Internet Engineering Task Force M-J. Saarinen, Ed. Internet-Draft Independent Consultant Intended status: Informational J-P. Aumasson Expires: August 9, 2015 Kudelski Security February 5, 2015 The BLAKE2 Cryptographic Hash and MAC draft-saarinen-blake2-02 Abstract This document describes the cryptographic hash function BLAKE2, making the algorithm specification and C source code conveniently available to the Internet community. BLAKE2 comes in two main flavors: BLAKE2b is optimized for 64-bit platforms, and BLAKE2s for smaller architectures. BLAKE2 can be directly keyed, making it functionally equivalent to a Message Authentication Code (MAC). 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 http://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 August 9, 2015. Copyright Notice Copyright (c) 2015 IETF Trust and the persons identified as the document authors. All rights reserved. This document is subject to BCP 78 and the IETF Trust's Legal Provisions Relating to IETF Documents (http://trustee.ietf.org/license-info) 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 Saarinen & Aumasson Expires August 9, 2015 [Page 1] Internet-Draft The BLAKE2 Cryptographic Hash and MAC February 2015 the Trust Legal Provisions and are provided without warranty as described in the Simplified BSD License. Table of Contents 1. Introduction and Terminology . . . . . . . . . . . . . . . . 2 2. Conventions, Variables, and Constants . . . . . . . . . . . . 3 2.1. Parameters . . . . . . . . . . . . . . . . . . . . . . . 3 2.2. Other Constants and Variables . . . . . . . . . . . . . . 4 2.3. Arithmetic Notation . . . . . . . . . . . . . . . . . . . 4 2.4. Little-Endian Interpretation of Words as Byte Sequences . 4 2.5. Parameter Block . . . . . . . . . . . . . . . . . . . . . 5 2.6. Initialization Vector . . . . . . . . . . . . . . . . . . 5 2.7. Message Schedule SIGMA . . . . . . . . . . . . . . . . . 6 3. BLAKE2 Processing . . . . . . . . . . . . . . . . . . . . . . 6 3.1. Mixing Function G . . . . . . . . . . . . . . . . . . . . 6 3.2. Compression Function F . . . . . . . . . . . . . . . . . 6 3.3. Padding data and Computing a BLAKE2 Digest . . . . . . . 8 4. Standard Parameter Sets and Algorithm Identifiers . . . . . . 9 5. Acknowledgements . . . . . . . . . . . . . . . . . . . . . . 10 6. IANA Considerations . . . . . . . . . . . . . . . . . . . . . 10 7. Security Considerations . . . . . . . . . . . . . . . . . . . 10 8. References . . . . . . . . . . . . . . . . . . . . . . . . . 10 8.1. Normative References . . . . . . . . . . . . . . . . . . 10 8.2. Informative References . . . . . . . . . . . . . . . . . 10 Appendix A. BLAKE2b Implementation C Source . . . . . . . . . . 11 A.1. blake2b.h . . . . . . . . . . . . . . . . . . . . . . . . 11 A.2. blake2b.c . . . . . . . . . . . . . . . . . . . . . . . . 12 Appendix B. BLAKE2s Implementation C Source . . . . . . . . . . 16 B.1. blake2s.h . . . . . . . . . . . . . . . . . . . . . . . . 16 B.2. blake2s.c . . . . . . . . . . . . . . . . . . . . . . . . 17 Appendix C. BLAKE2b and BLAKE2s Self Test Module C Source . . . 20 Authors' Addresses . . . . . . . . . . . . . . . . . . . . . . . 24 1. Introduction and Terminology The [BLAKE2] cryptographic hash function was designed by Jean- Philippe Aumasson, Samuel Neves, Zooko Wilcox-O'Hearn, and Christian Winnerlein. BLAKE2 comes in two basic flavors: o BLAKE2b (or just BLAKE2) is optimized for 64-bit platforms and produces digests of any size between 1 and 64 bytes. o BLAKE2s is optimized for 8- to 32-bit platforms, and produces digests of any size between 1 and 32 bytes. Saarinen & Aumasson Expires August 9, 2015 [Page 2] Internet-Draft The BLAKE2 Cryptographic Hash and MAC February 2015 Both BLAKE2b and BLAKE2s are believed to be highly secure and have good performance on any platform, software or hardware. BLAKE2 does not require a special "HMAC" construction for keyed message authentication as they have a built-in keying mechanism. The BLAKE2 hash function may be used by digital signature algorithms and message authentication and integrity protection mechanisms in applications such as Public Key Infrastructure (PKI), secure communication protocols, cloud storage, intrusion detection, forensic suites, and version control systems. The BLAKE2 suite provides a more efficient alternative