<pre>Internet Engineering Task Force (IETF)                       C. Percival
Request for Comments: 7914                                       Tarsnap
Category: Informational                                     S. Josefsson
ISSN: 2070-1721                                                   SJD AB
                                                             August 2016


           <span class="h1">The scrypt Password-Based Key Derivation Function</span>

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

   This document is not an Internet Standards Track specification; it is
   published for informational purposes.

   This document is a product of the Internet Engineering Task Force
   (IETF).  It represents the consensus of the IETF community.  It has
   received public review and has been approved for publication by the
   Internet Engineering Steering Group (IESG).  Not all documents
   approved by the IESG are a candidate for any level of Internet
   Standard; see <a href="./rfc7841#section-2">Section&nbsp;2 of RFC 7841</a>.

   Information about the current status of this document, any errata,
   and how to provide feedback on it may be obtained at
   <a href="http://www.rfc-editor.org/info/rfc7914">http://www.rfc-editor.org/info/rfc7914</a>.

Copyright Notice

   Copyright (c) 2016 IETF Trust and the persons identified as the
   document authors.  All rights reserved.

   This document is subject to <a href="https://www.rfc-editor.org/bcp/bcp78">BCP 78</a> and the IETF Trust's Legal
   Provisions Relating to IETF Documents
   (<a href="http://trustee.ietf.org/license-info">http://trustee.ietf.org/license-info</a>) 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.  Code Components extracted from this document must
   include Simplified BSD License text as described in Section 4.e of
   the Trust Legal Provisions and are provided without warranty as
   described in the Simplified BSD License.




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Table of Contents

   <a href="#section-1">1</a>.  Introduction  . . . . . . . . . . . . . . . . . . . . . . . .   <a href="#page-2">2</a>
   <a href="#section-2">2</a>.  scrypt Parameters . . . . . . . . . . . . . . . . . . . . . .   <a href="#page-3">3</a>
   <a href="#section-3">3</a>.  The Salsa20/8 Core Function . . . . . . . . . . . . . . . . .   <a href="#page-4">4</a>
   <a href="#section-4">4</a>.  The scryptBlockMix Algorithm  . . . . . . . . . . . . . . . .   <a href="#page-5">5</a>
   <a href="#section-5">5</a>.  The scryptROMix Algorithm . . . . . . . . . . . . . . . . . .   <a href="#page-6">6</a>
   <a href="#section-6">6</a>.  The scrypt Algorithm  . . . . . . . . . . . . . . . . . . . .   <a href="#page-7">7</a>
   <a href="#section-7">7</a>.  ASN.1 Syntax  . . . . . . . . . . . . . . . . . . . . . . . .   <a href="#page-8">8</a>
     <a href="#section-7.1">7.1</a>.  ASN.1 Module  . . . . . . . . . . . . . . . . . . . . . .   <a href="#page-9">9</a>
   <a href="#section-8">8</a>.  Test Vectors for Salsa20/8 Core . . . . . . . . . . . . . . .   <a href="#page-9">9</a>
   <a href="#section-9">9</a>.  Test Vectors for scryptBlockMix . . . . . . . . . . . . . . .  <a href="#page-10">10</a>
   <a href="#section-10">10</a>. Test Vectors for scryptROMix  . . . . . . . . . . . . . . . .  <a href="#page-11">11</a>
   <a href="#section-11">11</a>. Test Vectors for PBKDF2 with HMAC-SHA-256 . . . . . . . . . .  <a href="#page-12">12</a>
   <a href="#section-12">12</a>. Test Vectors for scrypt . . . . . . . . . . . . . . . . . . .  <a href="#page-13">13</a>
   <a href="#section-13">13</a>. Test Vectors for PKCS#8 . . . . . . . . . . . . . . . . . . .  <a href="#page-14">14</a>
   <a href="#section-14">14</a>. Security Considerations . . . . . . . . . . . . . . . . . . .  <a href="#page-14">14</a>
   <a href="#section-15">15</a>. References  . . . . . . . . . . . . . . . . . . . . . . . . .  <a href="#page-15">15</a>
     <a href="#section-15.1">15.1</a>.  Normative References . . . . . . . . . . . . . . . . . .  <a href="#page-15">15</a>
     <a href="#section-15.2">15.2</a>.  Informative References . . . . . . . . . . . . . . . . .  <a href="#page-15">15</a>
   Acknowledgements  . . . . . . . . . . . . . . . . . . . . . . . .  <a href="#page-16">16</a>
   Authors' Addresses  . . . . . . . . . . . . . . . . . . . . . . .  <a href="#page-16">16</a>

