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Run idnits with the --verbose option for more detailed information about the items above. -------------------------------------------------------------------------------- 2 CFRG A. Biryukov 3 Internet-Draft D. Dinu 4 Intended status: Informational University of Luxembourg 5 Expires: March 12, 2021 D. Khovratovich 6 ABDK Consulting 7 S. Josefsson 8 SJD AB 9 September 08, 2020 11 The memory-hard Argon2 password hash and proof-of-work function 12 draft-irtf-cfrg-argon2-12 14 Abstract 16 This document describes the Argon2 memory-hard function for password 17 hashing and proof-of-work applications. We provide an implementer- 18 oriented description with test vectors. The purpose is to simplify 19 adoption of Argon2 for Internet protocols. This document is a 20 product of the Crypto Forum Research Group (CFRG) in the IRTF. 22 Status of This Memo 24 This Internet-Draft is submitted in full conformance with the 25 provisions of BCP 78 and BCP 79. 27 Internet-Drafts are working documents of the Internet Engineering 28 Task Force (IETF). Note that other groups may also distribute 29 working documents as Internet-Drafts. The list of current Internet- 30 Drafts is at https://datatracker.ietf.org/drafts/current/. 32 Internet-Drafts are draft documents valid for a maximum of six months 33 and may be updated, replaced, or obsoleted by other documents at any 34 time. It is inappropriate to use Internet-Drafts as reference 35 material or to cite them other than as "work in progress." 37 This Internet-Draft will expire on March 12, 2021. 39 Copyright Notice 41 Copyright (c) 2020 IETF Trust and the persons identified as the 42 document authors. All rights reserved. 44 This document is subject to BCP 78 and the IETF Trust's Legal 45 Provisions Relating to IETF Documents 46 (https://trustee.ietf.org/license-info) in effect on the date of 47 publication of this document. Please review these documents 48 carefully, as they describe your rights and restrictions with respect 49 to this document. Code Components extracted from this document must 50 include Simplified BSD License text as described in Section 4.e of 51 the Trust Legal Provisions and are provided without warranty as 52 described in the Simplified BSD License. 54 Table of Contents 56 1. Introduction . . . . . . . . . . . . . . . . . . . . . . . . 2 57 2. Notation and Conventions . . . . . . . . . . . . . . . . . . 3 58 3. Argon2 Algorithm . . . . . . . . . . . . . . . . . . . . . . 4 59 3.1. Argon2 Inputs and Outputs . . . . . . . . . . . . . . . . 4 60 3.2. Argon2 Operation . . . . . . . . . . . . . . . . . . . . 5 61 3.3. Variable-length hash function H' . . . . . . . . . . . . 7 62 3.4. Indexing . . . . . . . . . . . . . . . . . . . . . . . . 7 63 3.4.1. Computing the 32-bit values J_1 and J_2 . . . . . . . 8 64 3.4.2. Mapping J_1 and J_2 to reference block index [l][z] . 9 65 3.5. Compression function G . . . . . . . . . . . . . . . . . 10 66 3.6. Permutation P . . . . . . . . . . . . . . . . . . . . . . 11 67 4. Parameter Choice . . . . . . . . . . . . . . . . . . . . . . 12 68 5. Test Vectors . . . . . . . . . . . . . . . . . . . . . . . . 14 69 5.1. Argon2d Test Vectors . . . . . . . . . . . . . . . . . . 14 70 5.2. Argon2i Test Vectors . . . . . . . . . . . . . . . . . . 15 71 5.3. Argon2id Test Vectors . . . . . . . . . . . . . . . . . . 