to US Secure Hash Algorithms SHA and HMAC-SHA [RFC6234]. BLAKE2-128 is especially suited as a fast and more secure drop-in replacement to MD5 and HMAC- MD5 in legacy applications [RFC6151]. A reference implementation in C programming language for BLAKE2b can be found in Appendix A and for BLAKE2s in Appendix B of this document. These implementations SHOULD be validated with the Test Module contained in Appendix C. Due to space constraints, this document does not contain a full set of test vectors for BLAKE2. We refer to [BLAKE2] for up to date information about compliance testing and integrating BLAKE2 into various applications. The key words "MUST", "MUST NOT", "REQUIRED", "SHALL", "SHALL NOT", "SHOULD", "SHOULD NOT", "RECOMMENDED", "MAY", and "OPTIONAL" in this document are to be interpreted as described in [RFC2119]. 2. Conventions, Variables, and Constants 2.1. Parameters The following table summarizes various parameters and their ranges: | BLAKE2b | BLAKE2s | --------------+------------------+------------------+ Bits in word | w = 64 | w = 32 | Rounds in F | r = 12 | r = 10 | Block bytes | bb = 128 | bb = 64 | Hash bytes | 1 <= nn <= 64 | 1 <= nn <= 32 | Key bytes | 0 <= kk <= 64 | 0 <= kk <= 32 | Input bytes | 0 <= ll < 2**128 | 0 <= ll < 2**64 | --------------+------------------+------------------+ G Rotation | (R1, R2, R3, R4) | (R1, R2, R3, R4) | constants = | (32, 24, 16, 63) | (16, 12, 8, 7) | --------------+------------------+------------------+ Saarinen & Aumasson Expires August 9, 2015 [Page 3] Internet-Draft The BLAKE2 Cryptographic Hash and MAC February 2015 2.2. Other Constants and Variables IV[0..7] Initialization Vector (constant). SIGMA[0..9] Message word permutations (constant). p[0..7] Parameter block (defines hash and key sizes). m[0..15] Sixteen words of a single message block. h[0..7] Internal state of the hash. d[0..dd-1] Padded input blocks. "dd" is the number of blocks. t Byte offset at the end of the current block. f Flag indicating the last block. 2.3. Arithmetic Notation For real-valued x we define: floor(x) Floor, the largest integer <= x. ceil(x) Ceiling, the smallest integer >= x. frac(x) Positive fractional part of x, frac(x) = x - floor(x). Operator notation in pseudocode: 2**n = 2 to the power "n". 2**0=1, 2**1=2, 2**2=4, 2**3=8, etc. a ^ b = Bitwise exclusive-or operation between "a" and "b". a mod b = Remainder "a" modulo "b", always in range [0, b-1]. x >> n = floor(x / 2**n). Logical shift "x" right by "n" bits. x << n = (x * 2**n) mod (2**w). Logical shift "x" left by "n". x >>> n = (x >> n) ^ (x << (w - n)). Rotate "x" right by "n" bits. 2.4. Little-Endian Interpretation of Words as Byte Sequences All mathematical operations are on 64-bit words in BLAKE2b and on 32-bit words on BLAKE2b. Saarinen & Aumasson Expires August 9, 2015 [Page 4] Internet-Draft The BLAKE2 Cryptographic Hash and MAC February 2015 We may also perform operations on vectors of words. Vector indexing is zero-based; the first element of an n-element vector "v" is v[0] and the last one is v[n - 1]. All elements is denoted by v[0..n-1]. Byte (octet) streams are interpreted as words in little-endian order, with the least significant byte first. Consider this sequence of eight hexadecimal bytes: x[0..7] = 0x01 0x23 0x45 0x67 0x89 0xAB 0xCD 0xEF When interpreted as a 32-bit word from the beginning memory address, x[0..3] has numerical value 0x67452301 or 1732584193. When interpreted as a 64-bit word, bytes x[0..7] have numerical value 0xEFCDAB8967452301 or 17279655951921914625. 2.5. Parameter Block We specify the parameter block words p[0..7] as follows: byte offset: 3 2 1 0 (otherwise zero) p[0] = 0x0101kknn p[1..7] = 0 Here the "nn" byte specifies the hash size in bytes. The second (little-endian) byte of parameter block, "kk", specifies key size in bytes. Set kk = 00 for for unkeyed hashing. Bytes 2 and 3 are set as 01. All other bytes in the parameter block are set as zero. NOTE. [BLAKE2] defines additional variants of BLAKE2 with features such as salting, personalized hashes, and tree hashing. These OPTIONAL features use fields in the parameter block which are not defined in this document. 