Network Working Group A. Biryukov Internet-Draft D. Dinu Intended status: Informational D. Khovratovich Expires: September 21, 2016 University of Luxembourg S. Josefsson SJD AB March 20, 2016 The memory-hard Argon2 password hash and proof-of-work function draft-irtf-cfrg-argon2-00 Abstract This document describes the Argon2 memory-hard function for password hashing and proof-of-work applications. We provide an 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 September 21, 2016. Copyright Notice Copyright (c) 2016 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 September 21, 2016 [Page 1] Internet-Draft Argon2 March 2016 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 . . . . . . . . . . . . . . . . . . . . . . 4 3.1. Argon2 Inputs and Outputs . . . . . . . . . . . . . . . . 4 3.2. Argon2 Operation . . . . . . . . . . . . . . . . . . . . 4 3.3. Variable-length hash function H' . . . . . . . . . . . . 6 3.4. Indexing . . . . . . . . . . . . . . . . . . . . . . . . 6 3.4.1. Getting the 32-bit integers J_1 and J_2 . . . . . . . 7 3.4.2. Mapping J_1 and J_2 to (i',j') . . . . . . . . . . . 7 3.5. Compression function G . . . . . . . . . . . . . . . . . 8 3.6. Permutation P . . . . . . . . . . . . . . . . . . . . . . 9 4. Parameter Choice . . . . . . . . . . . . . . . . . . . . . . 10 5. Example Code . . . . . . . . . . . . . . . . . . . . . . . . 11 6. Test Vectors . . . . . . . . . . . . . . . . . . . . . . . . 19 6.1. Argon2d Test Vectors . . . . . . . . . . . . . . . . . . 19 6.2. Argon2i Test Vectors . . . . . . . . . . . . . . . . . . 21 7. IANA Considerations . . . . . . . . . . . . . . . . . . . . . 22 8. Security Considerations . . . . . . . . . . . . . . . . . . . 22 9. References . . . . . . . . . . . . . . . . . . . . . . . . . 22 9.1. Normative References . . . . . . . . . . . . . . . . . . 22 9.2. Informative References . . . . . . . . . . . . . . . . . 23 Authors' Addresses . . . . . . . . . . . . . . . . . . . . . . . 23 1. Introduction This document describes the Argon2 memory-hard function for password hashing and proof-of-work applications. We provide an implementer oriented description together with sample code and test vectors. The purpose is to simplify adoption of Argon2 for Internet protocols. This document corresponds to version 1.3 of the Argon2 hash function. Biryukov, et al. Expires September 21, 2016 [Page 2] Internet-Draft Argon2 March 2016 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 proof-of-work 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. 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 parameter j K || L --- string K concatenated with string L a ^ b --- bitwise exclusive-or between a and b a mod b --- remainder of a modulo b, always in range [0, b-1] a >>> n --- rotation of a to the right by n bits trunc(a) --- the 64-bit value a truncated to the 32 least significant bits |A| --- the number of elements in set A Biryukov, et al. Expires September 21, 2016 [Page 3] Internet-Draft Argon2 March 2016 3. Argon2 Algorithm 3.1. Argon2 Inputs and Outputs Argon2 has the following input parameters: o Message string P, which is a password for password hashing applications. MAY have any length from 0 to 2**32 - 1 bytes. o Nonce S, which is a salt for password hashing applications. May have any length from 8 to 2**32-1 bytes. 16 bytes is recommended for password hashing. Salt MUST be unique for each password. o Degree of parallelism p determines how many independent (but synchronizing) computational chains (lanes) can be run. It MAY take any integer value from 1 to 2**24-1. o Tag length T MAY be any integer number of bytes from 4 to 2**32-1. o Memory size m MAY be any integer number of kibibytes 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) MAY be any integer number from 1 to 2**32-1. o Version number v MUST be one byte 0x13. 