<span class="h2"><a class="selflink" id="section-1" href="#section-1">1</a>.  Introduction</span>

   Password-based key derivation functions are used in cryptography and
   security protocols 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, Public-Key Cryptography
   Standards#5 (PKCS#5) PBKDF2 [<a href="./rfc2898" title="&quot;PKCS #5: Password-Based Cryptography Specification Version 2.0&quot;">RFC2898</a>] (typically used with SHA-1),
   GNU SHA-256/512 crypt [<a href="#ref-SHA2CRYPT">SHA2CRYPT</a>], Windows NT LAN Manager (NTLM)
   [<a href="#ref-NTLM" title="&quot;[MS-NLMP]: NT LAN Manager (NTLM) Authentication Protocol&quot;">NTLM</a>] hash, and the Blowfish-based bcrypt [<a href="#ref-BCRYPT" title="&quot;A Future-Adaptable Password Scheme&quot;">BCRYPT</a>].  These
   algorithms are all based on a cryptographic primitive combined with
   salting and/or iteration.  The iteration count is used to slow down
   the computation, and the salt is used to make pre-computation
   costlier.

   All password-based key derivation functions mentioned above share the
   same weakness against powerful attackers.  Provided 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 attackers' ever-increasing
   computing power -- as long as attackers are limited to the same
   software implementations as legitimate users.  While parallelized
   hardware implementations may not change the number of operations
   performed compared to software implementations, this does not prevent
   them from dramatically changing the asymptotic cost, since in many



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   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, with 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 that attackers can
   gain by using custom-designed parallel circuits for breaking
   password-based key derivation functions.

   This document does not introduce scrypt for the first time.  The
   original scrypt paper [<a href="#ref-SCRYPT" title="&quot;STRONGER KEY DERIVATION VIA SEQUENTIAL MEMORY-HARD FUNCTIONS&quot;">SCRYPT</a>] was published as a peer-reviewed
   scientific paper and contains further background and discussions.

   The purpose of this document is to serve as a stable reference for
   documents making use of scrypt.  The rest of this document is divided
   into sections that each describe parameter choices and algorithm
   steps needed for the final "scrypt" algorithm.

<span class="h2"><a class="selflink" id="section-2" href="#section-2">2</a>.  scrypt Parameters</span>

   The scrypt function takes several parameters.  The passphrase P is
   typically a human-chosen password.  The salt is normally uniquely and
   randomly generated [<a href="./rfc4086" title="&quot;Randomness Requirements for Security&quot;">RFC4086</a>].  The parameter r ("blockSize")
   specifies the block size.  The CPU/Memory cost parameter N
   ("costParameter") must be larger than 1, a power of 2, and less than
   2^(128 * r / 8).  The parallelization parameter p
   ("parallelizationParameter") is a positive integer less than or equal
   to ((2^32-1) * 32) / (128 * r).  The intended output length dkLen is
   the length in octets of the key to be derived ("keyLength"); it is a
   positive integer less than or equal to (2^32 - 1) * 32.

