The scrypt Password-Based Key Derivation Function
draft-josefsson-scrypt-kdf-03

 
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Network Working Group                                        C. Percival
Internet-Draft                                                   Tarsnap
Intended status: Informational                              S. Josefsson
Expires: November 14, 2015                                        SJD AB
                                                            May 13, 2015

           The scrypt Password-Based Key Derivation Function
                     draft-josefsson-scrypt-kdf-03

Abstract

   This document specifies the password-based key derivation function
   scrypt.  The function derives one or more secret keys from a secret
   string.  It is based on memory-hard functions which offer added
   protection against attacks using custom hardware.  The document also
   provides an ASN.1 schema.

Status of This Memo

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   Copyright (c) 2015 IETF Trust and the persons identified as the
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   the Trust Legal Provisions and are provided without warranty as
   described in the Simplified BSD License.

Table of Contents

   1.  Introduction  . . . . . . . . . . . . . . . . . . . . . . . .   2
   2.  The Salsa20/8 Core Function . . . . . . . . . . . . . . . . .   3
   3.  The scryptBlockMix Algorithm  . . . . . . . . . . . . . . . .   3
   4.  The scryptROMix Algorithm . . . . . . . . . . . . . . . . . .   4
   5.  The scrypt Algorithm  . . . . . . . . . . . . . . . . . . . .   5
   6.  ASN.1 Syntax  . . . . . . . . . . . . . . . . . . . . . . . .   6
     6.1.  ASN.1 Module  . . . . . . . . . . . . . . . . . . . . . .   7
   7.  Test Vectors for Salsa20/8 Core . . . . . . . . . . . . . . .   8
   8.  Test Vectors for scryptBlockMix . . . . . . . . . . . . . . .   8
   9.  Test Vectors for scryptROMix  . . . . . . . . . . . . . . . .   9
   10. Test Vectors for PBKDF2 with HMAC-SHA-256 . . . . . . . . . .  10
   11. Test Vectors for scrypt . . . . . . . . . . . . . . . . . . .  10
   12. Test Vectors for PKCS#8 . . . . . . . . . . . . . . . . . . .  11
   13. Copying Conditions  . . . . . . . . . . . . . . . . . . . . .  12
   14. Acknowledgements  . . . . . . . . . . . . . . . . . . . . . .  12
   15. IANA Considerations . . . . . . . . . . . . . . . . . . . . .  12
   16. Security Considerations . . . . . . . . . . . . . . . . . . .  12
   17. References  . . . . . . . . . . . . . . . . . . . . . . . . .  13
     17.1.  Normative References . . . . . . . . . . . . . . . . . .  13
     17.2.  Informative References . . . . . . . . . . . . . . . . .  13
   Authors' Addresses  . . . . . . . . . . . . . . . . . . . . . . .  13

1.  Introduction

   Password-based key derivation functions are used in cryptography for
   deriving one or more secret keys from a secret value.  Over the
   years, several password-based key derivation functions have been
   used, including the original DES-based UNIX Crypt-function, FreeBSD
   MD5 crypt, PKCS#5 PBKDF2 [RFC2898] (typically used with SHA-1), GNU
   SHA-256/512 crypt, Windows NT LAN Manager (NTLM) hash, and the
   Blowfish-based bcrypt.  These algorithms are based on similar
   techniques that employ a cryptographic primitive, salting and/or
   iteration.  The iteration count is used to slow down the computation.

   Providing that the number of iterations used is increased as computer
   systems get faster, this allows legitimate users to spend a constant
   amount of time on key derivation without losing ground to an
   attackers' ever-increasing computing power - as long as attackers are
   limited to the same software implementations as legitimate users.
   However, as Bernstein pointed out in the context of integer
   factorization, while parallelized hardware implementations may not
   change the number of operations performed compared to software
   implementations, this does not prevent them from dramatically

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   changing the asymptotic cost, since in many contexts - including the
   embarrassingly parallel task of performing a brute-force search for a
   passphrase - dollar-seconds are the most appropriate units for
   measuring the cost of a computation.  As semiconductor technology
   develops, circuits do not merely become faster; they also become
   smaller, allowing for a larger amount of parallelism at the same
   cost.  Consequently, existing key derivation algorithms, even when
   the iteration count is increased so that the time taken to verify a
   password remains constant, the cost of finding a password by using a
   brute force attack implemented in hardware drops each year.

