general key in the password-based schemes.

Status of This Memo

This Internet-Draft is submitted in full conformance with the provisions of BCP 78 and BCP 79.

Internet-Drafts are working documents of the Internet Engineering Task Force (IETF). Note that other groups may also distribute working documents as Internet-Drafts. The list of current Internet-Drafts is at https://datatracker.ietf.org/drafts/current/.

Internet-Drafts are draft documents valid for a maximum of six months and may be updated, replaced, or obsoleted by other documents at any time. It is inappropriate to use Internet-Drafts as reference material or to cite them other than as "work in progress."

This Internet-Draft will expire on 1 November 2021.

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Table of Contents

1. Introduction

This document supplements [RFC8018]. It describes the recommendations for using in the information systems with the realisations of the GOST 28147-89 and GOST R 34.12-2015 encryption algorithms and the GOST R 34.11-2012 hashing functions in public and corporate networks to protect non-state information. The use of the GOST 28147-89 encryption algorithm in these mechanisms remains for compatibility with existing implementations. The methods described in these recommendations are designed to generate key information using the user's password and 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 notations are used:

Table 1
P a password in Unicode UTF-8
S a random initializing value
c a number of iterations of algorithm, a positive integer
dkLen a length in bytes of derived key, a positive integer
DK a derived key of length dkLen
B_n a set of all byte row vectors of length n, n >= 0; if n = 0, then the set B_n consists of an empty string of length 0
A||C a concatenation of two byte 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
\xor a bit-wise exclusive-or of two byte strings of the same length
R^n_r: B_n -> B_r a truncating a byte string to size r by removing the least significant n-r bytes
Int(i) a four-byte 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 bytes 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
HMAC_GOSTR3411 Hashed-based Message Authentication Code. A function for calculating a message authentication code, based on the GOST R 34.11-2012 hash function with 512-bit output in accordance with [RFC2104].

4. Algorithm for generating a key from a password

The DK key is calculated as a diversification function PBKDF2(P, S, c, dkLen) using the HMAC_GOSTR3411 function as the PRF pseudo-random function:

The diversification function is calculated using the following algorithm:

  1. If dkLen > (2^32 - 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:

    • 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_{c-1}(i))
    • T(i) = U_1(i) \xor U_2(i) \xor ... \xor U_c(i)

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

    • DK = R^{n * 64}_dkLen(T(1)||T(2)||...||T(n))

5. Data encryption

5.1. GOST 28147-89 data encryption

Data encryption using the DK key is carried out in accordance with the PBES2 scheme (see [RFC8018], section 6.2) using GOST 28147-89 in the Cipher Feedback Mode (CFB) (see [RFC5830]).

5.1.1. Encryption

The encryption process for PBES2 consists of the following steps:

  1. Select the random value S of length from 8 to 32 bytes. The recommended length is 32 bytes.
  2. Select the iteration count c depending on the conditions of use. The minimum allowable value for the parameter is 1000, the recommended value is 2000.
  3. Set the value dkLen = 32.
  4. Apply the key derivation function to the password P, the salt S and the iteration count c to produce a derived key DK of length dkLen bytes in accordance with the algorithm from Section 4. Generate the sequence T(1) and trunc it to 32 bytes, i.e., DK = PBKFD2(P,S,c,32) = R^64_32(T(1)).
  5. Select the random value S^{'} of length from 8 bytes.
  6. Encrypt the message M with GOST 28147-89 algorithm in CFB mode under the derived key DK and the random value S^{'} to produce a ciphertext C.
  7. Save the parameters S, S^{'}, c as algorithm parameters in accordance with Appendix A.

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 to the password P, the salt S and the iteration count c to produce a derived key DK of length dkLen bytes in accordance with the algorithm from Section 4. Generate the sequence T(1) and trunc it to 32 bytes, i.e.,

    • DK = PBKFD2(P,S,c,32) = R^64_32(T(1)).
  3. Decrypt the ciphertext C with GOST 28147-89 algorithm in CFB mode under the derived key DK and the random value S^{'} to produce the message M.

5.2. GOST R 34.12-2015 data encryption

Data encryption using the DK key 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]).