16 72 6. IANA Considerations . . . . . . . . . . . . . . . . . . . . . 17 73 7. Security Considerations . . . . . . . . . . . . . . . . . . . 18 74 7.1. Security as hash function and KDF . . . . . . . . . . . . 18 75 7.2. Security against time-space tradeoff attacks . . . . . . 18 76 7.3. Security for time-bounded defenders . . . . . . . . . . . 19 77 7.4. Recommendations . . . . . . . . . . . . . . . . . . . . . 19 78 8. Acknowledgements . . . . . . . . . . . . . . . . . . . . . . 19 79 9. References . . . . . . . . . . . . . . . . . . . . . . . . . 19 80 9.1. Normative References . . . . . . . . . . . . . . . . . . 19 81 9.2. Informative References . . . . . . . . . . . . . . . . . 19 82 Authors' Addresses . . . . . . . . . . . . . . . . . . . . . . . 20 84 1. Introduction 86 This document describes the Argon2 [ARGON2ESP] memory-hard function 87 for password hashing and proof-of-work applications. We provide an 88 implementer oriented description with test vectors. The purpose is 89 to simplify adoption of Argon2 for Internet protocols. This document 90 corresponds to version 1.3 of the Argon2 hash function. 92 Argon2 is a traditional memory-hard function [HARD]. It is a 93 streamlined design. It aims at the highest memory filling rate and 94 effective use of multiple computing units, while still providing 95 defense against tradeoff attacks. Argon2 is optimized for the x86 96 architecture and exploits the cache and memory organization of the 97 recent Intel and AMD processors. Argon2 has one primary variant: 98 Argon2id and two supplementary variants: Argon2d and Argon2i. 99 Argon2d uses data-dependent memory access, which makes it suitable 100 for cryptocurrencies and proof-of-work applications with no threats 101 from side-channel timing attacks. Argon2i uses data-independent 102 memory access, which is preferred for password hashing and password- 103 based key derivation. Argon2id works as Argon2i for the first half 104 of the first pass over the memory, and as Argon2d for the rest, thus 105 providing both side-channel attack protection and brute-force cost 106 savings due to time-memory tradeoffs. Argon2i makes more passes over 107 the memory to protect from tradeoff attacks [AB15]. 109 Argon2id MUST be supported by any implementation of this document, 110 whereas Argon2d and Argon2i MAY be supported. 112 Argon2 is also a mode of operation over a fixed-input-length 113 compression function G and a variable-input-length hash function H. 114 Even though Argon2 can be potentially used with an arbitrary function 115 H, as long as it provides outputs up to 64 bytes, in this document it 116 is BLAKE2b [BLAKE2]. 118 For further background and discussion, see the Argon2 paper [ARGON2]. 120 The key words "MUST", "MUST NOT", "REQUIRED", "SHALL", "SHALL NOT", 121 "SHOULD", "SHOULD NOT", "RECOMMENDED", "MAY", and "OPTIONAL" in this 122 document are to be interpreted as described in RFC 2119 [RFC2119]. 124 This document represents the consensus of the Crypto Forum Research 125 Group (CFRG). 