   Users of scrypt can tune the parameters N, r, and p according to the
   amount of memory and computing power available, the latency-bandwidth
   product of the memory subsystem, and the amount of parallelism
   desired.  At the current time, r=8 and p=1 appears to yield good
   results, but as memory latency and CPU parallelism increase, it is
   likely that the optimum values for both r and p will increase.  Note
   also that since the computations of SMix are independent, a large
   value of p can be used to increase the computational cost of scrypt





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   without increasing the memory usage; so we can expect scrypt to
   remain useful even if the growth rates of CPU power and memory
   capacity diverge.

<span class="h2"><a class="selflink" id="section-3" href="#section-3">3</a>.  The Salsa20/8 Core Function</span>

   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 [<a href="#ref-SALSA20SPEC">SALSA20SPEC</a>] for its
   specification and [<a href="#ref-SALSA20CORE">SALSA20CORE</a>] for more information.  The algorithm
   description, in C language, is included below as a stable reference,
   without endianness conversion and alignment.

   #define R(a,b) (((a) &lt;&lt; (b)) | ((a) &gt;&gt; (32 - (b))))
   void salsa20_word_specification(uint32 out[16],uint32 in[16])
   {
     int i;
     uint32 x[16];
     for (i = 0;i &lt; 16;++i) x[i] = in[i];
     for (i = 8;i &gt; 0;i -= 2) {
       x[ 4] ^= R(x[ 0]+x[12], 7);  x[ 8] ^= R(x[ 4]+x[ 0], 9);
       x[12] ^= R(x[ 8]+x[ 4],13);  x[ 0] ^= R(x[12]+x[ 8],18);
       x[ 9] ^= R(x[ 5]+x[ 1], 7);  x[13] ^= R(x[ 9]+x[ 5], 9);
       x[ 1] ^= R(x[13]+x[ 9],13);  x[ 5] ^= R(x[ 1]+x[13],18);
       x[14] ^= R(x[10]+x[ 6], 7);  x[ 2] ^= R(x[14]+x[10], 9);
       x[ 6] ^= R(x[ 2]+x[14],13);  x[10] ^= R(x[ 6]+x[ 2],18);
       x[ 3] ^= R(x[15]+x[11], 7);  x[ 7] ^= R(x[ 3]+x[15], 9);
       x[11] ^= R(x[ 7]+x[ 3],13);  x[15] ^= R(x[11]+x[ 7],18);
       x[ 1] ^= R(x[ 0]+x[ 3], 7);  x[ 2] ^= R(x[ 1]+x[ 0], 9);
       x[ 3] ^= R(x[ 2]+x[ 1],13);  x[ 0] ^= R(x[ 3]+x[ 2],18);
       x[ 6] ^= R(x[ 5]+x[ 4], 7);  x[ 7] ^= R(x[ 6]+x[ 5], 9);
       x[ 4] ^= R(x[ 7]+x[ 6],13);  x[ 5] ^= R(x[ 4]+x[ 7],18);
       x[11] ^= R(x[10]+x[ 9], 7);  x[ 8] ^= R(x[11]+x[10], 9);
       x[ 9] ^= R(x[ 8]+x[11],13);  x[10] ^= R(x[ 9]+x[ 8],18);
       x[12] ^= R(x[15]+x[14], 7);  x[13] ^= R(x[12]+x[15], 9);
       x[14] ^= R(x[13]+x[12],13);  x[15] ^= R(x[14]+x[13],18);
     }
     for (i = 0;i &lt; 16;++i) out[i] = x[i] + in[i];
   }











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<span class="h2"><a class="selflink" id="section-4" href="#section-4">4</a>.  The scryptBlockMix Algorithm</span>

   The scryptBlockMix algorithm is the same as the BlockMix algorithm
   described in [<a href="#ref-SCRYPT" title="&quot;STRONGER KEY DERIVATION VIA SEQUENTIAL MEMORY-HARD FUNCTIONS&quot;">SCRYPT</a>] 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.

   Algorithm scryptBlockMix

   Parameters:
            r       Block size parameter.