   The scrypt function aims to reduce the advantage which attackers can
   gain by using custom-designed parallel circuits for breaking
   password-based key derivation functions.

   For further background, see the original scrypt paper [SCRYPT].

   The rest of this document is divided into sections that each describe
   algorithms needed for the final "scrypt" algorithm.

2.  The Salsa20/8 Core Function

   Salsa20/8 Core is a round-reduced variant of the Salsa20 Core.  It is
   a hash function from 64-octet strings to 64-octet strings.  Note that
   Salsa20/8 Core is not a cryptographic hash function since it is not
   collision-resistant.  See section 8 of [SALSA20SPEC] for its
   specification, and [SALSA20CORE] for more information.

3.  The scryptBlockMix Algorithm

   The scryptBlockMix algorithm is the same as the BlockMix algorithm
   described in [SCRYPT] but with Salsa20/8 Core used as the hash
   function H.  Below, Salsa(T) corresponds to the Salsa20/8 Core
   function applied to the octet vector T.

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   Algorithm scryptBlockMix

   Parameters:
            r       Block size parameter.

   Input:
            B[0], ..., B[2 * r - 1]
                    Input vector of 2 * r 64-octet blocks.

   Output:
            B'[0], ..., B'[2 * r - 1]
                    Output vector of 2 * r 64-octet blocks.

   Steps:

     1. X = B[2 * r - 1]

     2. for i = 0 to 2 * r - 1 do
          T = X xor B[i]
          X = Salsa (T)
          Y[i] = X
        end for

     3. B' = (Y[0], Y[2], ..., Y[2 * r - 2],
              Y[1], Y[3], ..., Y[2 * r - 1])

4.  The scryptROMix Algorithm

   The scryptROMix algorithm is the same as the ROMix algorithm
   described in [SCRYPT] but with scryptBlockMix used as the hash
   function H and the Integerify function explained inline.

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   Algorithm scryptROMix

   Input:
            r       Block size parameter.
            B       Input octet vector of length 128 * r octets.
            N       CPU/Memory cost parameter, must be larger than 1,
                    a power of 2 and less than 2^(128 * r / 8).

   Output:
            B'      Output octet vector of length 128 * r octets.

   Steps:

     1. X = B

     2. for i = 0 to N - 1 do
          V[i] = X
          X = scryptBlockMix (X)
        end for

     3. for i = 0 to N - 1 do
          j = Integerify (X) mod N
                 where Integerify (B[0] ... B[2 * r - 1]) is defined
                 as the result of interpreting B[2 * r - 1] as a
                 little-endian integer.
          T = X xor V[j]
          X = scryptBlockMix (T)
        end for

     4. B' = X

5.  The scrypt Algorithm

   The PBKDF2-HMAC-SHA-256 function used below denote the PBKDF2
   algorithm [RFC2898] used with HMAC-SHA-256 [RFC6234] as the PRF.  The
   HMAC-SHA-256 function generates 32 octet outputs.

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   Algorithm scrypt

   Input:
            P       Passphrase, an octet string.
            S       Salt, an octet string.
            N       CPU/Memory cost parameter, must be larger than 1,
                    a power of 2 and less than 2^(128 * r / 8).
            r       Block size parameter.
            p       Parallelization parameter, a positive integer
                    less than or equal to ((2^32-1) * hLen) / MFLen
                    where hLen is 32 and MFlen is 128 * r.
            dkLen   Intended output length in octets of the derived
                    key; a positive integer less than or equal to
                    (2^32 - 1) * hLen where hLen is 32.

   Output:
            DK      Derived key, of length dkLen octets.