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 MUST be 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. Biryukov, et al. Expires September 21, 2016 [Page 4] Internet-Draft Argon2 March 2016 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 p lanes, 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'(H_0, 0, i) Here integers are padded to 4 bytes and encoded in little endian. 4. Compute B[i][1] for all i ranging from (and including) 0 to (not including) p. B[i][1] = H'(H_0, 1, i) Here integers are padded to 4 bytes and encoded in little endian. 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 (see section ``Indexing''). 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 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, the final block C is computed as the XOR of the last column: C = B[0][q-1] XOR B[1][q-1] XOR ... XOR B[p-1][q-1] Biryukov, et al. Expires September 21, 2016 [Page 5] Internet-Draft Argon2 March 2016 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, encoded in little-endian as 32-bit integer. Then we define: if T <= 64 H'(X) = H_T(T||X) else r = ceil(T/32)-2 V_1 = H_64(T||X) V_2 = H_64(V_1) ... V_r = H_64(V_{r-1}) V_{r+1} = H_{T-32*r}(V_{r}) H'(X) = A_1 || A_2 || ... || A_r || V_{r+1} 3.4. Indexing The memory matrix is partitioned into S = 4 vertical slices. The intersection of a slice and a lane is a segment of length q/S. Segments of the same slice are computed in parallel and may not reference blocks from each other. All other blocks can be referenced. slice 0 slice 1 slice 2 slice 3 ___/\___ ___/\___ ___/\___ ___/\___ / \ / \ / \ / \ +----------+----------+----------+----------+ | | | | | > lane 0 +----------+----------+----------+----------+ | | | | | > lane 1 +----------+----------+----------+----------+ | | | | | > lane 2 +----------+----------+----------+----------+ | ... ... ... | ... +----------+----------+----------+----------+ | | | | | > lane p - 1 +----------+----------+----------+----------+ Single-pass Argon2 with p lanes and 4 slices For each block B[i][j] at pass p we determine the index [i'][j'], which determines the block B[i'][j'] taken as input to G to compute Biryukov, et al. Expires September 21, 2016 [Page 6] Internet-Draft Argon2 March 2016 B[i][j]. The pair (i',j') is determined by B[i][j-1] and tuple (i,j,p) as follows. 3.4.1. Getting the 32-bit integers J_1 and J_2 3.4.1.1. Argon2d J_1 is given by the first 32 bits of block B[i][j-1], treated as little endian. while J_2 is given by the next 32-bits of block B[i][j-1], treated as little endian. 3.4.1.2. Argon2i For each segment of q blocks we compose a full-zero block X and w=ceil(q/128) blocks Y_1,Y_2,...,Y_w. application of the 2-round compression function G in the counter mode gives 128 64-bit values J_1 || J_2. The first input is the all zero block and the second input is constructed as follows: Y_i=( r || l || s || m' || t || y || i || 0 ), where r -- the pass number, starting from 0 l -- the lane number, starting from 0 s -- the slice number, starting from 0 m' -- the total number of memory blocks, defined above t -- the total number of passes y -- the Argon2 type (0 for Argon2d and 1 for Argon2i) i -- the counter (starts from 1 in each segment) The values r, l, s, m', t, y, i are represented on 8 bytes in little- endian. 0 stands for 968 zero bytes. Then we compute Z_i for i from 1 to w inclusive as Z_i = G(X,G(X,Y_i)). The sequence Z_1||Z_2||...||Z_w is partitioned into w*128 pairs of 8-byte values (J_1,J_2). 