   Input:
            B[0] || B[1] || ... || B[2 * r - 1]
                   Input octet string (of size 128 * r octets),
                   treated as 2 * r 64-octet blocks,
                   where each element in B is a 64-octet block.

   Output:
            B'[0] || B'[1] || ... || B'[2 * r - 1]
                   Output octet string.

   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])

















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<span class="h2"><a class="selflink" id="section-5" href="#section-5">5</a>.  The scryptROMix Algorithm</span>

   The scryptROMix algorithm is the same as the ROMix algorithm
   described in [<a href="#ref-SCRYPT" title="&quot;STRONGER KEY DERIVATION VIA SEQUENTIAL MEMORY-HARD FUNCTIONS&quot;">SCRYPT</a>] but with scryptBlockMix used as the hash
   function H and the Integerify function explained inline.

   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















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<span class="h2"><a class="selflink" id="section-6" href="#section-6">6</a>.  The scrypt Algorithm</span>

   The PBKDF2-HMAC-SHA-256 function used below denotes the PBKDF2
   algorithm [<a href="./rfc2898" title="&quot;PKCS #5: Password-Based Cryptography Specification Version 2.0&quot;">RFC2898</a>] used with HMAC-SHA-256 [<a href="./rfc6234" title="&quot;US Secure Hash Algorithms (SHA and SHA-based HMAC and HKDF)&quot;">RFC6234</a>] as the
   Pseudorandom Function (PRF).  The HMAC-SHA-256 function generates
   32-octet outputs.

   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. Initialize an array B consisting of p blocks of 128 * r octets
       each:
        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)













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<span class="h2"><a class="selflink" id="section-7" href="#section-7">7</a>.  ASN.1 Syntax</span>

   This section defines ASN.1 syntax for the scrypt key derivation
   function (KDF).  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:

   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 [<a href="./rfc5208" title="&quot;Public-Key Cryptography Standards (PKCS) #8: Private-Key Information Syntax Specification Version 1.2&quot;">RFC5208</a>] and Asymmetric Key Packages
   [<a href="./rfc5958" title="&quot;Asymmetric Key Packages&quot;">RFC5958</a>], the following extension of the PBES2-KDFs type is needed:

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






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<span class="h3"><a class="selflink" id="section-7.1" href="#section-7.1">7.1</a>.  ASN.1 Module</span>

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

   -- 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

<span class="h2"><a class="selflink" id="section-8" href="#section-8">8</a>.  Test Vectors for Salsa20/8 Core</span>

   Below is a sequence of octets that 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







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<span class="h2"><a class="selflink" id="section-9" href="#section-9">9</a>.  Test Vectors for scryptBlockMix</span>

   Below is a sequence of octets that 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.

   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






















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<span class="h2"><a class="selflink" id="section-10" href="#section-10">10</a>.  Test Vectors for scryptROMix</span>

   Below is a sequence of octets that 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.

   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
























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<span class="grey"><a href="./rfc7914">RFC 7914</a>                      scrypt PBKDF                   August 2016</span>


<span class="h2"><a class="selflink" id="section-11" href="#section-11">11</a>.  Test Vectors for PBKDF2 with HMAC-SHA-256</span>

   Below is a sequence of octets that illustrate 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 [<a href="./rfc2898" title="&quot;PKCS #5: Password-Based Cryptography Specification Version 2.0&quot;">RFC2898</a>] function.  The password and
   salt strings are passed as sequences of ASCII [<a href="./rfc20" title="&quot;ASCII format for network interchange&quot;">RFC20</a>] 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






























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<span class="grey"><a href="./rfc7914">RFC 7914</a>                      scrypt PBKDF                   August 2016</span>


<span class="h2"><a class="selflink" id="section-12" href="#section-12">12</a>.  Test Vectors for scrypt</span>

   For reference purposes, we provide the following test vectors for
   scrypt, where the password and salt strings are passed as sequences
   of ASCII [<a href="./rfc20" title="&quot;ASCII format for network interchange&quot;">RFC20</a>] octets.