127 2. Notation and Conventions 129 x^y --- integer x multiplied by itself integer y times 131 a*b --- multiplication of integer a and integer b 133 c-d --- subtraction of integer d from integer c 135 E_f --- variable E with subscript index f 137 g / h --- integer g divided by integer h. The result is a rational 138 number 140 I(j) --- function I evaluated at j 142 K || L --- string K concatenated with string L 144 a XOR b --- bitwise exclusive-or between bitstrings a and b 145 a mod b --- remainder of integer a modulo integer b, always in range 146 [0, b-1] 148 a >>> n --- rotation of 64-bit string a to the right by n bits 150 trunc(a) --- the 64-bit value, truncated to the 32 least significant 151 bits 153 floor(a) --- the largest integer not bigger than a 155 ceil(a) --- the smallest integer not smaller than a 157 extract(a, i) --- the i-th set of 32-bits from bitstring a, starting 158 from 0-th 160 |A| --- the number of elements in set A 162 LE32(a) --- 32-bit integer a converted to a bytestring in little 163 endian. Example: 123456 (decimal) is 40 E2 01 00. 165 LE64(a) --- 64-bit integer a converted to a bytestring in little 166 endian. Example: 123456 (decimal) is 40 E2 01 00 00 00 00 00. 168 int32(s) --- 32-bit string s is converted to non-negative integer in 169 little endian. 171 int64(s) --- 64-bit string s is converted to non-negative integer in 172 little endian. 174 length(P) --- the bytelength of string P expressed as 32-bit integer 176 ZERO(P) --- the P-byte zero string 178 3. Argon2 Algorithm 180 3.1. Argon2 Inputs and Outputs 182 Argon2 has the following input parameters: 184 o Message string P, which is a password for password hashing 185 applications. MUST have length from 0 to 2^(32) - 1 bytes. 187 o Nonce S, which is a salt for password hashing applications. MUST 188 have length not greater than 2^(32)-1 bytes. 16 bytes is 189 RECOMMENDED for password hashing. Salt SHOULD be unique for each 190 password. 192 o Degree of parallelism p determines how many independent (but 193 synchronizing) computational chains (lanes) can be run. It MUST 194 be an integer value from 1 to 2^(24)-1. 196 o Tag length T MUST be an integer number of bytes from 4 to 2^(32)- 197 1. 199 o Memory size m MUST be an integer number of kibibytes from 8*p to 200 2^(32)-1. The actual number of blocks is m', which is m rounded 201 down to the nearest multiple of 4*p. 203 o Number of passes t (used to tune the running time independently of 204 the memory size) MUST be an integer number from 1 to 2^(32)-1. 206 o Version number v MUST be one byte 0x13. 208 o Secret value K is OPTIONAL. If used, it MUST have length not 209 greater than 2^(32)-1 bytes. 211 o Associated data X is OPTIONAL. If used, it MUST have length not 212 greater than 2^(32)-1 bytes. 214 o Type y of Argon2: MUST be 0 for Argon2d, 1 for Argon2i, 2 for 215 Argon2id. 217 The Argon2 output, or "tag" is a string T bytes long. 219 3.2. Argon2 Operation 221 Argon2 uses an internal compression function G with two 1024-byte 222 inputs and a 1024-byte output, and an internal hash function H^x() 223 with x being its output length in bytes. Here H^x() applied to 224 string A is the BLAKE2b [BLAKE2] function, which takes 225 (d,|dd|,kk=0,nn=x) as parameters where d is A padded to a multiple of 226 128 bytes and partitioned into 128-byte blocks. The compression 227 function G is based on its internal permutation. A variable-length 228 hash function H' built upon H is also used. G is described in 229 Section 3.5 and H' is described in Section 3.3. 231 The Argon2 operation is as follows. 233 1. Establish H_0 as the 64-byte value as shown below. If K, X, or S 234 has zero length it is just absent but its length field remains. 