   Steps:

     1. B[0] || B[1] || ... || B[p - 1] =
          PBKDF2-HMAC-SHA256 (P, S, 1, p * 128 * r)

     2. for i = 0 to p - 1 do
          B[i] = scryptROMix (r, B[i], N)
        end for

     3. DK = PBKDF2-HMAC-SHA256 (P, B[0] || B[1] || ... || B[p - 1],
                                 1, dkLen)

6.  ASN.1 Syntax

   This section defines ASN.1 syntax for the scrypt key derivation
   function.  This is intended to operate on the same abstraction level
   as PKCS#5's PBKDF2.  The OID id-scrypt below can be used where id-
   PBKDF2 is used, with scrypt-params corresponding to PBKDF2-params.
   The intended application of these definitions includes PKCS #8 and
   other syntax for key management.

   The object identifier id-scrypt identifies the scrypt key derivation
   function.

   id-scrypt OBJECT IDENTIFIER ::= {1 3 6 1 4 1 11591 4 11}

   The parameters field associated with this OID in an
   AlgorithmIdentifier shall have type scrypt-params:

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   scrypt-params ::= SEQUENCE {
          salt OCTET STRING,
          costParameter INTEGER (1..MAX),
          blockSize INTEGER (1..MAX),
          parallelizationParameter INTEGER (1..MAX),
          keyLength INTEGER (1..MAX) OPTIONAL }

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

   - salt specifies the salt value.  It shall be an octet string.

   - costParameter specifies the CPU/Memory cost parameter N.

   - blockSize specifies the block size parameter r.

   - parallelizationParameter specifies the parallelization parameter.

   - keyLength, an optional field, is the length in octets of the
   derived key.  The maximum key length allowed depends on the
   implementation; it is expected that implementation profiles may
   further constrain the bounds.  This field only provides convenience;
   the key length is not cryptographically protected.

   To be usable in PKCS#8 [RFC5208] and Asymmetric Key Packages
   [RFC5958] the following extension of the PBES2-KDFs type is needed.

      PBES2-KDFs ALGORITHM-IDENTIFIER ::=
          { {scrypt-params IDENTIFIED BY id-scrypt}, ... }

6.1.  ASN.1 Module

   For reference purposes, the ASN.1 syntax is presented as an ASN.1
   module here.

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   -- scrypt ASN.1 Module

   scrypt-0 {1 3 6 1 4 1 11591 4 10}

   DEFINITIONS ::= BEGIN

   id-scrypt OBJECT IDENTIFIER ::= {1 3 6 1 4 1 11591 4 11}

   scrypt-params ::= SEQUENCE {
       salt OCTET STRING,
       costParameter INTEGER (1..MAX),
       blockSize INTEGER (1..MAX),
       parallelizationParameter INTEGER (1..MAX),
       keyLength INTEGER (1..MAX) OPTIONAL
   }

   PBES2-KDFs ALGORITHM-IDENTIFIER ::=
          { {scrypt-params IDENTIFIED BY id-scrypt}, ... }

   END

7.  Test Vectors for Salsa20/8 Core

   Below is a sequence of octets to illustrate input and output values
   for the Salsa20/8 Core.  The octets are hex encoded and whitespace is
   inserted for readability.  The value corresponds to the first input
   and output pair generated by the first scrypt test vector below.

   INPUT:
   7e 87 9a 21 4f 3e c9 86 7c a9 40 e6 41 71 8f 26
   ba ee 55 5b 8c 61 c1 b5 0d f8 46 11 6d cd 3b 1d
   ee 24 f3 19 df 9b 3d 85 14 12 1e 4b 5a c5 aa 32
   76 02 1d 29 09 c7 48 29 ed eb c6 8d b8 b8 c2 5e

   OUTPUT:
   a4 1f 85 9c 66 08 cc 99 3b 81 ca cb 02 0c ef 05
   04 4b 21 81 a2 fd 33 7d fd 7b 1c 63 96 68 2f 29
   b4 39 31 68 e3 c9 e6 bc fe 6b c5 b7 a0 6d 96 ba
   e4 24 cc 10 2c 91 74 5c 24 ad 67 3d c7 61 8f 81

8.  Test Vectors for scryptBlockMix

   Below is a sequence of octets to illustrate input and output values
   for scryptBlockMix.  The test vector uses an r value of 1.  The
   octets are hex encoded and whitespace is inserted for readability.
   The value corresponds to the first input and output pair generated by
   the first scrypt test vector below.