   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, 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












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<span class="grey"><a href="./rfc7914">RFC 7914</a>                      scrypt PBKDF                   August 2016</span>


<span class="h2"><a class="selflink" id="section-13" href="#section-13">13</a>.  Test Vectors for PKCS#8</span>

   PKCS#8 [<a href="./rfc5208" title="&quot;Public-Key Cryptography Standards (PKCS) #8: Private-Key Information Syntax Specification Version 1.2&quot;">RFC5208</a>] and Asymmetric Key Packages [<a href="./rfc5958" title="&quot;Asymmetric Key Packages&quot;">RFC5958</a>] 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.

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

<span class="h2"><a class="selflink" id="section-14" href="#section-14">14</a>.  Security Considerations</span>

   This document specifies a cryptographic algorithm, and there is
   always a risk that someone will find a weakness in it.  By following
   the cryptographic research area, you may learn of publications
   relevant to scrypt.

   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" that would allow it to be iterated more easily than a
   random oracle.  For other claims about the security properties, see
   [<a href="#ref-SCRYPT" title="&quot;STRONGER KEY DERIVATION VIA SEQUENTIAL MEMORY-HARD FUNCTIONS&quot;">SCRYPT</a>].

   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.

   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.

   Poor parameter choices can be harmful for security; for example, if
   you tune the parameters so that memory use is reduced to small
   amounts that will affect the properties of the algorithm.




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<span class="grey"><a href="./rfc7914">RFC 7914</a>                      scrypt PBKDF                   August 2016</span>


<span class="h2"><a class="selflink" id="section-15" href="#section-15">15</a>.  References</span>

<span class="h3"><a class="selflink" id="section-15.1" href="#section-15.1">15.1</a>.  Normative References</span>

   [<a id="ref-RFC2898">RFC2898</a>]  Kaliski, B., "PKCS #5: Password-Based Cryptography
              Specification Version 2.0", <a href="./rfc2898">RFC 2898</a>,
              DOI 10.17487/RFC2898, September 2000,
              &lt;<a href="http://www.rfc-editor.org/info/rfc2898">http://www.rfc-editor.org/info/rfc2898</a>&gt;.

   [<a id="ref-RFC6234">RFC6234</a>]  Eastlake 3rd, D. and T. Hansen, "US Secure Hash Algorithms
              (SHA and SHA-based HMAC and HKDF)", <a href="./rfc6234">RFC 6234</a>,
              DOI 10.17487/RFC6234, May 2011,
              &lt;<a href="http://www.rfc-editor.org/info/rfc6234">http://www.rfc-editor.org/info/rfc6234</a>&gt;.

<span class="h3"><a class="selflink" id="section-15.2" href="#section-15.2">15.2</a>.  Informative References</span>

   [<a id="ref-BCRYPT">BCRYPT</a>]   Provos, N. and D. Mazieres, "A Future-Adaptable Password
              Scheme", USENIX 1999, June 1999,
              &lt;<a href="https://www.usenix.org/legacy/event/usenix99/provos/provos.pdf">https://www.usenix.org/legacy/event/usenix99/provos/</a>
              <a href="https://www.usenix.org/legacy/event/usenix99/provos/provos.pdf">provos.pdf</a>&gt;.

   [<a id="ref-NTLM">NTLM</a>]     Microsoft, "[MS-NLMP]: NT LAN Manager (NTLM)
              Authentication Protocol", 2015,
              &lt;<a href="https://msdn.microsoft.com/en-us/library/cc236621.aspx">https://msdn.microsoft.com/en-us/library/cc236621.aspx</a>&gt;.

   [<a id="ref-RFC20">RFC20</a>]    Cerf, V., "ASCII format for network interchange", STD 80,
              <a href="./rfc20">RFC 20</a>, DOI 10.17487/RFC0020, October 1969,
              &lt;<a href="http://www.rfc-editor.org/info/rfc20">http://www.rfc-editor.org/info/rfc20</a>&gt;.