2.6. Initialization Vector We define the Initialization Vector constant IV mathematically as: IV[i] = floor(2**w * frac(sqrt(prime(i+1)))), where prime(i) is the i:th prime number ( 2, 3, 5, 7, 11, 13, 17, 19 ) and sqrt(x) is the square root of x. The numerical values of IV can be also found in implementations in Appendix A and Appendix B for BLAkE2b and BLAKE2s, respectively. NOTE. BLAKE2b IV is the same as SHA-512 IV and BLAKE2s IV is the same as SHA-256 IV; see [RFC6234]. Saarinen & Aumasson Expires August 9, 2015 [Page 5] Internet-Draft The BLAKE2 Cryptographic Hash and MAC February 2015 2.7. Message Schedule SIGMA Message word schedule permutations for each round of both BLAKE2b and BLAKE2s are defined by SIGMA. For BLAKE2b the two extra permutations for rounds 10 and 11 are SIGMA[10..11] = SIGMA[0..1]. Round | 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 | ----------+-------------------------------------------------+ SIGMA[0] | 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 | SIGMA[1] | 14 10 4 8 9 15 13 6 1 12 0 2 11 7 5 3 | SIGMA[2] | 11 8 12 0 5 2 15 13 10 14 3 6 7 1 9 4 | SIGMA[3] | 7 9 3 1 13 12 11 14 2 6 5 10 4 0 15 8 | SIGMA[4] | 9 0 5 7 2 4 10 15 14 1 11 12 6 8 3 13 | SIGMA[5] | 2 12 6 10 0 11 8 3 4 13 7 5 15 14 1 9 | SIGMA[6] | 12 5 1 15 14 13 4 10 0 7 6 3 9 2 8 11 | SIGMA[7] | 13 11 7 14 12 1 3 9 5 0 15 4 8 6 2 10 | SIGMA[8] | 6 15 14 9 11 3 0 8 12 2 13 7 1 4 10 5 | SIGMA[9] | 10 2 8 4 7 6 1 5 15 11 9 14 3 12 13 0 | ----------+-------------------------------------------------+ 3. BLAKE2 Processing 3.1. Mixing Function G The G primitive function mixes two input words "x" and "y" into four words indexed by "a", "b", "c", and "d" in the working vector v[0..15]. The full modified vector is returned. The rotation constants (R1, R2, R3, R4) are given in Section 2.1. FUNCTION G( v[0..15], a, b, c, d, x, y ) | | v[a] := (v[a] + v[b] + x) mod 2**w | v[d] := (v[d] ^ v[a]) >>> R1 | v[c] := (v[c] + v[d]) mod 2**w | v[b] := (v[b] ^ v[c]) >>> R2 | v[a] := (v[a] + v[b] + y) mod 2**w | v[d] := (v[d] ^ v[a]) >>> R3 | v[c] := (v[c] + v[d]) mod 2**w | v[b] := (v[b] ^ v[c]) >>> R4 | | RETURN v[0..15] | END FUNCTION. 3.2. Compression Function F Compression function F takes as an argument the state vector "h", zero-padded message block vector "m", 2w-bit offset counter "t", and Saarinen & Aumasson Expires August 9, 2015 [Page 6] Internet-Draft The BLAKE2 Cryptographic Hash and MAC February 2015 final block indicator flag "f". Local vector v[0..15] is used in processing. F returns a new state vector. The number of rounds "r" is 12 for BLAKE2b and 10 for BLAKE2s. Rounds are numbered from 0 to r - 1. FUNCTION F( h[0..7], m[0..15], t, f ) | | // Initialize local work vector v[0..15] | v[0..7] := h[0..7] // First half from state. | v[8..15] := IV[0..7] // Second half from IV. | | v[12] := v[12] ^ (t mod 2**w) // Low word of the offset. | v[13] := v[13] ^ (t >> w) // High word. | | IF f = TRUE THEN // last block flag? | | v[14] := v[14] ^ 0xFF..FF // Invert all bits. | END IF. | | // Cryptographic mixing | FOR i = 0 TO r - 1 DO // Ten or twelve rounds. | | | | // Message word selection permutation for this round. | | s[0..15] := SIGMA[i mod 10][0..15] | | | | v := G( v, 0, 4, 8, 12, m[s[ 0]], m[s[ 1]] ) | | v := G( v, 1, 5, 9, 13, m[s[ 2]], m[s[ 3]] ) | | v := G( v, 2, 6, 10, 14, m[s[ 4]], m[s[ 5]] ) | | v := G( v, 3, 7, 11, 15, m[s[ 6]], m[s[ 7]] ) | | | | v := G( v, 0, 5, 10, 15, m[s[ 8]], m[s[ 9]] ) | | v := G( v, 1, 6, 11, 12, m[s[10]], m[s[11]] ) | | v := G( v, 2, 7, 8, 13, m[s[12]], m[s[13]] ) | | v := G( v, 3, 4, 9, 14, m[s[14]], m[s[15]] ) | | | END FOR | | FOR i = 0 TO 7 DO // XOR the two halves. | | h[i] := h[i] ^ v[i] ^ v[i + 8] | END FOR. | | RETURN h[0..7] // New state. | END FUNCTION. Saarinen & Aumasson Expires August 9, 2015 [Page 7] Internet-Draft The BLAKE2 Cryptographic Hash and MAC February 2015 3.3. Padding data and Computing a BLAKE2 Digest We refer the reader to Appendix A and Appendix B for reference C language implementations of BLAkE2b and BLAKE2s, respectively. Key and data input is split and padded into "dd" message blocks d[0..dd-1], each consisting of 16 words (or "bb" bytes). If a secret key is used (kk > 0), it is padded with zero bytes and set as d[0]. Otherwise d[0] is the first data block. The final data block d[dd-1] is also padded with zero to "bb" bytes (16 words). Number of blocks is therefore dd = ceil(kk / bb) + ceil(ll / bb). However in special case of unkeyed empty message (kk = 0 and ll = 