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   INPUT
   B[0] =  f7 ce 0b 65 3d 2d 72 a4 10 8c f5 ab e9 12 ff dd
           77 76 16 db bb 27 a7 0e 82 04 f3 ae 2d 0f 6f ad
           89 f6 8f 48 11 d1 e8 7b cc 3b d7 40 0a 9f fd 29
           09 4f 01 84 63 95 74 f3 9a e5 a1 31 52 17 bc d7

   B[1] =  89 49 91 44 72 13 bb 22 6c 25 b5 4d a8 63 70 fb
           cd 98 43 80 37 46 66 bb 8f fc b5 bf 40 c2 54 b0
           67 d2 7c 51 ce 4a d5 fe d8 29 c9 0b 50 5a 57 1b
           7f 4d 1c ad 6a 52 3c da 77 0e 67 bc ea af 7e 89

   OUTPUT
   B'[0] = a4 1f 85 9c 66 08 cc 99 3b 81 ca cb 02 0c ef 05
           04 4b 21 81 a2 fd 33 7d fd 7b 1c 63 96 68 2f 29
           b4 39 31 68 e3 c9 e6 bc fe 6b c5 b7 a0 6d 96 ba
           e4 24 cc 10 2c 91 74 5c 24 ad 67 3d c7 61 8f 81

   B'[1] = 20 ed c9 75 32 38 81 a8 05 40 f6 4c 16 2d cd 3c
           21 07 7c fe 5f 8d 5f e2 b1 a4 16 8f 95 36 78 b7
           7d 3b 3d 80 3b 60 e4 ab 92 09 96 e5 9b 4d 53 b6
           5d 2a 22 58 77 d5 ed f5 84 2c b9 f1 4e ef e4 25

9.  Test Vectors for scryptROMix

   Below is a sequence of octets to illustrate input and output values
   for scryptROMix.  The test vector uses an r value of 1 and an N value
   of 16.  The octets are hex encoded and whitespace is inserted for
   readability.  The value corresponds to the first input and output
   pair generated by the first scrypt test vector below.

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   INPUT:
   B = f7 ce 0b 65 3d 2d 72 a4 10 8c f5 ab e9 12 ff dd
       77 76 16 db bb 27 a7 0e 82 04 f3 ae 2d 0f 6f ad
       89 f6 8f 48 11 d1 e8 7b cc 3b d7 40 0a 9f fd 29
       09 4f 01 84 63 95 74 f3 9a e5 a1 31 52 17 bc d7
       89 49 91 44 72 13 bb 22 6c 25 b5 4d a8 63 70 fb
       cd 98 43 80 37 46 66 bb 8f fc b5 bf 40 c2 54 b0
       67 d2 7c 51 ce 4a d5 fe d8 29 c9 0b 50 5a 57 1b
       7f 4d 1c ad 6a 52 3c da 77 0e 67 bc ea af 7e 89

   OUTPUT:
   B = 79 cc c1 93 62 9d eb ca 04 7f 0b 70 60 4b f6 b6
       2c e3 dd 4a 96 26 e3 55 fa fc 61 98 e6 ea 2b 46
       d5 84 13 67 3b 99 b0 29 d6 65 c3 57 60 1f b4 26
       a0 b2 f4 bb a2 00 ee 9f 0a 43 d1 9b 57 1a 9c 71
       ef 11 42 e6 5d 5a 26 6f dd ca 83 2c e5 9f aa 7c
       ac 0b 9c f1 be 2b ff ca 30 0d 01 ee 38 76 19 c4
       ae 12 fd 44 38 f2 03 a0 e4 e1 c4 7e c3 14 86 1f
       4e 90 87 cb 33 39 6a 68 73 e8 f9 d2 53 9a 4b 8e

10.  Test Vectors for PBKDF2 with HMAC-SHA-256

   Below is a sequence of octets illustring input and output values for
   PBKDF2-HMAC-SHA-256.  The octets are hex encoded and whitespace is
   inserted for readability.  The test vectors below can be used to
   verify the PBKDF2-HMAC-SHA-256 [RFC2898] function.  The password and
   salt strings are passed as sequences of ASCII [RFC0020] octets.