   [<a id="ref-RFC4086">RFC4086</a>]  Eastlake 3rd, D., Schiller, J., and S. Crocker,
              "Randomness Requirements for Security", <a href="https://www.rfc-editor.org/bcp/bcp106">BCP 106</a>, <a href="./rfc4086">RFC 4086</a>,
              DOI 10.17487/RFC4086, June 2005,
              &lt;<a href="http://www.rfc-editor.org/info/rfc4086">http://www.rfc-editor.org/info/rfc4086</a>&gt;.

   [<a id="ref-RFC5208">RFC5208</a>]  Kaliski, B., "Public-Key Cryptography Standards (PKCS) #8:
              Private-Key Information Syntax Specification Version 1.2",
              <a href="./rfc5208">RFC 5208</a>, DOI 10.17487/RFC5208, May 2008,
              &lt;<a href="http://www.rfc-editor.org/info/rfc5208">http://www.rfc-editor.org/info/rfc5208</a>&gt;.

   [<a id="ref-RFC5958">RFC5958</a>]  Turner, S., "Asymmetric Key Packages", <a href="./rfc5958">RFC 5958</a>,
              DOI 10.17487/RFC5958, August 2010,
              &lt;<a href="http://www.rfc-editor.org/info/rfc5958">http://www.rfc-editor.org/info/rfc5958</a>&gt;.

   [<a id="ref-SALSA20CORE">SALSA20CORE</a>]
              Bernstein, D., "The Salsa20 Core", March 2005,
              &lt;<a href="http://cr.yp.to/salsa20.html">http://cr.yp.to/salsa20.html</a>&gt;.





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<span class="grey"><a href="./rfc7914">RFC 7914</a>                      scrypt PBKDF                   August 2016</span>


   [<a id="ref-SALSA20SPEC">SALSA20SPEC</a>]
              Bernstein, D., "Salsa20 specification", April 2005,
              &lt;<a href="http://cr.yp.to/snuffle/spec.pdf">http://cr.yp.to/snuffle/spec.pdf</a>&gt;.

   [<a id="ref-SCRYPT">SCRYPT</a>]   Percival, C., "STRONGER KEY DERIVATION VIA SEQUENTIAL
              MEMORY-HARD FUNCTIONS",  BSDCan'09, May 2009,
              &lt;<a href="http://www.tarsnap.com/scrypt/scrypt.pdf">http://www.tarsnap.com/scrypt/scrypt.pdf</a>&gt;.

   [<a id="ref-SHA2CRYPT">SHA2CRYPT</a>]
              Drepper, U., "Unix crypt using SHA-256 and SHA-512", April
              2008, &lt;<a href="http://www.akkadia.org/drepper/SHA-crypt.txt">http://www.akkadia.org/drepper/SHA-crypt.txt</a>&gt;.

Acknowledgements

   Text in this document was borrowed from [<a href="#ref-SCRYPT" title="&quot;STRONGER KEY DERIVATION VIA SEQUENTIAL MEMORY-HARD FUNCTIONS&quot;">SCRYPT</a>] and [<a href="./rfc2898" title="&quot;PKCS #5: Password-Based Cryptography Specification Version 2.0&quot;">RFC2898</a>].  The
   PKCS#8 test vector was provided by Stephen N. Henson.

   Feedback on this document was received from Dmitry Chestnykh,
   Alexander Klink, Rob Kendrick, Royce Williams, Ted Rolle, Jr., Eitan
   Adler, Stephen Farrel, Nikos Mavrogiannopoulos, and Paul Kyzivat.

Authors' Addresses

   Colin Percival
   Tarsnap

   Email: cperciva@tarsnap.com


   Simon Josefsson
   SJD AB

   Email: simon@josefsson.org
   URI:   <a href="http://josefsson.org/">http://josefsson.org/</a>

















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