0), we still set dd = 1 and d[0] consists of all zeros. The following procedure for processes the padded data blocks into an "nn"-byte final hash value. See Section 2 for description of various variables and constants used. FUNCTION BLAKE2( d[0..dd-1], ll, kk, nn ) | | h[0..7] := IV[0..7] // Initialization Vector. | | // Parameter block p[0] | h[0] := h[0] ^ 0x01010000 ^ (kk << 8) ^ nn | | // Process padded key and data blocks | IF dd > 1 THEN | | FOR i = 0 TO dd - 2 DO | | | h := COMPRESS( h, d[i], (i + 1) * bb, FALSE ) | | END FOR. | END IF. | | // Final block. | IF kk = 0 THEN | | h := COMPRESS( h, d[dd - 1], ll, TRUE ) | ELSE | | h := COMPRESS( h, d[dd - 1], ll + bb, TRUE ) | END IF. | | RETURN first "nn" bytes from little-endian word array h[]. | END FUNCTION. Saarinen & Aumasson Expires August 9, 2015 [Page 8] Internet-Draft The BLAKE2 Cryptographic Hash and MAC February 2015 4. Standard Parameter Sets and Algorithm Identifiers An implementation of BLAKE2b and / or BLAKE2s SHOULD support the following digest size parameters for interoperability (e.g. digital signatures), as long as sufficient level of security is attained by the parameter selections. These parameters and identifiers are intended to be suitable as drop-in replacements to corresponding SHA algorithms. For unkeyed hashing, developers adapting BLAKE2 to ASN.1 - based message formats SHOULD use the OID tree at x = 1.3.6.1.4.1.1722.12.2. Algorithm | Target | Collision | Hash | Hash ASN.1 | Identifier | Arch | Security | nn | OID Suffix | ---------------+--------+-----------+------+------------+ id-blake2b160 | 64-bit | 2**80 | 20 | x.1.20 | id-blake2b256 | 64-bit | 2**128 | 32 | x.1.32 | id-blake2b384 | 64-bit | 2**192 | 48 | x.1.48 | id-blake2b512 | 64-bit | 2**256 | 64 | x.1.64 | ---------------+--------+-----------+------+------------+ id-blake2s128 | 32-bit | 2**64 | 16 | x.2.16 | id-blake2s160 | 32-bit | 2**80 | 20 | x.2.20 | id-blake2s224 | 32-bit | 2**112 | 28 | x.2.28 | id-blake2s256 | 32-bit | 2**128 | 32 | x.2.32 | ---------------+--------+-----------+------+------------+ hashAlgs OBJECT IDENTIFIER ::= { iso(1) identified-organization(3) dod(6) internet(1) private(4) enterprise(1) kudelski(1722) cryptography(12) 2 } -- the two BLAKE2 variants -- blake2b OBJECT IDENTIFIER ::= { hashAlgs 1 } blake2s OBJECT IDENTIFIER ::= { hashAlgs 2 } -- BLAKE2b Identifiers -- id-blake2b160 OBJECT IDENTIFIER ::= { blake2b 20 } id-blake2b256 OBJECT IDENTIFIER ::= { blake2b 32 } id-blake2b384 OBJECT IDENTIFIER ::= { blake2b 48 } id-blake2b512 OBJECT IDENTIFIER ::= { blake2b 64 } -- BLAKE2s Identifiers -- id-blake2s128 OBJECT IDENTIFIER ::= { blake2s 16 } id-blake2s160 OBJECT IDENTIFIER ::= { blake2s 20 } id-blake2s224 OBJECT IDENTIFIER ::= { blake2s 28 } id-blake2s256 OBJECT IDENTIFIER ::= { blake2s 32 } Saarinen & Aumasson Expires August 9, 2015 [Page 9] Internet-Draft The BLAKE2 Cryptographic Hash and MAC February 2015 5. Acknowledgements The editor wishes to thank the [BLAKE2] team for their encouragement: Jean-Philippe Aumasson, Samuel Neves, Zooko Wilcox-O'Hearn, and Christian Winnerlein. We have borrowed passages from [BLAKE] and [BLAKE2] with permission. BLAKE2 is based on the SHA-3 proposal [BLAKE], designed by Jean- Philippe Aumasson, Luca Henzen, Willi Meier, and Raphael C.-W. Phan. BLAKE2, like BLAKE, relies on a core algorithm borrowed from the ChaCha stream cipher, designed by Daniel J. Bernstein. 6. IANA Considerations This memo includes no request to IANA. 7. Security Considerations This document is intended to provide convenient open source access by the Internet community to the BLAKE2 cryptographic hash algorithm. We wish to make no independent assertion to its security in this document. We refer the reader to [BLAKE] and [BLAKE2] for detailed cryptanalytic rationale behind its design. In order to avoid bloat, the reference implementations in Appendix A and Appendix B may not erase all sensitive data (such as secret keys) immediately from process memory after use. Such cleanups can be added if needed. 8. References 8.1. Normative References [BLAKE2] Aumasson, J-P., Neves, S., Wilcox-O'Hearn, Z., and C. Winnerlein, "BLAKE2: simpler, smaller, fast as MD5", January 2013, . 