236 H_0 = H^(64)(LE32(p) || LE32(T) || LE32(m) || LE32(t) || 237 LE32(v) || LE32(y) || LE32(length(P)) || P || 238 LE32(length(S)) || S || LE32(length(K)) || K || 239 LE32(length(X)) || X) 241 H_0 generation 243 2. Allocate the memory as m' 1024-byte blocks where m' is derived 244 as: 246 m' = 4 * p * floor (m / 4p) 248 Memory allocation 250 For p lanes, the memory is organized in a matrix B[i][j] of 251 blocks with p rows (lanes) and q = m' / p columns. 253 3. Compute B[i][0] for all i ranging from (and including) 0 to (not 254 including) p. 256 B[i][0] = H'^(1024)(H_0 || LE32(0) || LE32(i)) 258 Lane starting blocks 260 4. Compute B[i][1] for all i ranging from (and including) 0 to (not 261 including) p. 263 B[i][1] = H'^(1024)(H_0 || LE32(1) || LE32(i)) 265 Second lane blocks 267 5. Compute B[i][j] for all i ranging from (and including) 0 to (not 268 including) p, and for all j ranging from (and including) 2) to 269 (not including) q. The computation MUST proceed slicewise 270 (Section 3.4): first blocks from slice 0 are computed for all 271 lanes (in an arbitrary order of lanes), then blocks from slice 1 272 are computed etc. The block indices l and z are determined for 273 each i, j differently for Argon2d, Argon2i, and Argon2id. 275 B[i][j] = G(B[i][j-1], B[l][z]) 277 Further block generation 279 6. If the number of passes t is larger than 1, we repeat the steps. 280 However blocks are computed differently as the old value is XORed 281 with the new one: 283 B[i][0] = G(B[i][q-1], B[l][z]) XOR B[i][0]; 284 B[i][j] = G(B[i][j-1], B[l][z]) XOR B[i][j]. 286 Further passes 288 7. After t steps have been iterated, the final block C is computed 289 as the XOR of the last column: 291 C = B[0][q-1] XOR B[1][q-1] XOR ... XOR B[p-1][q-1] 293 Final block 295 8. The output tag is computed as H'^T(C). 297 3.3. Variable-length hash function H' 299 Let V_i be a 64-byte block, and W_i be its first 32 bytes. Then we 300 define: 302 if T <= 64 303 H'^T(A) = H^T(LE32(T)||A) 304 else 305 r = ceil(T/32)-2 306 V_1 = H^(64)(LE32(T)||A) 307 V_2 = H^(64)(V_1) 308 ... 309 V_r = H^(64)(V_{r-1}) 310 V_{r+1} = H^(T-32*r)(V_{r}) 311 H'^T(X) = W_1 || W_2 || ... || W_r || V_{r+1} 313 Function H' for tag and initial block computations 315 3.4. Indexing 317 To enable parallel block computation, we further partition the memory 318 matrix into SL = 4 vertical slices. The intersection of a slice and 319 a lane is called a segment, which has length q/SL. Segments of the 320 same slice can be computed in parallel and do not reference blocks 321 from each other. All other blocks can be referenced. 323 slice 0 slice 1 slice 2 slice 3 324 ___/\___ ___/\___ ___/\___ ___/\___ 325 / \ / \ / \ / \ 326 +----------+----------+----------+----------+ 327 | | | | | > lane 0 328 +----------+----------+----------+----------+ 329 | | | | | > lane 1 330 +----------+----------+----------+----------+ 331 | | | | | > lane 2 332 +----------+----------+----------+----------+ 333 | ... ... ... | ... 