5.2.1. Encryption

The encryption process for PBES2 consists of the following steps:

  1. Select the random value S of length from 8 to 32 bytes. The recommended length is 32 bytes.
  2. Select the iteration count c depending on the conditions of use. The minimum allowable value for the parameter is 1000, the recommended value is 2000.
  3. Set the value dkLen = 32.

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

    • DK = PBKFD2(P,S,c,32) = R^64_32(T(1)).

  5. Generate the value ukm of size n, where n takes a value of 12 or 16 bytes, 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 id-gostr3412-2015-magma-ctracpkm and id-gostr3412-2015-kuznyechik-ctracpkm algorithms (see Appendix A.4) encrypt the message M with GOST R 34.12-2015 algorithm under the derived key DK and the random value S^{'} to produce a ciphertext C.

  8. For id-gostr3412-2015-magma-ctracpkm-omac and id-gostr3412-2015-kuznyechik-ctracpkm-omac algorithms (see Appendix A.4) encrypt the message M with GOST R 34.12-2015 algorithm under 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 takes the folowing values:

      • K_in = DK
      • label = "kdf tree"
      • seed = ukm[n-7..n]
      • R = 1
    • - Compute MAC for the message M using the K(2) key. Append to the end of the message M the computing MAC value.
    • - Encrypt the resulting byte string with MAC with GOST R 34.12-2015 algorithm under the derived key K(1) and the random value S^{'} to produce a ciphertext C.
  9. Save the parameters S, c, ukm as algorithm parameters in accordance with Appendix A.

5.2.2. Decryption

The decryption process for PBES2 consists of the following steps:

  1. Set the value dkLen = 32.
  2. Apply the key derivation function to the password P, the salt S and the iteration count c to produce a derived key DK of length dkLen bytes in accordance with the algorithm from Section 4. Generate the sequence T(1) and trunc it to 32 bytes, i.e., DK = PBKFD2(P,S,c,32) = R^64_32(T(1)).
  3. Set the value S^{'} = ukm[1..n-8], where n is the size of ukm in bytes.
  4. For id-gostr3412-2015-magma-ctracpkm and id-gostr3412-2015-kuznyechik-ctracpkm algorithms (see Appendix A.4) decrypt the ciphertext C with GOST R 34.12-2015 algorithm under 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 Appendix A.4) decrypt the ciphertext C with GOST R 34.12-2015 algorithm under 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 takes the folowing values:

      • K_in = DK
      • label = "kdf tree"
      • seed = ukm[n-7..n]
      • R = 1
    • - Decrypt the ciphertext C with GOST R 34.12-2015 algorithm under the derived key K(1) and the random value S^{'} to produce the text. The last k bytes of the text are the mac, where k depends on the selected encryption algorithm.
    • - Compute MAC for the text[1..m - k] using the K(2) key, where m is the size of text.
    • - Compare the original mac and the receiving MAC. If the sizes or values do not match, the message is distorted.

6. Message Authentication

PBMAC1 scheme is used for message authentication (see [RFC8018]. This scheme bases on the HMAC_GOSTR3411 function with the key DK = PBKDF2 (P, S, c, 32).

6.1. The MAC generation

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

  1. Select the random value S of length from 8 to 32 bytes. The recommended length is 32 bytes.
  2. Select the iteration count c depending on the conditions of use. The minimum allowable value for the parameter is 1000, the recommended value is 2000.
  3. Set the dkLen at least 32 bytes. It depend on the selected key generation scheme.
  4. Apply the key derivation function to the password P, the salt S and the iteration count c to produce a derived key DK of length dkLen bytes in accordance with the algorithm from Section 4. Generate the sequence T(1) and trunc it to 32 bytes, i.e., DK = PBKFD2(P,S,c,32) = R^64_32(T(1)).
  5. Process the message M with the underlying message authentication scheme under the derived key DK to generate a message authentication code T.
  6. Save the parameters S, c, ukm as algorithm parameters in accordance with Appendix A.