8.2. Informative References [BLAKE] Aumasson, J-P., Meier, W., Phan, R., and L. Henzen, "The Hash Function BLAKE", February 2015, . [FIPS140-2IG] NIST, US., "Implementation Guidance for FIPS PUB 140-2 and the Cryptographic Module Validation Program", January 2015. Saarinen & Aumasson Expires August 9, 2015 [Page 10] Internet-Draft The BLAKE2 Cryptographic Hash and MAC February 2015 [RFC2119] Bradner, S., "Key words for use in RFCs to Indicate Requirement Levels", RFC 2119, BCP 14, March 1997. [RFC6151] Turner, S. and L. Chen, "Updated Security Considerations for the MD5 Message-Digest and the HMAC-MD5 Algorithms", RFC 6151, March 2011. [RFC6234] Eastlake, D. and T. Hansen, "US Secure Hash Algorithms (SHA and SHA-based HMAC and HKDF)", RFC 6234, May 2011. Appendix A. BLAKE2b Implementation C Source A.1. blake2b.h // blake2b.h // BLAKE2b Hashing Context and API Prototypes #ifndef BLAKE2B_H #define BLAKE2B_H #include #include // state context typedef struct { uint8_t b[128]; // input buffer uint64_t h[8]; // chained state uint64_t t[2]; // total number of bytes size_t c; // pointer for b[] size_t outlen; // digest size } blake2b_ctx; // Initialize the hashing context "ctx" with optional key "key". // 1 <= outlen <= 64 gives the digest size in bytes. // Secret key (also <= 64 bytes) is optional (keylen = 0). int blake2b_init(blake2b_ctx *ctx, size_t outlen, const void *key, size_t keylen); // secret key // Add "inlen" bytes from "in" into the hash. void blake2b_update(blake2b_ctx *ctx, // context const void *in, size_t inlen); // data to be hashed // Generate the message digest (size given in init). // Result placed in "out" void blake2b_final(blake2b_ctx *ctx, void *out); Saarinen & Aumasson Expires August 9, 2015 [Page 11] Internet-Draft The BLAKE2 Cryptographic Hash and MAC February 2015 // All-in-one convenience function. int blake2b(void *out, size_t outlen, // return buffer for digest const void *key, size_t keylen, // optional secret key const void *in, size_t inlen); // data to be hashed #endif A.2. blake2b.c // blake2b.c // A simple BLAKE2b Reference Implementation #include "blake2b.h" // cyclic right rotation #ifndef ROTR64 #define ROTR64(x, y) (((x) >> (y)) ^ ((x) << (64 - (y)))) #endif // little-endian byte access #define B2B_GET64(p) \ (((uint64_t) ((uint8_t *) (p))[0]) ^ \ (((uint64_t) ((uint8_t *) (p))[1]) << 8) ^ \ (((uint64_t) ((uint8_t *) (p))[2]) << 16) ^ \ (((uint64_t) ((uint8_t *) (p))[3]) << 24) ^ \ (((uint64_t) ((uint8_t *) (p))[4]) << 32) ^ \ (((uint64_t) ((uint8_t *) (p))[5]) << 40) ^ \ (((uint64_t) ((uint8_t *) (p))[6]) << 48) ^ \ (((uint64_t) ((uint8_t *) (p))[7]) << 56)) // G Mixing function #define B2B_G(a, b, c, d, x, y) { \ v[a] = v[a] + v[b] + x; \ v[d] = ROTR64(v[d] ^ v[a], 32); \ v[c] = v[c] + v[d]; \ v[b] = ROTR64(v[b] ^ v[c], 24); \ v[a] = v[a] + v[b] + y; \ v[d] = ROTR64(v[d] ^ v[a], 16); \ v[c] = v[c] + v[d]; \ v[b] = ROTR64(v[b] ^ v[c], 63); } Saarinen & Aumasson Expires August 9, 2015 [Page 12] Internet-Draft The BLAKE2 Cryptographic Hash and MAC February 2015 // Initialization Vector static const uint64_t blake2b_iv[8] = { 0x6A09E667F3BCC908, 0xBB67AE8584CAA73B, 0x3C6EF372FE94F82B, 0xA54FF53A5F1D36F1, 0x510E527FADE682D1, 0x9B05688C2B3E6C1F, 0x1F83D9ABFB41BD6B, 0x5BE0CD19137E2179 }; // Compression function. "last" flag indicates last block. static void blake2b_compress(blake2b_ctx *ctx, int last) { const uint8_t sigma[12][16] = { { 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15 }, { 14, 10, 4, 8, 9, 15, 13, 6, 1, 12, 0, 2, 11, 7, 5, 3 }, { 11, 8, 12, 0, 5, 2, 15, 13, 10, 14, 3, 6, 7, 1, 9, 4 }, { 7, 9, 3, 1, 13, 12, 11, 14, 2, 6, 5, 10, 4, 0, 15, 8 }, { 9, 0, 5, 7, 2, 4, 10, 15, 14, 1, 11, 12, 6, 8, 3, 13 }, { 2, 12, 6, 10, 0, 11, 8, 3, 4, 13, 7, 5, 15, 14, 1, 9 }, { 12, 5, 1, 15, 14, 13, 4, 10, 0, 7, 6, 3, 9, 2, 8, 11 }, { 13, 11, 7, 14, 12, 1, 3, 9, 5, 0, 15, 4, 8, 6, 2, 10 }, { 6, 15, 14, 9, 11, 3, 0, 8, 12, 2, 13, 7, 1, 4, 10, 5 }, { 10, 2, 8, 4, 7, 6, 1, 5, 15, 11, 9, 14, 3, 12, 13, 0 }, { 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15 }, { 14, 10, 4, 8, 9, 15, 13, 6, 1, 12, 0, 2, 11, 7, 5, 3 } }; int i; uint64_t v[16], m[16]; for (i = 0; i < 8; i++) { // init work variables v[i] = ctx->h[i]; v[i + 8] = blake2b_iv[i]; } v[12] ^= ctx->t[0]; // low 64 bits of offset v[13] ^= ctx->t[1]; // high 64 bits if (last) // last block flag set ? v[14] = ~v[14]; for (i = 0; i < 16; i++) // get little-endian words m[i] = B2B_GET64(&ctx->b[8 * i]); for (i = 0; i < 12; i++) { // twelve rounds B2B_G( 0, 4, 8, 12, m[sigma[i][ 0]], m[sigma[i][ 1]]); B2B_G( 1, 5, 9, 13, m[sigma[i][ 2]], m[sigma[i][ 3]]); B2B_G( 2, 6, 10, 14, m[sigma[i][ 4]], m[sigma[i][ 5]]); B2B_G( 3, 7, 11, 15, m[sigma[i][ 6]], m[sigma[i][ 7]]); Saarinen & Aumasson Expires August 9, 2015 [Page 13] Internet-Draft The BLAKE2 Cryptographic Hash and MAC February 2015 B2B_G( 0, 5, 10, 15, m[sigma[i][ 8]], m[sigma[i][ 9]]); B2B_G( 1, 6, 11, 12, m[sigma[i][10]], m[sigma[i][11]]); B2B_G( 2, 7, 8, 13, m[sigma[i][12]], m[sigma[i][13]]); B2B_G( 3, 4, 9, 14, m[sigma[i][14]], m[sigma[i][15]]); } for( i = 0; i < 8; ++i ) ctx->h[i] ^= v[i] ^ v[i + 8]; } // Initialize the state. key is optional int blake2b_init(blake2b_ctx *ctx, size_t outlen, const void *key, size_t keylen) // (keylen=0: no key) { size_t i; if (outlen == 0 || outlen > 64 || keylen > 64) return -1; // illegal parameters for (i = 0; i < 8; i++) // state, "param block" ctx->h[i] = blake2b_iv[i]; ctx->h[0] ^= 0x01010000 ^ (keylen << 8) ^ outlen; ctx->t[0] = 0; // input count low word ctx->t[1] = 0; // input count high word ctx->c = 0; // pointer within buffer ctx->outlen = outlen; for (i = keylen; i < 128; i++) // zero input block ctx->b[i] = 0; if (keylen > 0) { blake2b_update(ctx, key, keylen); ctx->c = 128; // at the end } return 0; } // update with new data void blake2b_update(blake2b_ctx *ctx, const void *in, size_t inlen) // data bytes { size_t i; for (i = 0; i < inlen; i++) { if (ctx->c == 128) { // buffer full ? Saarinen & Aumasson Expires August 9, 2015 [Page 14] Internet-Draft The BLAKE2 Cryptographic Hash and MAC February 2015 ctx->t[0] += ctx->c; // add counters if (ctx->t[0] < ctx->c) // carry overflow ? ctx->t[1]++; // high word blake2b_compress(ctx, 0); // compress (not last) ctx->c = 0; // counter to zero } ctx->b[ctx->c++] = ((const uint8_t *) in)[i]; } } // finalize void blake2b_final(blake2b_ctx *ctx, void *out) { size_t i; ctx->t[0] += ctx->c; // mark last block offset if (ctx->t[0] < ctx->c) // carry overflow ctx->t[1]++; // high word while (ctx->c < 128) // fill up with zeros ctx->b[ctx->c++] = 0; blake2b_compress(ctx, 1); // final block flag = 1 // little endian convert and store for (i = 0; i < ctx->outlen; i++) { ((uint8_t *) out)[i] = (ctx->h[i >> 3] >> (8 * (i & 7))) & 0xFF; } } // convenience function for all-in-one computation int blake2b(void *out, size_t outlen, const void *key, size_t keylen, const void *in, size_t inlen) { blake2b_ctx ctx; if (blake2b_init(&ctx, outlen, key, keylen)) return -1; blake2b_update(&ctx, in, inlen); blake2b_final(&ctx, out); return 0; } Saarinen & Aumasson Expires August 9, 2015 [Page 15] Internet-Draft The BLAKE2 Cryptographic Hash and MAC February 2015 Appendix B. BLAKE2s Implementation C Source B.1. blake2s.h // blake2s.h // BLAKE2s Hashing Context and API Prototypes #ifndef BLAKE2S_H #define BLAKE2S_H #include #include // state context typedef struct { uint8_t b[64]; // input buffer uint32_t h[8]; // chained state uint32_t t[2]; // total number of bytes size_t c; // pointer for b[] size_t outlen; // digest size } blake2s_ctx; // Initialize the hashing context "ctx" with optional key "key". // 1 <= outlen <= 32 gives the digest size in bytes. // Secret key (also <= 32 bytes) is optional (keylen = 0). int blake2s_init(blake2s_ctx *ctx, size_t outlen, const void *key, size_t keylen); // secret key // Add "inlen" bytes from "in" into the hash. void blake2s_update(blake2s_ctx *ctx, // context const void *in, size_t inlen); // data to be hashed // Generate the message digest (size given in init). // Result placed in "out" void blake2s_final(blake2s_ctx *ctx, void *out); // All-in-one convenience function. int blake2s(void *out, size_t outlen, // return buffer for digest const void *key, size_t keylen, // optional secret key const void *in, size_t inlen); // data to be hashed #endif Saarinen & Aumasson Expires August 9, 2015 [Page 16] Internet-Draft The BLAKE2 Cryptographic Hash and MAC February 2015 B.2. blake2s.c // blake2s.c // A simple BLAKE2 Reference Implementation #include "blake2s.h" // cyclic right rotation #ifndef ROTR32 #define ROTR32(x, y) (((x) >> (y)) ^ ((x) << (32 - (y)))) #endif // little-endian byte access #define B2S_GET32(p) \ (((uint32_t) ((uint8_t *) (p))[0]) ^ \ (((uint32_t) ((uint8_t *) (p))[1]) << 8) ^ \ (((uint32_t) ((uint8_t *) (p))[2]) << 16) ^ \ (((uint32_t) ((uint8_t *) (p))[3]) << 24)) // Mixing function G #define B2S_G(a, b, c, d, x, y) { \ v[a] = v[a] + v[b] + x; \ v[d] = ROTR32(v[d] ^ v[a], 16); \ v[c] = v[c] + v[d]; \ v[b] = ROTR32(v[b] ^ v[c], 12); \ v[a] = v[a] + v[b] + y; \ v[d] = ROTR32(v[d] ^ v[a], 8); \ v[c] = v[c] + v[d]; \ v[b] = ROTR32(v[b] ^ v[c], 7); } // Initialization Vector static const uint32_t blake2s_iv[8] = { 0x6A09E667, 0xBB67AE85, 0x3C6EF372, 0xA54FF53A, 0x510E527F, 0x9B05688C, 0x1F83D9AB, 0x5BE0CD19 }; // Compression function. "last" flag indicates last block. static void blake2s_compress(blake2s_ctx *ctx, int last) { const uint8_t sigma[10][16] = { { 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15 }, { 14, 10, 4, 8, 9, 15, 13, 6, 1, 12, 0, 2, 11, 7, 5, 3 }, Saarinen & Aumasson Expires August 9, 2015 [Page 17] Internet-Draft The BLAKE2 Cryptographic Hash and MAC February 2015 { 11, 8, 12, 0, 5, 2, 15, 13, 10, 14, 3, 6, 7, 1, 9, 4 }, { 7, 9, 3, 1, 13, 12, 11, 14, 2, 6, 5, 10, 4, 0, 15, 8 }, { 9, 0, 5, 7, 2, 4, 10, 15, 14, 1, 11, 12, 6, 8, 3, 13 }, { 2, 12, 6, 10, 0, 11, 8, 3, 4, 13, 7, 5, 15, 14, 1, 9 }, { 12, 5, 1, 15, 14, 13, 4, 10, 0, 7, 6, 3, 9, 2, 8, 11 }, { 13, 11, 7, 14, 12, 1, 3, 9, 5, 0, 15, 4, 8, 6, 2, 10 }, { 6, 15, 14, 9, 11, 3, 0, 8, 12, 2, 13, 7, 1, 4, 10, 5 }, { 10, 2, 8, 4, 7, 6, 1, 5, 15, 11, 9, 14, 3, 12, 13, 0 } }; int i; uint32_t v[16], m[16]; for (i = 0; i < 8; i++) { // init work variables v[i] = ctx->h[i]; v[i + 8] = blake2s_iv[i]; } v[12] ^= ctx->t[0]; // low 32 bits of offset v[13] ^= ctx->t[1]; // high 32 bits if (last) // last block flag set ? v[14] = ~v[14]; for (i = 0; i < 16; i++) // get little-endian words m[i] = B2S_GET32(&ctx->b[4 * i]); for (i = 0; i < 10; i++) { // ten rounds B2S_G( 0, 4, 8, 12, m[sigma[i][ 0]], m[sigma[i][ 1]]); B2S_G( 1, 5, 9, 13, m[sigma[i][ 2]], m[sigma[i][ 3]]); B2S_G( 2, 6, 10, 14, m[sigma[i][ 4]], m[sigma[i][ 5]]); B2S_G( 3, 7, 11, 15, m[sigma[i][ 6]], m[sigma[i][ 7]]); B2S_G( 0, 5, 10, 15, m[sigma[i][ 8]], m[sigma[i][ 9]]); B2S_G( 1, 6, 11, 12, m[sigma[i][10]], m[sigma[i][11]]); B2S_G( 2, 7, 8, 13, m[sigma[i][12]], m[sigma[i][13]]); B2S_G( 3, 4, 9, 14, m[sigma[i][14]], m[sigma[i][15]]); } for( i = 0; i < 8; ++i ) ctx->h[i] ^= v[i] ^ v[i + 8]; } // Initialize the state. key is optional int blake2s_init(blake2s_ctx *ctx, size_t outlen, const void *key, size_t keylen) // (keylen=0: no key) { size_t i; if (outlen == 0 || outlen > 32 || keylen > 32) Saarinen & Aumasson Expires August 9, 2015 [Page 18] Internet-Draft The BLAKE2 Cryptographic Hash and MAC February 2015 return -1; // illegal parameters for (i = 0; i < 8; i++) // state, "param block" ctx->h[i] = blake2s_iv[i]; ctx->h[0] ^= 0x01010000 ^ (keylen << 8) ^ outlen; ctx->t[0] = 0; // input count low word ctx->t[1] = 0; // input count high word ctx->c = 0; // pointer within buffer ctx->outlen = outlen; for (i = keylen; i < 64; i++) // zero input block ctx->b[i] = 0; if (keylen > 0) { blake2s_update(ctx, key, keylen); ctx->c = 64; // at the end } return 0; } // update with new data void blake2s_update(blake2s_ctx *ctx, const void *in, size_t inlen) // data bytes { size_t i; for (i = 0; i < inlen; i++) { if (ctx->c == 64) { // buffer full ? ctx->t[0] += ctx->c; // add counters if (ctx->t[0] < ctx->c) // carry overflow ? ctx->t[1]++; // high word blake2s_compress(ctx, 0); // compress (not last) ctx->c = 0; // counter to zero } ctx->b[ctx->c++] = ((const uint8_t *) in)[i]; } } // finalize void blake2s_final(blake2s_ctx *ctx, void *out) { size_t i; ctx->t[0] += ctx->c; // mark last block offset if (ctx->t[0] < ctx->c) // carry overflow Saarinen & Aumasson Expires August 9, 2015 [Page 19] Internet-Draft The BLAKE2 Cryptographic Hash and MAC February 2015 ctx->t[1]++; // high word while (ctx->c < 64) // fill up with zeros ctx->b[ctx->c++] = 0; blake2s_compress(ctx, 1); // final block flag = 1 // little endian convert and store for (i = 0; i < ctx->outlen; i++) { ((uint8_t *) out)[i] = (ctx->h[i >> 2] >> (8 * (i & 3))) & 0xFF; } } // convenience function for all-in-one computation int blake2s(void *out, size_t outlen, const void *key, size_t keylen, const void *in, size_t inlen) { blake2s_ctx ctx; if (blake2s_init(&ctx, outlen, key, keylen)) return -1; blake2s_update(&ctx, in, inlen); blake2s_final(&ctx, out); return 0; } Appendix C. BLAKE2b and BLAKE2s