334 +----------+----------+----------+----------+ 335 | | | | | > lane p - 1 336 +----------+----------+----------+----------+ 338 Single-pass Argon2 with p lanes and 4 slices 340 3.4.1. Computing the 32-bit values J_1 and J_2 342 3.4.1.1. Argon2d 344 J_1 is given by the first 32 bits of block B[i][j-1], while J_2 is 345 given by the next 32-bits of block B[i][j-1]: 347 J_1 = int32(extract(B[i][j-1], 0)) 348 J_2 = int32(extract(B[i][j-1], 1)) 350 Deriving J1,J2 in Argon2d 352 3.4.1.2. Argon2i 354 For each segment we do the following. First we compute the value Z 355 as 357 Z= ( LE64(r) || LE64(l) || LE64(s) || LE64(m') || 358 LE64(t) || LE64(y) ), where 360 r -- the pass number 361 l -- the lane number 362 sl -- the slice number 363 m' -- the total number of memory blocks 364 t -- the total number of passes 365 y -- the Argon2 type (0 for Argon2d, 366 1 for Argon2i, 2 for Argon2id) 368 Input to compute J1,J2 in Argon2i 370 Then we compute q/(128*SL) 1024-byte values G(ZERO(1024), Z || 371 LE64(1) || ZERO(968) ), G(ZERO(1024), Z || LE64(2) || ZERO(968) ),... 372 , G(ZERO(1024), Z || LE64(q/(128*SL)) || ZERO(968) ), which are 373 partitioned into q/(SL) 8-byte values X, which are viewed as X1||X2 374 and converted to J_1=int32(X1) and J_2=int32(X2). The values r, l, 375 sl, m', t, y, i are represented as 8 bytes in little-endian. 377 3.4.1.3. Argon2id 379 If the pass number is 0 and the slice number is 0 or 1, then compute 380 J_1 and J_2 as for Argon2i, else compute J_1 and J_2 as for Argon2d. 382 3.4.2. Mapping J_1 and J_2 to reference block index [l][z] 384 The value of l = J_2 mod p gives the index of the lane from which the 385 block will be taken. For the first pass (r=0) and the first slice 386 (sl=0) the block is taken from the current lane. 388 The set W contains the indices that are referenced according to the 389 following rules: 391 1. If l is the current lane, then W includes the indices of all 392 blocks in the last SL - 1 = 3 segments computed and finished, as 393 well as the blocks computed in the current segment in the current 394 pass excluding B[i][j-1]. 396 2. If l is not the current lane, then W includes the indices of all 397 blocks in the last SL - 1 = 3 segments computed and finished in 398 lane l. If B[i][j] is the first block of a segment, then the 399 very last index from W is excluded. 401 Then take a block from W with a non-uniform distribution over 402 [0, |W|) using the mapping 404 J_1 -> |W|(1 - J_1^2 / 2^(64)) 406 Computing J1 408 To avoid floating point computation, the following approximation is 409 used: 411 x = J_1^2 / 2^(32) 412 y = (|W| * x) / 2^(32) 413 zz = |W| - 1 - y 415 Computing J1, part 2 417 Then take the zz-th index from W, it will be the z value for the 418 reference block index [l][z]. 420 3.5. Compression function G 422 The compression function G is built upon the BLAKE2b-based 423 transformation P. P operates on the 128-byte input, which can be 424 viewed as 8 16-byte registers: 426 P(A_0, A_1, ... ,A_7) = (B_0, B_1, ... ,B_7) 428 Blake round function P 430 The compression function G(X, Y) operates on two 1024-byte blocks X 431 and Y. It first computes R = X XOR Y. Then R is viewed as a 8x8 432 matrix of 16-byte registers R_0, R_1, ... , R_63. Then P is first 433 applied to each row, and then to each column to get Z: 435 ( Q_0, Q_1, Q_2, ... , Q_7) <- P( R_0, R_1, R_2, ... , R_7) 436 ( Q_8, Q_9, Q_10, ... , Q_15) <- P( R_8, R_9, R_10, ... , R_15) 437 ... 438 (Q_56, Q_57, Q_58, ... , Q_63) <- P(R_56, R_57, R_58, ... , R_63) 439 ( Z_0, Z_8, Z_16, ... , Z_56) <- P( Q_0, Q_8, Q_16, ... , Q_56) 440 ( Z_1, Z_9, Z_17, ... , Z_57) <- P( Q_1, Q_9, Q_17, ... , Q_57) 441 ... 