Network Working Group A. Biryukov Internet-Draft D. Dinu Intended status: Informational D. Khovratovich Expires: May 8, 2016 University of Luxembourg S. Josefsson SJD AB November 5, 2015 The memory-hard Argon2 password hash function draft-josefsson-argon2-00 Abstract This document describes the Argon2 memory-hard function for password hashing and other applications. We provide a implementer oriented description together with sample code and test vectors. The purpose is to simplify adoption of Argon2 for Internet protocols. 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 May 8, 2016. 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 Biryukov, et al. Expires May 8, 2016 [Page 1]

Internet-Draft Argon2 November 2015 the Trust Legal Provisions and are provided without warranty as described in the Simplified BSD License. Table of Contents 1. Introduction . . . . . . . . . . . . . . . . . . . . . . . . 2 2. Notation and Conventions . . . . . . . . . . . . . . . . . . 3 3. Argon2 Algorithm . . . . . . . . . . . . . . . . . . . . . . 3 3.1. Argon2 Inputs and Outputs . . . . . . . . . . . . . . . . 3 3.2. Argon2 Operation . . . . . . . . . . . . . . . . . . . . 4 3.3. Variable-length hash function H' . . . . . . . . . . . . 5 3.4. Indexing . . . . . . . . . . . . . . . . . . . . . . . . 5 3.5. Compression function G . . . . . . . . . . . . . . . . . 6 3.6. Permutation P . . . . . . . . . . . . . . . . . . . . . . 6 4. Parameter Choice . . . . . . . . . . . . . . . . . . . . . . 6 5. Example Code . . . . . . . . . . . . . . . . . . . . . . . . 8 6. Test Vectors . . . . . . . . . . . . . . . . . . . . . . . . 8 6.1. Argon2d Test Vectors . . . . . . . . . . . . . . . . . . 8 6.2. Argon2i Test Vectors . . . . . . . . . . . . . . . . . . 9 7. Acknowledgements . . . . . . . . . . . . . . . . . . . . . . 10 8. IANA Considerations . . . . . . . . . . . . . . . . . . . . . 10 9. Security Considerations . . . . . . . . . . . . . . . . . . . 10 10. References . . . . . . . . . . . . . . . . . . . . . . . . . 11 10.1. Normative References . . . . . . . . . . . . . . . . . . 11 10.2. Informative References . . . . . . . . . . . . . . . . . 11 Authors' Addresses . . . . . . . . . . . . . . . . . . . . . . . 11 1. Introduction This document describes the Argon2 memory-hard function for password hashing and other applications. We provide a implementer oriented description together with sample code and test vectors. The purpose is to simplify adoption of Argon2 for Internet protocols. Argon2 summarizes the state of the art in the design of memory-hard functions. It is a streamlined and simple design. It aims at the highest memory filling rate and effective use of multiple computing units, while still providing defense against tradeoff attacks. Argon2 is optimized for the x86 architecture and exploits the cache and memory organization of the recent Intel and AMD processors. Argon2 has two variants: Argon2d and Argon2i. Argon2d is faster and uses data-depending memory access, which makes it suitable for cryptocurrencies and applications with no threats from side-channel timing attacks. Argon2i uses data-independent memory access, which is preferred for password hashing and password-based key derivation. Argon2i is slower as it makes more passes over the memory to protect from tradeoff attacks. Biryukov, et al. Expires May 8, 2016 [Page 2]

Internet-Draft Argon2 November 2015 For further background and discussion, see the Argon2 paper [ARGON2]. 2. Notation and Conventions x^y --- x multiplied by itself y times a*b --- multiplication of a and b c-d --- substraction of c with d E_f --- variable E with subscript index f g / h --- g divided by h I(j) --- function I evaluated on parameters j K || L --- string K concatenated with string L 3. Argon2 Algorithm 3.1. Argon2 Inputs and Outputs Argon2 have the following input parameters: o Message string P, typically a password. May have any length from 0 to 2^32 - 1 bytes. o Nonce S, typically a random salt. May have any length from 8 to 2^32 - 1 bytes. 16 bytes is recommended for password hashing. See [RFC4086] for discussion about randomness. o Degree of parallelism p determines how many independent (but synchronizing) computational chains can be run. It may take any integer value from 1 to 255. o Tag length T may be any integer number of bytes from 4 to 2^32-1. o Memory size m can be any integer number of kilobytes from 8*p to 2^32-1. The actual number of blocks is m', which is m rounded down to the nearest multiple of 4*p. o Number of iterations t (used to tune the running time independently of the memory size) can be any integer number from 1 to 2^32-1. o Version number v is one byte 0x10. Biryukov, et al. Expires May 8, 2016 [Page 3]