6.2. The MAC verification

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

  1. Set the dkLen at least 32 bytes. It depend on the selected key generation scheme.
  2. Apply the key derivation function to the password P, the salt S and the iteration count c to produce a derived key DK of length dkLen bytes in accordance with the algorithm from Section 4. Generate the sequence T(1) and trunc it to 32 bytes, i.e., DK = PBKFD2(P,S,c,32) = R^64_32(T(1)).
  3. Process the message M with the underlying message authentication scheme under the derived key DK to generate a message authentication code T^{'}.
  4. Compare the original message authentication code T and the receiving message authentication code T^{'}. If the sizes or values do not match, the message is distorted.

7. Security Considerations

The focus of this document is security; hence security considerations permeate this specification.

8. Normative References

[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>.
[RFC5830]
Dolmatov, V., Ed., "GOST 28147-89: Encryption, Decryption, and Message Authentication Code (MAC) Algorithms", RFC 5830, DOI 10.17487/RFC5830, , <https://www.rfc-editor.org/info/rfc5830>.
[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>.
[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>.

Appendix A. Identifiers and parameters

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

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

A.1. PBKDF2

The object identifier 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 bytes. It is optional field for PBES2 sheme since it is always 32 bytes. It must be present for PBMAC1 sheme and must be at least 32 bytes 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, 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)
}

A.2. PBES2

The object identifier 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:

A.3. Identifier and parametrs of Gost28147-89 encryption sheme

The GOST 28147-89 encryption algorithm identifier should take the following value:

id-Gost28147-89 OBJECT IDENTIFIER ::=
{
    iso(1) member-body(2) ru(643) rans(2)
    cryptopro(2) gost28147-89(21)
}

The parameters field associated with this OID in an AlgorithmIdentifier shall have type Gost28147-89-Parameters:

Gost28147-89-Parameters ::= SEQUENCE
{
    iv                      Gost28147-89-IV,
    encryptionParamSet      OBJECT IDENTIFIER
}
Gost28147-89-IV ::= OCTET STRING (SIZE (8))

The fields of type Gost28147-89-Parameters have the following meanings:

  • - iv contains the random value S^{'} in OCTET STRING.
  • - encryptionParamSet identifies the substitution block for encryption. For PBES2 sheme it is recommended to use the set of substitutions described in [RFC7836]. The OID of this block is: 
id-tc26-gost-28147-param-Z OBJECT IDENTIFIER ::=
{
    iso(1) member-body(2) ru(643) rosstandart(7)
    tc26(1) constants(2) cipher(5) gost28147(1) paramZ(1)
}

A.4. Identifier and parametrs of Gost34.12-2015 encryption sheme

The Gost34.12-2015 encryption algorithm identifier SHOULD 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)
}

In case of use id-gostr3412-2015-magma-ctracpkm identifier the data is encrypted by the GOST R 34.12-2015 Magma cipher in CTR_ACPKM mode in accordance with [RFC8645]. The length of gamma block s is 64 bits, 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)
}

In case of use id-gostr3412-2015-magma-ctracpkm-omac identifier the data is encrypted by the GOST R 34.12-2015 Magma cipher in CTR_ACPKM mode in accordance with [RFC8645], and MAC is computed by the GOST R 34.12-2015 Magma cipher in MAC mode (MAC size is 64 bits). The length of gamma block s is 64 bits, 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)
}

In case of use id-gostr3412-2015-kuznyechik-ctracpkm identifier the data is encrypted by the GOST R 34.12-2015 Kuznyechik cipher in CTR_ACPKM mode in accordance with [RFC8645]. The length of gamma block s is 128 bits, 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)
}

In case of use id-gostr3412-2015-kuznyechik-ctracpkm-omac identifier 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 length of gamma block s is 128 bits, 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 bytes. It's 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])

A.5. PBMAC1

The object identifier 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 identifier and parameters of key diversification function in accordance with Appendix A.1
  • - messageAuthScheme is identifier and parameters of HMAC_GOSTR3411 algorithm.

Appendix B. 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. 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

Appendix C. Acknowledgments

Author's Address

Karelina Ekaterina (editor)
InfoTeCS
2B stroenie 1, ul. Otradnaya
Moscow
127273
Russian Federation
Phone: +7 (495) 737-61-92