Self Test Module C Source This module computes a series of keyed and unkeyed hashes from deterministically generated pseudo-random data, and computes a hash over those results. This is fairly a exhaustive, yet compact and fast method for verifying that the hashing module is functioning correctly. Such testing is recommended especially when compiling the implementation for a new a target platform configuration. Furthermore, some security standards such as FIPS-140 may require a Power-On Self Test (POST) to be performed every time the cryptographic module is loaded [FIPS140-2IG]. // test_main.c Saarinen & Aumasson Expires August 9, 2015 [Page 20] Internet-Draft The BLAKE2 Cryptographic Hash and MAC February 2015 // Self test Modules for BLAKE2b and BLAKE2s -- and a stub main(). #include #include "blake2b.h" #include "blake2s.h" // Deterministic sequences (Fibonacci generator) static void selftest_seq(uint8_t *out, size_t len, uint32_t seed) { size_t i; uint32_t t, a , b; a = 0xDEAD4BAD * seed; // prime b = 1; for (i = 0; i < len; i++) { // fill the buf t = a + b; a = b; b = t; out[i] = (t >> 24) & 0xFF; } } // BLAKE2b self-test validation. Return 0 when OK. int blake2b_selftest() { // grand hash of hash results const uint8_t blake2b_res[32] = { 0xC2, 0x3A, 0x78, 0x00, 0xD9, 0x81, 0x23, 0xBD, 0x10, 0xF5, 0x06, 0xC6, 0x1E, 0x29, 0xDA, 0x56, 0x03, 0xD7, 0x63, 0xB8, 0xBB, 0xAD, 0x2E, 0x73, 0x7F, 0x5E, 0x76, 0x5A, 0x7B, 0xCC, 0xD4, 0x75 }; // parameter sets const size_t b2b_md_len[4] = { 20, 32, 48, 64 }; const size_t b2b_in_len[6] = { 0, 3, 128, 129, 255, 1024 }; size_t i, j, outlen, inlen; uint8_t in[1024], md[64], key[64]; blake2b_ctx ctx; // 256-bit hash for testing if (blake2b_init(&ctx, 32, NULL, 0)) return -1; Saarinen & Aumasson Expires August 9, 2015 [Page 21] Internet-Draft The BLAKE2 Cryptographic Hash and MAC February 2015 for (i = 0; i < 4; i++) { outlen = b2b_md_len[i]; for (j = 0; j < 6; j++) { inlen = b2b_in_len[j]; selftest_seq(in, inlen, inlen); // unkeyed hash blake2b(md, outlen, NULL, 0, in, inlen); blake2b_update(&ctx, md, outlen); // hash the hash selftest_seq(key, outlen, outlen); // keyed hash blake2b(md, outlen, key, outlen, in, inlen); blake2b_update(&ctx, md, outlen); // hash the hash } } // compute and compare the hash of hashes blake2b_final(&ctx, md); for (i = 0; i < 32; i++) { if (md[i] != blake2b_res[i]) return -1; } return 0; } // BLAKE2s self-test validation. Return 0 when OK. int blake2s_selftest() { // grand hash of hash results const uint8_t blake2s_res[32] = { 0x6A, 0x41, 0x1F, 0x08, 0xCE, 0x25, 0xAD, 0xCD, 0xFB, 0x02, 0xAB, 0xA6, 0x41, 0x45, 0x1C, 0xEC, 0x53, 0xC5, 0x98, 0xB2, 0x4F, 0x4F, 0xC7, 0x87, 0xFB, 0xDC, 0x88, 0x79, 0x7F, 0x4C, 0x1D, 0xFE }; // parameter sets const size_t b2s_md_len[4] = { 16, 20, 28, 32 }; const size_t b2s_in_len[6] = { 0, 3, 64, 65, 255, 1024 }; size_t i, j, outlen, inlen; uint8_t in[1024], md[32], key[32]; blake2s_ctx ctx; // 256-bit hash for testing if (blake2s_init(&ctx, 32, NULL, 0)) return -1; Saarinen & Aumasson Expires August 9, 2015 [Page 22] Internet-Draft The BLAKE2 Cryptographic Hash and MAC February 2015 for (i = 0; i < 4; i++) { outlen = b2s_md_len[i]; for (j = 0; j < 6; j++) { inlen = b2s_in_len[j]; selftest_seq(in, inlen, inlen); // unkeyed hash blake2s(md, outlen, NULL, 0, in, inlen); blake2s_update(&ctx, md, outlen); // hash the hash selftest_seq(key, outlen, outlen); // keyed hash blake2s(md, outlen, key, outlen, in, inlen); blake2s_update(&ctx, md, outlen); // hash the hash } } // compute and compare the hash of hashes blake2s_final(&ctx, md); for (i = 0; i < 32; i++) { if (md[i] != blake2s_res[i]) return -1; } return 0; } // test driver int main(int argc, char **argv) { printf("blake2b_selftest() = %s\n", blake2b_selftest() ? "FAIL" : "OK"); printf("blake2s_selftest() = %s\n", blake2s_selftest() ? "FAIL" : "OK"); return 0; } Saarinen & Aumasson Expires August 9, 2015 [Page 23] Internet-Draft The BLAKE2 Cryptographic Hash and MAC February 2015 Authors' Addresses Markku-Juhani O. Saarinen (editor) Independent Consultant Email: mjos@iki.fi URI: https://mjos.fi Jean-Philippe Aumasson Kudelski Security 22-24, Route de Geneve Case Postale 134 Cheseaux 1033 Switzerland Email: jean-philippe.aumasson@nagra.com URI: https://www.kudelskisecurity.com Saarinen & Aumasson Expires August 9, 2015 [Page 24]