Internet-Draft Argon2 November 2015 o Secret value K (serves as key if necessary, but we do not assume any key use by default) may have any length from 0 to 32 bytes. o Associated data X may have any length from 0 to 2^32-1 bytes. o Type y of Argon2: 0 for Argon2d, 1 for Argon2i. The Argon2 output is a T-length string. 3.2. Argon2 Operation Argon2 uses an internal compression function G with two 1024-byte inputs and a 1024-byte output, and an internal hash function H. Here H is the Blake2b [I-D.saarinen-blake2] hash function, and the compression function G is based on its internal permutation. A variable-length hash function H' built upon H is also used. G and H' are described in later section. The Argon2 operation is as follows. 1. Establish H_0 as the 64-bit value as shown in the figure below. H is BLAKE2b and the non-strings p, T, m, t, v, y, length(P), length(S), length(K), and length(X) are treated as a 32-bit little-endian encoding of the integer. H_0 = H(p, T, m, t, v, y, length(P), P, length(S), S, length(K), K, length(X), X) 2. Allocate the memory as m' 1024-byte blocks where m' is derived as: m' = 4 * p * floor (m / 4p) For tunable parallelism with p threads, the memory is organized in a matrix B[i][j] of blocks with p rows (lanes) and q = m' / p columns. 3. Compute B[i][0] for all i ranging from (and including) 0 to (not including) p. B[i][0] = H'(H0, 4byteencode(i), 4byteencode(0)) Here 4byteencode is a function which takes an integer and little- endian encode and padds it to 4 bytes. 4. Compute B[i][1] for all i ranging from (and including) 0 to (not including) p. Biryukov, et al. Expires May 8, 2016 [Page 4]

Internet-Draft Argon2 November 2015 B[i][1] = H'(H0, 4byteencode(i), 4byteencode(1)) 5. Compute B[i][j] for all i ranging from (and including) 0 to (not including) p, and for all j ranging from (and including) 2) to (not including) q. The block indices i' and j' are determined differently for Argon2d and Argon2i. B[i][j] = G(B[i][j-1], B[i'][j']) 6. If the number of iterations t is larger than 1, we repeat the steps however replacing the computations with with the following expression: B[i][0] = G(B[i][q-1], B[i'][j']) B[i][j] = G(B[i][j-1], B[i'][j']) 7. After t steps have been iterated, we compute the final block C as the XOR of the last column: C = B[0][q-1] XOR B[1][q-1] XOR ... XOR B[p-1][q-1] 8. The output tag is computed as H'(C). 3.3. Variable-length hash function H' Let H_x be a hash function with x-byte output (in our case H_x is Blake2b, which supports x between 1 and 64 inclusive). Let V_i be a 64-byte block, and A_i be its first 32 bytes, and T < 2^32 be the tag length in bytes. Then we define V_0 = T||X V_1 = H_64(V_0) V_2 = H_64(V_1) ... V_r = H_64(V_{r-1}) with r=floor(T/32)-1 V_{r+1} = H_{T mod 64}(V_{r-1}) absent if 64 divides T H'(X) = A_1 || A_2 || ... || A_r || V_{r+1} FIXME: improve this description. FIXME2: V_{r+1} is not properly described, is it a 64-byte block or a {T mod 64} block? 3.4. Indexing TBD Biryukov, et al. Expires May 8, 2016 [Page 5]

Internet-Draft Argon2 November 2015 3.5. Compression function G Compression function G is built upon the Blake2b round function P. P operates on the 128-byte input, which can be viewed as 8 16-byte registers: P(A_0, A_1, ... ,A_7) = (B_0, B_1, ... ,B_7) Compression function G(X, Y) operates on two 1024-byte blocks X and Y. It first computes R = X XOR Y. Then R is viewed as a 8x8-matrix of 16-byte registers R_0, R_1, ... , R_63. Then P is first applied rowwise, and then columnwise to get Z: (Q_0, Q_1, ... , Q_7 ) <- P(R_0, R_1, ... , R_7) (Q_8, Q_9, ... , Q_15) <- P(R_8, R_9, ... , R_15) ... (Q_56, Q_57, ... , Q_63 ) <- P(R_56, R_57, ... , R_63) (Z_0, Z_8, Z_16 , ... , Z_56) < P(Q_0, Q_8, Q_16, ... , Q_56) (Z_1, Z_9, Z_17 , ... , Z_57) < P(Q_1, Q_9, Q_17, ... , Q_57) ... (Z_7, Z_15, Z 23 , ... , Z_63) < P(Q_7, Q_15, Q_23, ... , Q_63) Finally, G outputs Z XOR R: G: (X,Y) -> R = X XOR Y -P-> Q -P-> Z -P-> Z XOR R FIXME: improve this description. 3.6. Permutation P TBD 4. Parameter Choice Argon2d is optimized for settings where the adversary does not get regular access to system memory or CPU, i.e. he can not run side- channel attacks based on the timing information, nor he can recover the password much faster using garbage collection. These settings are more typical for backend servers and cryptocurrency minings. For practice we suggest the following settings: o Cryptocurrency mining, that takes 0.1 seconds on a 2 Ghz CPU using 1 core -- Argon2d with 2 lanes and 250 MB of RAM. o Backend server authentication, that takes 0.5 seconds on a 2 GHz CPU using 4 cores -- Argon2d with 8 lanes and 4 GB of RAM. Biryukov, et al. Expires May 8, 2016 [Page 6]