442 ( Z_7, Z_15, Z 23, ... , Z_63) <- P( Q_7, Q_15, Q_23, ... , Q_63) 444 Core of compression function G 446 Finally, G outputs Z XOR R: 448 G: (X, Y) -> R -> Q -> Z -> Z XOR R 449 +---+ +---+ 450 | X | | Y | 451 +---+ +---+ 452 | | 453 ---->XOR<---- 454 --------| 455 | \ / 456 | +---+ 457 | | R | 458 | +---+ 459 | | 460 | \ / 461 | P rowwise 462 | | 463 | \ / 464 | +---+ 465 | | Q | 466 | +---+ 467 | | 468 | \ / 469 | P columnwise 470 | | 471 | \ / 472 | +---+ 473 | | Z | 474 | +---+ 475 | | 476 | \ / 477 ------>XOR 478 | 479 \ / 481 Argon2 compression function G. 483 3.6. Permutation P 485 Permutation P is based on the round function of BLAKE2b. The 8 486 16-byte inputs S_0, S_1, ... , S_7 are viewed as a 4x4 matrix of 487 64-bit words, where S_i = (v_{2*i+1} || v_{2*i}): 489 v_0 v_1 v_2 v_3 490 v_4 v_5 v_6 v_7 491 v_8 v_9 v_10 v_11 492 v_12 v_13 v_14 v_15 494 Matrix element labeling 496 It works as follows: 498 GB(v_0, v_4, v_8, v_12) 499 GB(v_1, v_5, v_9, v_13) 500 GB(v_2, v_6, v_10, v_14) 501 GB(v_3, v_7, v_11, v_15) 503 GB(v_0, v_5, v_10, v_15) 504 GB(v_1, v_6, v_11, v_12) 505 GB(v_2, v_7, v_8, v_13) 506 GB(v_3, v_4, v_9, v_14) 508 Feeding matrix elements to GB 510 GB(a, b, c, d) is defined as follows: 512 a = (a + b + 2 * trunc(a) * trunc(b)) mod 2^(64) 513 d = (d XOR a) >>> 32 514 c = (c + d + 2 * trunc(c) * trunc(d)) mod 2^(64) 515 b = (b XOR c) >>> 24 517 a = (a + b + 2 * trunc(a) * trunc(b)) mod 2^(64) 518 d = (d XOR a) >>> 16 519 c = (c + d + 2 * trunc(c) * trunc(d)) mod 2^(64) 520 b = (b XOR c) >>> 63 522 Details of GB 524 The modular additions in GB are combined with 64-bit multiplications. 525 Multiplications are the only difference to the original BLAKE2b 526 design. This choice is done to increase the circuit depth and thus 527 the running time of ASIC implementations, while having roughly the 528 same running time on CPUs thanks to parallelism and pipelining. 530 4. Parameter Choice 532 Argon2d is optimized for settings where the adversary does not get 533 regular access to system memory or CPU, i.e. he can not run side- 534 channel attacks based on the timing information, nor he can recover 535 the password much faster using garbage collection. These settings 536 are more typical for backend servers and cryptocurrency minings. For 537 practice we suggest the following settings: 539 o Cryptocurrency mining, that takes 0.1 seconds on a 2 Ghz CPU using 540 1 core -- Argon2d with 2 lanes and 250 MB of RAM. 542 Argon2id is optimized for more realistic settings, where the 543 adversary possibly can access the same machine, use its CPU or mount 544 cold-boot attacks. We suggest the following settings: 546 o Backend server authentication, that takes 0.5 seconds on a 2 GHz 547 CPU using 4 cores -- Argon2id with 8 lanes and 4 GiB of RAM. 549 o Key derivation for hard-drive encryption, that takes 3 seconds on 550 a 2 GHz CPU using 2 cores - Argon2id with 4 lanes and 6 GiB of 551 RAM. 553 o Frontend server authentication, that takes 0.5 seconds on a 2 GHz 554 CPU using 2 cores - Argon2id with 4 lanes and 1 GiB of RAM. 556 We recommend the following procedure to select the type and the 557 parameters for practical use of Argon2. 559 1. Select the type y. If you do not know the difference between 560 them or you consider side-channel attacks as viable threat, 561 choose Argon2id. 563 2. Figure out the maximum number h of threads that can be initiated 564 by each call to Argon2. 