   PBKDF2-HMAC-SHA-256 (P="passwd", S="salt",
                       c=1, dkLen=64) =
   55 ac 04 6e 56 e3 08 9f ec 16 91 c2 25 44 b6 05
   f9 41 85 21 6d de 04 65 e6 8b 9d 57 c2 0d ac bc
   49 ca 9c cc f1 79 b6 45 99 16 64 b3 9d 77 ef 31
   7c 71 b8 45 b1 e3 0b d5 09 11 20 41 d3 a1 97 83

   PBKDF2-HMAC-SHA-256 (P="Password", S="NaCl",
                        c=80000, dkLen=64) =
   4d dc d8 f6 0b 98 be 21 83 0c ee 5e f2 27 01 f9
   64 1a 44 18 d0 4c 04 14 ae ff 08 87 6b 34 ab 56
   a1 d4 25 a1 22 58 33 54 9a db 84 1b 51 c9 b3 17
   6a 27 2b de bb a1 d0 78 47 8f 62 b3 97 f3 3c 8d

11.  Test Vectors for scrypt

   For reference purposes, we provide the following test vectors for
   scrypt, where the password and salt strings are passed as sequences
   of ASCII [RFC0020] octets.

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   The parameters to the scrypt function below are, in order, the
   password P (octet string), the salt S (octet string), the CPU/Memory
   cost parameter N, the block size parameter r, and the parallelization
   parameter p, and the output size dkLen.  The output is hex encoded
   and whitespace is inserted for readability.

   scrypt (P="", S="",
           N=16, r=1, p=1, dklen=64) =
   77 d6 57 62 38 65 7b 20 3b 19 ca 42 c1 8a 04 97
   f1 6b 48 44 e3 07 4a e8 df df fa 3f ed e2 14 42
   fc d0 06 9d ed 09 48 f8 32 6a 75 3a 0f c8 1f 17
   e8 d3 e0 fb 2e 0d 36 28 cf 35 e2 0c 38 d1 89 06

   scrypt (P="password", S="NaCl",
           N=1024, r=8, p=16, dkLen=64) =
   fd ba be 1c 9d 34 72 00 78 56 e7 19 0d 01 e9 fe
   7c 6a d7 cb c8 23 78 30 e7 73 76 63 4b 37 31 62
   2e af 30 d9 2e 22 a3 88 6f f1 09 27 9d 98 30 da
   c7 27 af b9 4a 83 ee 6d 83 60 cb df a2 cc 06 40

   scrypt (P="pleaseletmein", S="SodiumChloride",
           N=16384, r=8, p=1, dkLen=64) =
   70 23 bd cb 3a fd 73 48 46 1c 06 cd 81 fd 38 eb
   fd a8 fb ba 90 4f 8e 3e a9 b5 43 f6 54 5d a1 f2
   d5 43 29 55 61 3f 0f cf 62 d4 97 05 24 2a 9a f9
   e6 1e 85 dc 0d 65 1e 40 df cf 01 7b 45 57 58 87

   scrypt (P="pleaseletmein", S="SodiumChloride",
           N=1048576, r=8, p=1, dkLen=64) =
   21 01 cb 9b 6a 51 1a ae ad db be 09 cf 70 f8 81
   ec 56 8d 57 4a 2f fd 4d ab e5 ee 98 20 ad aa 47
   8e 56 fd 8f 4b a5 d0 9f fa 1c 6d 92 7c 40 f4 c3
   37 30 40 49 e8 a9 52 fb cb f4 5c 6f a7 7a 41 a4

12.  Test Vectors for PKCS#8

   PKCS#8 [RFC5208] and Asymmetric Key Packages [RFC5958] encode
   encrypted private-keys.  Using PBES2 with scrypt as the KDF, the
   following illustrates an example of a PKCS#8 encoded private-key.
   The password is "Rabbit" (without the quotes) with N=1048576, r=8 and
   p=1.  The salt is "Mouse" and the encryption algorithm used is
   aes256-CBC.  The derived key is: E2 77 EA 2C AC B2 3E DA-FC 03 9D 22
   9B 79 DC 13 EC ED B6 01 D9 9B 18 2A-9F ED BA 1E 2B FB 4F 58.