Internet-Draft Argon2 November 2015 Argon2i is optimized for more realistic settings, where the adversary possibly can access the same machine, use its CPU or mount cold-boot attacks. We use three passes to get rid entirely of the password in the memory. We suggest the following settings: o Key derivation for hard-drive encryption, that takes 3 seconds on a 2 GHz CPU using 2 cores - Argon2i with 4 lanes and 6 GB of RAM o Frontend server authentication, that takes 0.5 seconds on a 2 GHz CPU using 2 cores - Argon2i with 4 lanes and 1 GB of RAM. We recommend the following procedure to select the type and the parameters for practical use of Argon2. 1. Select the type y. If you do not know the difference between them or you consider side-channel attacks as viable threat, choose Argon2i. 2. Figure out the maximum number h of threads that can be initiated by each call to Argon2. 3. Figure out the maximum amount m of memory that each call can afford. 4. Figure out the maximum amount x of time (in seconds) that each call can afford. 5. Select the salt length. 128 bits is sufficient for all applications, but can be reduced to 64 bits in the case of space constraints. 6. Select the tag length. 128 bits is sufficient for most applications, including key derivation. If longer keys are needed, select longer tags. 7. If side-channel attacks is a viable threat, enable the memory wiping option in the library call. 8. Run the scheme of type y, memory m and h lanes and threads, using different number of passes t. Figure out the maximum t such that the running time does not exceed x. If it exceeds x even for t = 1, reduce m accordingly. 9. Hash all the passwords with the just determined values m, h, and t. Biryukov, et al. Expires May 8, 2016 [Page 7]

Internet-Draft Argon2 November 2015 5. Example Code TBD -- is there a python implementation? 6. Test Vectors This section contains test vectors for Argon2. 6.1. Argon2d Test Vectors =======================================Argon2d Memory: 16 KiB Iterations: 3 Parallelism: 4 lanes Tag length: 32 bytes Password[32]: 01 01 01 01 01 01 01 01 01 01 01 01 01 01 01 01 01 01 01 01 01 01 01 01 01 01 01 01 01 01 01 01 Salt[16]: 02 02 02 02 02 02 02 02 02 02 02 02 02 02 02 02 Secret[8]: 03 03 03 03 03 03 03 03 Associated data[12]: 04 04 04 04 04 04 04 04 04 04 04 04 Pre-hashing digest: ec a9 db ff fa c9 87 5c d2 dc 32 67 cb 82 7f 48 79 af db 2f 6c b3 a5 29 c5 87 7c 60 7d 72 92 02 7c 23 15 47 fc 64 4f b8 81 16 1f ee f6 e2 b3 d1 63 49 1a 98 e8 a8 8c 8a 40 15 b8 b5 dc 85 ec 1b After pass 0: Block 0000 [ 0]: 7ddae3a315a45d2d Block 0000 [ 1]: 50d8b9a49514a996 Block 0000 [ 2]: d5fd2f56c5085520 Block 0000 [ 3]: 81fa720dcf94e004 ... Block 0031 [124]: 40b2d44e241f7a2a Block 0031 [125]: 9b9658c82ba08f84 Block 0031 [126]: 917242b2a7a533f2 Block 0031 [127]: 4169db73ebcc9e9c After pass 1: Block 0000 [ 0]: a8daed017254d662 Block 0000 [ 1]: 1564d0fc4f5d07f4 Block 0000 [ 2]: 6a18ece1fd7d79ff Block 0000 [ 3]: d04eb389a8ac7324 ... Biryukov, et al. Expires May 8, 2016 [Page 8]