3.4.2. Mapping J_1 and J_2 to (i',j') The value of i' = J_2 mod p gives the index of the lane from which the block will be taken. For the first pass (r=0) and the first slice (s=0) then i' MUST be equal to the current lane index. The set R contains the indices that can be referenced according to the following rules: 1. If i' is the current lane index, then R includes the indices of all blocks computed in this lane that are not overwritten yet, excluding B[i'][j-1] and all blocks from the current segment not overwritten in this pass. Biryukov, et al. Expires September 21, 2016 [Page 7] Internet-Draft Argon2 March 2016 2. If i' is not the current lane index, then R includes the indices of all blocks in the last S - 1 = 3 segments computed and finished in lane i'. If B[i][j] is the first block of a segment, then the very last index from R is excluded. We are going to take a block from R with a non-uniform distribution over [0, |R|): x = floor(J_1**2 / 2**32); y = floor((|R| * x) / 2**32); z = |R| - 1 - y; Let [i'][j''] be the index of the block computed chronologically first among the blocks in R. Then we define j' = j''+z (mod q). 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_2, ... , Q_7) <- P( R_0, R_1, R_2, ... , R_7) ( Q_8, Q_9, Q_10, ... , Q_15) <- P( R_8, R_9, R_10, ... , R_15) ... (Q_56, Q_57, Q_58, ... , Q_63) <- P(R_56, R_57, R_58, ... , 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 +---+ +---+ | X | | Y | +---+ +---+ | | ---->XOR<---- --------| | \ / Biryukov, et al. Expires September 21, 2016 [Page 8] Internet-Draft Argon2 March 2016 | +---+ | | R | | +---+ | | | \ / | P rowwise | | | \ / | +---+ | | Q | | +---+ | | | \ / | P columnwise | | | \ / | +---+ | | Z | | +---+ | | | \ / ------>XOR | \ / Argon2 compression function G. 3.6. Permutation P Permutation P is based on the round function of BLAKE2b. The 8 16-byte inputs S_0, S_1, ... , S_7 are viewed as a 4x4 matrix of 64-bit words, where S_i = (v_{2*i+1} || v_{2*i}): v_0 v_1 v_2 v_3 v_4 v_5 v_6 v_7 v_8 v_9 v_10 v_11 v_12 v_13 v_14 v_15 It works as follows: Biryukov, et al. Expires September 21, 2016 [Page 9] Internet-Draft Argon2 March 2016 G(v_0, v_4, v_8, v_12) G(v_1, v_5, v_9, v_13) G(v_2, v_6, v_10, v_14) G(v_3, v_7, v_11, v_15) G(v_0, v_5, v_10, v_15) G(v_1, v_6, v_11, v_12) G(v_2, v_7, v_8, v_13) G(v_3, v_4, v_9, v_14) G(a, b, c, d) is defined as follows: a <- (a + b + 2 * trunc(a) * trunc(b)) mod 2**64 d <- (d ^ a) >>> 32 c <- (c + d + 2 * trunc(c) * trunc(d)) mod 2**64 b <- (b ^ c) >>> 24 a <- (a + b + 2 * trunc(a) * trunc(b)) mod 2**64 d <- (d ^ a) >>> 16 c <- (c + d + 2 * trunc(c) * trunc(d)) mod 2**64 b <- (b ^ c) >>> 63 The modular additions in G are combined with 64-bit multiplications. Multiplications are the only difference to the original BLAKE2b design. This choice is done to increase the circuit depth and thus the running time of ASIC implementations, while having roughly the same running time on CPUs thanks to parallelism and pipelining. 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 -\u002D 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 -\u002D Argon2d with 8 lanes and 4 GB of RAM. 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: Biryukov, et al. Expires September 21, 2016 [Page 10] Internet-Draft Argon2 March 2016 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. 