566 3. Figure out the maximum amount m of memory that each call can 567 afford. 569 4. Figure out the maximum amount x of time (in seconds) that each 570 call can afford. 572 5. Select the salt length. 128 bits is sufficient for all 573 applications, but can be reduced to 64 bits in the case of space 574 constraints. 576 6. Select the tag length. 128 bits is sufficient for most 577 applications, including key derivation. If longer keys are 578 needed, select longer tags. 580 7. If side-channel attacks are a viable threat, or if you're 581 uncertain, enable the memory wiping option in the library call. 583 8. Run the scheme of type y, memory m and h lanes and threads, using 584 different number of passes t. Figure out the maximum t such that 585 the running time does not exceed x. If it exceeds x even for t = 586 1, reduce m accordingly. 588 9. Hash all the passwords with the just determined values m, h, and 589 t. 591 5. Test Vectors 593 This section contains test vectors for Argon2. 595 5.1. Argon2d Test Vectors 597 We provide test vectors with complete outputs (tags). For the 598 convenience of developers, we also provide some interim variables, 599 concretely, first and last memory blocks of each pass. 601 ======================================= 602 Argon2d version number 19 603 ======================================= 604 Memory: 32 KiB 605 Passes: 3 606 Parallelism: 4 lanes 607 Tag length: 32 bytes 608 Password[32]: 01 01 01 01 01 01 01 01 609 01 01 01 01 01 01 01 01 610 01 01 01 01 01 01 01 01 611 01 01 01 01 01 01 01 01 612 Salt[16]: 02 02 02 02 02 02 02 02 02 02 02 02 02 02 02 02 613 Secret[8]: 03 03 03 03 03 03 03 03 614 Associated data[12]: 04 04 04 04 04 04 04 04 04 04 04 04 615 Pre-hashing digest: b8 81 97 91 a0 35 96 60 616 bb 77 09 c8 5f a4 8f 04 617 d5 d8 2c 05 c5 f2 15 cc 618 db 88 54 91 71 7c f7 57 619 08 2c 28 b9 51 be 38 14 620 10 b5 fc 2e b7 27 40 33 621 b9 fd c7 ae 67 2b ca ac 622 5d 17 90 97 a4 af 31 09 624 After pass 0: 625 Block 0000 [ 0]: db2fea6b2c6f5c8a 626 Block 0000 [ 1]: 719413be00f82634 627 Block 0000 [ 2]: a1e3f6dd42aa25cc 628 Block 0000 [ 3]: 3ea8efd4d55ac0d1 629 ... 630 Block 0031 [124]: 28d17914aea9734c 631 Block 0031 [125]: 6a4622176522e398 632 Block 0031 [126]: 951aa08aeecb2c05 633 Block 0031 [127]: 6a6c49d2cb75d5b6 635 After pass 1: 636 Block 0000 [ 0]: d3801200410f8c0d 637 Block 0000 [ 1]: 0bf9e8a6e442ba6d 638 Block 0000 [ 2]: e2ca92fe9c541fcc 639 Block 0000 [ 3]: 6269fe6db177a388 640 ... 641 Block 0031 [124]: 9eacfcfbdb3ce0fc 642 Block 0031 [125]: 07dedaeb0aee71ac 643 Block 0031 [126]: 074435fad91548f4 644 Block 0031 [127]: 2dbfff23f31b5883 646 After pass 2: 647 Block 0000 [ 0]: 5f047b575c5ff4d2 648 Block 0000 [ 1]: f06985dbf11c91a8 649 Block 0000 [ 2]: 89efb2759f9a8964 650 Block 0000 [ 3]: 7486a73f62f9b142 651 ... 