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   -----BEGIN ENCRYPTED PRIVATE KEY-----
   MIHiME0GCSqGSIb3DQEFDTBAMB8GCSsGAQQB2kcECzASBAVNb3VzZQIDEAAAAgEI
   AgEBMB0GCWCGSAFlAwQBKgQQyYmguHMsOwzGMPoyObk/JgSBkJb47EWd5iAqJlyy
   +ni5ftd6gZgOPaLQClL7mEZc2KQay0VhjZm/7MbBUNbqOAXNM6OGebXxVp6sHUAL
   iBGY/Dls7B1TsWeGObE0sS1MXEpuREuloZjcsNVcNXWPlLdZtkSH6uwWzR0PyG/Z
   +ZXfNodZtd/voKlvLOw5B3opGIFaLkbtLZQwMiGtl42AS89lZg==
   -----END ENCRYPTED PRIVATE KEY-----

13.  Copying Conditions

   The authors agree to grant third parties the irrevocable right to
   copy, use and distribute this entire document or any portion of it,
   with or without modification, in any medium, without royalty,
   provided that, unless separate permission is granted, redistributed
   modified works do not contain misleading author, version, name of
   work, or endorsement information.

14.  Acknowledgements

   Text in this document was borrowed from [SCRYPT] and [RFC2898].  The
   PKCS#8 test vector was provided by Stephen N.  Henson.

   Feedback on this document were received from Dmitry Chestnykh,
   Alexander Klink, Rob Kendrick, Royce Williams Ted Rolle, Jr., and
   Eitan Adler.

15.  IANA Considerations

   None.

16.  Security Considerations

   This document specifies a cryptographic algorithm.  The reader must
   follow cryptographic research of published attacks.  ROMix has been
   proven sequential memory-hard under the Random Oracle model for the
   hash function.  The security of scrypt relies on the assumption that
   BlockMix with Salsa20/8 Core does not exhibit any "shortcuts" which
   would allow it to be iterated more easily than a random oracle.  For
   other claims about the security properties see [SCRYPT].

   Passwords and other sensitive data, such as intermediate values, may
   continue to be stored in memory, core dumps, swap areas, etc, for a
   long time after the implementation has processed them.  This makes
   attacks on the implementation easier.  Thus, implementation should
   consider storing sensitive data in protected memory areas.  How to
   achieve this is system dependent.

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   By nature and depending on parameters, running the scrypt algorithm
   may require large amounts of memory.  Systems should protect against
   a denial of service attack resulting from attackers presenting
   unreasonably large parameters.

17.  References

17.1.  Normative References

   [RFC2898]  Kaliski, B., "PKCS #5: Password-Based Cryptography
              Specification Version 2.0", RFC 2898, September 2000.

   [RFC6234]  Eastlake, D. and T. Hansen, "US Secure Hash Algorithms
              (SHA and SHA-based HMAC and HKDF)", RFC 6234, May 2011.

   [SALSA20SPEC]
              Bernstein, D., "Salsa20 specification", WWW
              http://cr.yp.to/snuffle/spec.pdf, April 2005.

   [SALSA20CORE]
              Bernstein, D., "The Salsa20 Core", WWW
              http://cr.yp.to/salsa20.html, March 2005.

17.2.  Informative References

   [RFC0020]  Cerf, V., "ASCII format for network interchange", RFC 20,
              October 1969.

   [RFC5208]  Kaliski, B., "Public-Key Cryptography Standards (PKCS) #8:
              Private-Key Information Syntax Specification Version 1.2",
              RFC 5208, May 2008.

   [RFC5958]  Turner, S., "Asymmetric Key Packages", RFC 5958, August
              2010.

   [SCRYPT]   Percival, C., "Stronger key derivation via sequential
              memory-hard functions", BSDCan'09
              http://www.tarsnap.com/scrypt/scrypt.pdf, May 2009.

Authors' Addresses

   Colin Percival
   Tarsnap

   Email: cperciva@tarsnap.com

Percival & Josefsson    Expires November 14, 2015              [Page 13]
Internet-Draft                   scrypt                         May 2015

   Simon Josefsson
   SJD AB

   Email: simon@josefsson.org
   URI:   http://josefsson.org/

Percival & Josefsson    Expires November 14, 2015              [Page 14]