5. Example Code void fill_block(const block *prev_block, const block *ref_block, block *next_block) { block blockR, block_tmp; unsigned i; Biryukov, et al. Expires September 21, 2016 [Page 11] Internet-Draft Argon2 March 2016 copy_block(&blockR, ref_block); xor_block(&blockR, prev_block); copy_block(&block_tmp, &blockR); /* Now blockR = ref_block + prev_block and bloc_tmp = ref_block + prev_block */ /* Apply Blake2 on columns of 64-bit words: (0,1,...,15), then (16,17,..31)... finally (112,113,...127) */ for (i = 0; i < 8; ++i) { BLAKE2_ROUND_NOMSG( blockR.v[16 * i], blockR.v[16 * i + 1], blockR.v[16 * i + 2], blockR.v[16 * i + 3], blockR.v[16 * i + 4], blockR.v[16 * i + 5], blockR.v[16 * i + 6], blockR.v[16 * i + 7], blockR.v[16 * i + 8], blockR.v[16 * i + 9], blockR.v[16 * i + 10], blockR.v[16 * i + 11], blockR.v[16 * i + 12], blockR.v[16 * i + 13], blockR.v[16 * i + 14], blockR.v[16 * i + 15]); } /* Apply Blake2 on rows of 64-bit words: (0,1,16,17,...112,113), then (2,3,18,19,...,114,115), ... and finally (14,15,30,31,...,126,127) */ for (i = 0; i < 8; i++) { BLAKE2_ROUND_NOMSG( blockR.v[2 * i], blockR.v[2 * i + 1], blockR.v[2 * i + 16], blockR.v[2 * i + 17], blockR.v[2 * i + 32], blockR.v[2 * i + 33], blockR.v[2 * i + 48], blockR.v[2 * i + 49], blockR.v[2 * i + 64], blockR.v[2 * i + 65], blockR.v[2 * i + 80], blockR.v[2 * i + 81], blockR.v[2 * i + 96], blockR.v[2 * i + 97], blockR.v[2 * i + 112], blockR.v[2 * i + 113]); } copy_block(next_block, &block_tmp); xor_block(next_block, &blockR); } void fill_block_with_xor(const block *prev_block, const block *ref_block, block *next_block) { block blockR, block_tmp; unsigned i; copy_block(&blockR, ref_block); xor_block(&blockR, prev_block); Biryukov, et al. Expires September 21, 2016 [Page 12] Internet-Draft Argon2 March 2016 copy_block(&block_tmp, &blockR); /* Saving the next block contents for XOR over */ xor_block(&block_tmp, next_block); /* Now blockR = ref_block + prev_block and bloc_tmp = ref_block + prev_block + next_block*/ /* Apply Blake2 on columns of 64-bit words: (0,1,...,15) , then (16,17,..31),... and finally (112,113,...127) */ for (i = 0; i < 8; ++i) { BLAKE2_ROUND_NOMSG( blockR.v[16 * i], blockR.v[16 * i + 1], blockR.v[16 * i + 2], blockR.v[16 * i + 3], blockR.v[16 * i + 4], blockR.v[16 * i + 5], blockR.v[16 * i + 6], blockR.v[16 * i + 7], blockR.v[16 * i + 8], blockR.v[16 * i + 9], blockR.v[16 * i + 10], blockR.v[16 * i + 11], blockR.v[16 * i + 12], blockR.v[16 * i + 13], blockR.v[16 * i + 14], blockR.v[16 * i + 15]); } /* Apply Blake2 on rows of 64-bit words: (0,1,16,17,...112,113), then (2,3,18,19,...,114,115), ... and finally (14,15,30,31,...,126,127) */ for (i = 0; i < 8; i++) { BLAKE2_ROUND_NOMSG( blockR.v[2 * i], blockR.v[2 * i + 1], blockR.v[2 * i + 16], blockR.v[2 * i + 17], blockR.v[2 * i + 32], blockR.v[2 * i + 33], blockR.v[2 * i + 48], blockR.v[2 * i + 49], blockR.v[2 * i + 64], blockR.v[2 * i + 65], blockR.v[2 * i + 80], blockR.v[2 * i + 81], blockR.v[2 * i + 96], blockR.v[2 * i + 97], blockR.v[2 * i + 112], blockR.v[2 * i + 113]); } copy_block(next_block, &block_tmp); xor_block(next_block, &blockR); } void generate_addresses(const argon2_instance_t *instance, const argon2_position_t *position, uint64_t *pseudo_rands) { block zero_block, input_block, address_block,tmp_block; uint32_t i; init_block_value(&zero_block, 0); Biryukov, et al. Expires September 21, 2016 [Page 13] Internet-Draft Argon2 March 2016 init_block_value(&input_block, 0); if (instance != NULL && position != NULL) { input_block.v[0] = position->pass; input_block.v[1] = position->lane; input_block.v[2] = position->slice; input_block.v[3] = instance->memory_blocks; input_block.v[4] = instance->passes; input_block.v[5] = instance->type; for (i = 0; i < instance->segment_length; ++i) { if (i % ARGON2_ADDRESSES_IN_BLOCK == 0) { input_block.v[6]++; init_block_value(&tmp_block, 0); init_block_value(&address_block, 