Internet-Draft Argon2 November 2015 Block 0031 [124]: c859e8ba37e79999 Block 0031 [125]: 0bb980cfe6552a4d Block 0031 [126]: 300cea2895f4459e Block 0031 [127]: 37af5d23a18f9d58 After pass 2: Block 0000 [ 0]: e86fc8e713dbf6d3 Block 0000 [ 1]: b30f1bdf8b4219d6 Block 0000 [ 2]: a84aec198d1eaff0 Block 0000 [ 3]: 1be35c5c8bfc52e0 ... Block 0031 [124]: 9ffab191789d7380 Block 0031 [125]: 4237012fc73e8d3e Block 0031 [126]: fbea11160fe7b50e Block 0031 [127]: 692210628c981931 Tag: 57 b0 61 3b fd d4 13 1a 0c 34 88 34 c6 72 9c 2c 72 29 92 1e 6b ba 37 66 5d 97 8c 4f e7 17 5e d2 6.2. Argon2i Test Vectors =======================================Argon2i Memory: 16 KiB Iterations: 3 Parallelism: 4 lanes Tag length: 32 bytes Password[32]: 01 01 01 01 01 01 01 01 01 01 01 01 01 01 01 01 01 01 01 01 01 01 01 01 01 01 01 01 01 01 01 01 Salt[16]: 02 02 02 02 02 02 02 02 02 02 02 02 02 02 02 02 Secret[8]: 03 03 03 03 03 03 03 03 Associated data[12]: 04 04 04 04 04 04 04 04 04 04 04 04 Pre-hashing digest: c0 4e 5c 19 98 fc b1 12 09 3e 36 a0 76 3e 2f 95 57 f2 cf 53 6f b8 89 c9 9c c6 d8 cd b3 49 cd 0c 9d 48 db cc 94 57 59 8c 6c 2d a1 e1 d1 8b 3b aa 7a 37 43 cb d1 7a d8 5c 61 df dc 7e 7a 8e 64 2f After pass 0: Block 0000 [ 0]: 34e7ba2a71020326 Block 0000 [ 1]: 3a4e252bf033a4cb Block 0000 [ 2]: 3fb8e27bb8ab6a2b Biryukov, et al. Expires May 8, 2016 [Page 9]

Internet-Draft Argon2 November 2015 Block 0000 [ 3]: 65bb946635366867 ... Block 0031 [124]: 433d8954deddd5d6 Block 0031 [125]: c76ead72f0c08a23 Block 0031 [126]: b7c6ce1154c1fdd1 Block 0031 [127]: 0e766420b2ee181c After pass 1: Block 0000 [ 0]: 614a404c54646531 Block 0000 [ 1]: 79f220080bfac514 Block 0000 [ 2]: e9da047d0e4406b4 Block 0000 [ 3]: 0995bc6d95590353 ... Block 0031 [124]: 9b89e743afa7b916 Block 0031 [125]: 9b3f7ca7cfff2db9 Block 0031 [126]: 0065ff067978eab8 Block 0031 [127]: 0a78fa2cea2b8bb2 After pass 2: Block 0000 [ 0]: 3fea10517d1a7476 Block 0000 [ 1]: e44c8bece4b3ecb2 Block 0000 [ 2]: e348b27d988671cb Block 0000 [ 3]: 5f7f7cd33ef59e4d ... Block 0031 [124]: f60cb937689b55f8 Block 0031 [125]: 418c55d7f343df3f Block 0031 [126]: 26899dd11adc7474 Block 0031 [127]: dd3afa472ff1d124 Tag: 91 3b a4 37 68 5b 61 3c f1 2b 94 46 79 53 40 37 ac 46 cf a8 8a 02 f6 c7 ba 28 0e 08 89 40 19 f2 7. Acknowledgements TBA 8. IANA Considerations None. 9. Security Considerations TBA Biryukov, et al. Expires May 8, 2016 [Page 10]

Internet-Draft Argon2 November 2015 10. References 10.1. Normative References [I-D.saarinen-blake2] Saarinen, M. and J. Aumasson, "The BLAKE2 Cryptographic Hash and MAC", draft-saarinen-blake2-06 (work in progress), August 2015. 10.2. Informative References [RFC4086] Eastlake, D., Schiller, J., and S. Crocker, "Randomness Requirements for Security", BCP 106, RFC 4086, June 2005. [ARGON2] Biryukov, A., Dinu, D., and D. Khovratovich, "Argon2: the memory-hard function for password hashing and other applications", WWW https://password-hashing.net/ argon2-specs.pdf, October 2015. Authors' Addresses Alex Biryukov University of Luxembourg Daniel Dinu University of Luxembourg Dmitry Khovratovich University of Luxembourg Simon Josefsson SJD AB Email: simon@josefsson.org URI: http://josefsson.org/ Biryukov, et al. Expires May 8, 2016 [Page 11]