0); fill_block_with_xor(&zero_block, &input_block, &tmp_block); fill_block_with_xor(&zero_block, &tmp_block, &address_block); } pseudo_rands[i] = address_block.v[i % ARGON2_ADDRESSES_IN_BLOCK]; } } void fill_segment(const argon2_instance_t *instance, argon2_position_t position) { block *ref_block = NULL, *curr_block = NULL; uint64_t pseudo_rand, ref_index, ref_lane; uint32_t prev_offset, curr_offset; uint32_t starting_index; uint32_t i; int data_independent_addressing; /* Pseudo-random values that determine the reference block position */ uint64_t *pseudo_rands = NULL; if (instance == NULL) { return; } data_independent_addressing = (instance->type == Argon2_i); pseudo_rands = (uint64_t *)malloc(sizeof(uint64_t) * (instance->segment_length)); if (pseudo_rands == NULL) { return; } Biryukov, et al. Expires September 21, 2016 [Page 14] Internet-Draft Argon2 March 2016 if (data_independent_addressing) { generate_addresses(instance, &position, pseudo_rands); } starting_index = 0; if ((0 == position.pass) && (0 == position.slice)) { /* we have already generated the first two blocks */ starting_index = 2; } /* Offset of the current block */ curr_offset = position.lane * instance->lane_length + position.slice * instance->segment_length + starting_index; if (0 == curr_offset % instance->lane_length) { /* Last block in this lane */ prev_offset = curr_offset + instance->lane_length - 1; } else { /* Previous block */ prev_offset = curr_offset - 1; } for (i = starting_index; i < instance->segment_length; ++i, ++curr_offset, ++prev_offset) { /*1.1 Rotating prev_offset if needed */ if (curr_offset % instance->lane_length == 1) { prev_offset = curr_offset - 1; } /* 1.2 Computing the index of the reference block */ /* 1.2.1 Taking pseudo-random value from the previous block */ if (data_independent_addressing) { pseudo_rand = pseudo_rands[i]; } else { pseudo_rand = instance->memory[prev_offset].v[0]; } /* 1.2.2 Computing the lane of the reference block */ ref_lane = ((pseudo_rand >> 32)) % instance->lanes; if ((position.pass == 0) && (position.slice == 0)) { /* Can not reference other lanes yet */ ref_lane = position.lane; } /* 1.2.3 Computing the number of possible reference block Biryukov, et al. Expires September 21, 2016 [Page 15] Internet-Draft Argon2 March 2016 within the lane. */ position.index = i; ref_index = index_alpha(instance, &position, pseudo_rand & 0xFFFFFFFF, ref_lane == position.lane); /* 2 Creating a new block */ ref_block = instance->memory + instance->lane_length * ref_lane + ref_index; curr_block = instance->memory + curr_offset; if (instance->version == ARGON2_OLD_VERSION_NUMBER) { /* version 1.2.1 and earlier: overwrite, not XOR */ fill_block(instance->memory + prev_offset, ref_block, curr_block); } else { if(0 == position.pass) { fill_block(instance->memory + prev_offset, ref_block, curr_block); } else { fill_block_with_xor(instance->memory + prev_offset, ref_block, curr_block); } } } free(pseudo_rands); } uint32_t index_alpha(const argon2_instance_t *instance, const argon2_position_t *position, uint32_t pseudo_rand, int same_lane) { /* * Pass 0: * This lane : all already finished segments plus already * constructed blocks in this segment * Other lanes : all already finished segments * Pass 1+: * This lane : (SYNC_POINTS - 1) last segments plus * already constructed blocks in this segment * Other lanes : (SYNC_POINTS - 1) last segments */ uint32_t reference_area_size; uint64_t relative_position; uint32_t start_position, absolute_position; if (0 == position->pass) { /* First pass */ Biryukov, et al. Expires September 21, 2016 [Page 16] Internet-Draft Argon2 March 2016 if (0 == position->slice) { /* First slice */ reference_area_size = position->index - 1; /* all but the previous */ } else { if (same_lane) { /* The same lane => add current segment */ reference_area_size = position->slice * instance->segment_length + position->index - 1; } else { reference_area_size = position->slice * instance->segment_length + ((position->index == 0) ? (-1) : 0); } } } else { /* Second pass */ if (same_lane) { reference_area_size = instance->lane_length - instance->segment_length + position->index - 1; } else { reference_area_size = instance->lane_length - instance->segment_length + ((position->index == 0) ? (-1) : 0); } } /* 1.2.4. Mapping pseudo_rand to 0.. and produce relative position */ relative_position = pseudo_rand; relative_position = relative_position * relative_position >> 32; relative_position = reference_area_size - 1 - (reference_area_size * relative_position >> 32); /* 1.2.5 Computing starting position */ start_position = 0; if (0 != position->pass) { start_position = (position->slice == ARGON2_SYNC_POINTS - 1) ? 0 : (position->slice + 1) * instance->segment_length; } /* 1.2.6. Computing absolute position */ absolute_position = (start_position + relative_position) % Biryukov, et al. Expires September 21, 2016 [Page 17] Internet-Draft Argon2 March 2016 instance->lane_length; /* absolute position */ return absolute_position; } int fill_memory_blocks(argon2_instance_t *instance) { uint32_t r, s; argon2_thread_handle_t *thread = NULL; argon2_thread_data *thr_data = NULL; if (instance == NULL || instance->lanes == 0) { return ARGON2_THREAD_FAIL; } /* 1. Allocating space for threads */ thread = calloc(instance->lanes, sizeof(argon2_thread_handle_t)); if (thread == NULL) { return ARGON2_MEMORY_ALLOCATION_ERROR; } thr_data = calloc(instance->lanes, sizeof(argon2_thread_data)); if (thr_data == NULL) { free(thread); return ARGON2_MEMORY_ALLOCATION_ERROR; } for (r = 0; r < instance->passes; ++r) { for (s = 0; s < ARGON2_SYNC_POINTS; ++s) { int rc; uint32_t l; /* 2. Calling threads */ for (l = 0; l < instance->lanes; ++l) { argon2_position_t position; /* 2.1 Join a thread if limit is exceeded */ if (l >= instance->threads) { rc = argon2_thread_join(thread[l - instance->threads]); if (rc) { free(thr_data); free(thread); return ARGON2_THREAD_FAIL; } } /* 2.2 Create thread */ position.pass = r; position.lane = l; position.slice = (uint8_t)s; Biryukov, et al. Expires September 21, 2016 [Page 18] Internet-Draft Argon2 March 2016 position.index = 0; /* preparing the thread input */ thr_data[l].instance_ptr = instance; memcpy(&(thr_data[l].pos), &position, sizeof(argon2_position_t)); rc = argon2_thread_create(&thread[l], &fill_segment_thr, (void *)&thr_data[l]); if (rc) { free(thr_data); free(thread); return ARGON2_THREAD_FAIL; } /* fill_segment(instance, position); */ /*Non-thread equivalent of the lines above */ } /* 3. Joining remaining threads */ for (l = instance->lanes - instance->threads; l < instance->lanes; ++l) { rc = argon2_thread_join(thread[l]); if (rc) { return ARGON2_THREAD_FAIL; } } } } if (thread != NULL) { free(thread); } if (thr_data != NULL) { free(thr_data); } return ARGON2_OK; } 6. Test Vectors This section contains test vectors for Argon2. 6.1. Argon2d Test Vectors ======================================= Argon2d version number 19 ======================================= Memory: 32 KiB Biryukov, et al. Expires September 21, 2016 [Page 19] Internet-Draft Argon2 March 2016 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: b8 81 97 91 a0 35 96 60 bb 77 09 c8 5f a4 8f 04 d5 d8 2c 05 c5 f2 15 cc db 88 54 91 71 7c f7 57 08 2c 28 b9 51 be 38 14 10 b5 fc 2e b7 27 40 33 b9 fd c7 ae 67 2b ca ac 5d 17 90 97 a4 af 31 09 After pass 0: Block 0000 [ 0]: db2fea6b2c6f5c8a Block 0000 [ 1]: 719413be00f82634 Block 0000 [ 2]: a1e3f6dd42aa25cc Block 0000 [ 3]: 3ea8efd4d55ac0d1 ... Block 0031 [124]: 28d17914aea9734c Block 0031 [125]: 6a4622176522e398 Block 0031 [126]: 951aa08aeecb2c05 Block 0031 [127]: 6a6c49d2cb75d5b6 After pass 1: Block 0000 [ 0]: d3801200410f8c0d Block 0000 [ 1]: 0bf9e8a6e442ba6d Block 0000 [ 2]: e2ca92fe9c541fcc Block 0000 [ 3]: 6269fe6db177a388 ... Block 0031 [124]: 9eacfcfbdb3ce0fc Block 0031 [125]: 07dedaeb0aee71ac Block 0031 [126]: 074435fad91548f4 Block 0031 [127]: 2dbfff23f31b5883 After pass 2: Block 0000 [ 0]: 5f047b575c5ff4d2 Block 0000 [ 1]: f06985dbf11c91a8 Block 0000 [ 2]: 89efb2759f9a8964 Block 0000 [ 3]: 7486a73f62f9b142 ... Block 0031 [124]: 57cfb9d20479da49 Biryukov, et al. Expires September 21, 2016 [Page 20] Internet-Draft Argon2 March 2016 Block 0031 [125]: 4099654bc6607f69 Block 0031 [126]: f142a1126075a5c8 Block 0031 [127]: c341b3ca45c10da5 Tag: 51 2b 39 1b 6f 11 62 97 53 71 d3 09 19 73 42 94 f8 68 e3 be 39 84 f3 c1 a1 3a 4d b9 fa be 4a cb 6.2. Argon2i Test Vectors ======================================= Argon2i version number 19 ======================================= Memory: 32 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: c4 60 65 81 52 76 a0 b3 e7 31 73 1c 90 2f 1f d8 0c f7 76 90 7f bb 7b 6a 5c a7 2e 7b 56 01 1f ee ca 44 6c 86 dd 75 b9 46 9a 5e 68 79 de c4 b7 2d 08 63 fb 93 9b 98 2e 5f 39 7c c7 d1 64 fd da a9 After pass 0: Block 0000 [ 0]: f8f9e84545db08f6 Block 0000 [ 1]: 9b073a5c87aa2d97 Block 0000 [ 2]: d1e868d75ca8d8e4 Block 0000 [ 3]: 349634174e1aebcc ... Block 0031 [124]: 975f596583745e30 Block 0031 [125]: e349bdd7edeb3092 Block 0031 [126]: b751a689b7a83659 Block 0031 [127]: c570f2ab2a86cf00 After pass 1: Block 0000 [ 0]: b2e4ddfcf76dc85a Block 0000 [ 1]: 4ffd0626c89a2327 Block 0000 [ 2]: 4af1440fff212980 Biryukov, et al. Expires September 21, 2016 [Page 21] Internet-Draft Argon2 March 2016 Block 0000 [ 3]: 1e77299c7408505b ... Block 0031 [124]: e4274fd675d1e1d6 Block 0031 [125]: 903fffb7c4a14c98 Block 0031 [126]: 7e5db55def471966 Block 0031 [127]: 421b3c6e9555b79d After pass 2: Block 0000 [ 0]: af2a8bd8482c2f11 Block 0000 [ 1]: 785442294fa55e6d Block 0000 [ 2]: 9256a768529a7f96 Block 0000 [ 3]: 25a1c1f5bb953766 ... Block 0031 [124]: 68cf72fccc7112b9 Block 0031 [125]: 91e8c6f8bb0ad70d Block 0031 [126]: 4f59c8bd65cbb765 Block 0031 [127]: 71e436f035f30ed0 Tag: c8 14 d9 d1 dc 7f 37 aa 13 f0 d7 7f 24 94 bd a1 c8 de 6b 01 6d d3 88 d2 99 52 a4 c4 67 2b 6c e8 7. IANA Considerations None. 8. Security Considerations This document describes the memory-hard Argon2 password hash function. The best attacks on the 1-pass and 2-pass Argon2i is the low-storage attack described in [CBS16], which reduces the time-area product (using the peak memory value) by the factor of 5. The best attack on t-pass (t>2) Argon2i is the ranking tradeoff attack, which reduces the time-area product by the factor of 3. The best attack on t-pass Argon2d is the ranking tradeoff attack, which reduces the time-area product by the factor of 1.33. 9. References 9.1. 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. Biryukov, et al. Expires September 21, 2016 [Page 22] Internet-Draft Argon2 March 2016 9.2. Informative References [ARGON2] Biryukov, A., Dinu, D., and D. Khovratovich, "Argon2: the memory-hard function for password hashing and other applications", WWW , October 2015. [CBS16] Corrigan-Gibbs, H., Boneh, D., and S. Schechter, "Balloon Hashing: Provably Space-Hard Hash Functions with Data- Independent Access Patterns", WWW , January 2016. 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 September 21, 2016 [Page 23]