652 Block 0031 [124]: 57cfb9d20479da49 653 Block 0031 [125]: 4099654bc6607f69 654 Block 0031 [126]: f142a1126075a5c8 655 Block 0031 [127]: c341b3ca45c10da5 656 Tag: 51 2b 39 1b 6f 11 62 97 657 53 71 d3 09 19 73 42 94 658 f8 68 e3 be 39 84 f3 c1 659 a1 3a 4d b9 fa be 4a cb 661 5.2. Argon2i Test Vectors 663 ======================================= 664 Argon2i version number 19 665 ======================================= 666 Memory: 32 KiB 667 Passes: 3 668 Parallelism: 4 lanes 669 Tag length: 32 bytes 670 Password[32]: 01 01 01 01 01 01 01 01 671 01 01 01 01 01 01 01 01 672 01 01 01 01 01 01 01 01 673 01 01 01 01 01 01 01 01 674 Salt[16]: 02 02 02 02 02 02 02 02 02 02 02 02 02 02 02 02 675 Secret[8]: 03 03 03 03 03 03 03 03 676 Associated data[12]: 04 04 04 04 04 04 04 04 04 04 04 04 677 Pre-hashing digest: c4 60 65 81 52 76 a0 b3 678 e7 31 73 1c 90 2f 1f d8 679 0c f7 76 90 7f bb 7b 6a 680 5c a7 2e 7b 56 01 1f ee 681 ca 44 6c 86 dd 75 b9 46 682 9a 5e 68 79 de c4 b7 2d 683 08 63 fb 93 9b 98 2e 5f 684 39 7c c7 d1 64 fd da a9 686 After pass 0: 688 Block 0000 [ 0]: f8f9e84545db08f6 689 Block 0000 [ 1]: 9b073a5c87aa2d97 690 Block 0000 [ 2]: d1e868d75ca8d8e4 691 Block 0000 [ 3]: 349634174e1aebcc 692 ... 693 Block 0031 [124]: 975f596583745e30 694 Block 0031 [125]: e349bdd7edeb3092 695 Block 0031 [126]: b751a689b7a83659 696 Block 0031 [127]: c570f2ab2a86cf00 698 After pass 1: 699 Block 0000 [ 0]: b2e4ddfcf76dc85a 700 Block 0000 [ 1]: 4ffd0626c89a2327 701 Block 0000 [ 2]: 4af1440fff212980 702 Block 0000 [ 3]: 1e77299c7408505b 703 ... 704 Block 0031 [124]: e4274fd675d1e1d6 705 Block 0031 [125]: 903fffb7c4a14c98 706 Block 0031 [126]: 7e5db55def471966 707 Block 0031 [127]: 421b3c6e9555b79d 709 After pass 2: 710 Block 0000 [ 0]: af2a8bd8482c2f11 711 Block 0000 [ 1]: 785442294fa55e6d 712 Block 0000 [ 2]: 9256a768529a7f96 713 Block 0000 [ 3]: 25a1c1f5bb953766 714 ... 715 Block 0031 [124]: 68cf72fccc7112b9 716 Block 0031 [125]: 91e8c6f8bb0ad70d 717 Block 0031 [126]: 4f59c8bd65cbb765 718 Block 0031 [127]: 71e436f035f30ed0 719 Tag: c8 14 d9 d1 dc 7f 37 aa 720 13 f0 d7 7f 24 94 bd a1 721 c8 de 6b 01 6d d3 88 d2 722 99 52 a4 c4 67 2b 6c e8 724 5.3. Argon2id Test Vectors 726 ======================================= 727 Argon2id version number 19 728 ======================================= 729 Memory: 32 KiB, Passes: 3, 730 Parallelism: 4 lanes, Tag length: 32 bytes 731 Password[32]: 01 01 01 01 01 01 01 01 01 01 01 01 01 01 01 01 732 01 01 01 01 01 01 01 01 01 01 01 01 01 01 01 01 733 Salt[16]: 02 02 02 02 02 02 02 02 02 02 02 02 02 02 02 02 734 Secret[8]: 03 03 03 03 03 03 03 03 735 Associated data[12]: 04 04 04 04 04 04 04 04 04 04 04 04 736 Pre-hashing digest: 28 89 de 48 7e b4 2a e5 00 c0 00 7e d9 25 2f 737 10 69 ea de c4 0d 57 65 b4 85 de 6d c2 43 7a 67 b8 54 6a 2f 0a 738 cc 1a 08 82 db 8f cf 74 71 4b 47 2e 94 df 42 1a 5d a1 11 2f fa 739 11 43 43 70 a1 e9 97 741 After pass 0: 742 Block 0000 [ 0]: 6b2e09f10671bd43 743 Block 0000 [ 1]: f69f5c27918a21be 744 Block 0000 [ 2]: dea7810ea41290e1 745 Block 0000 [ 3]: 6787f7171870f893 746 ... 747 Block 0031 [124]: 377fa81666dc7f2b 748 Block 0031 [125]: 50e586398a9c39c8 749 Block 0031 [126]: 6f732732a550924a 750 Block 0031 [127]: 81f88b28683ea8e5 752 After pass 1: 753 Block 0000 [ 0]: 3653ec9d01583df9 754 Block 0000 [ 1]: 69ef53a72d1e1fd3 755 Block 0000 [ 2]: 35635631744ab54f 756 Block 0000 [ 3]: 599512e96a37ab6e 757 ... 758 Block 0031 [124]: 4d4b435cea35caa6 759 Block 0031 [125]: c582210d99ad1359 760 Block 0031 [126]: d087971b36fd6d77 761 Block 0031 [127]: a55222a93754c692 763 After pass 2: 764 Block 0000 [ 0]: 942363968ce597a4 765 Block 0000 [ 1]: a22448c0bdad5760 766 Block 0000 [ 2]: a5f80662b6fa8748 767 Block 0000 [ 3]: a0f9b9ce392f719f 768 ... 769 Block 0031 [124]: d723359b485f509b 770 Block 0031 [125]: cb78824f42375111 771 Block 0031 [126]: 35bc8cc6e83b1875 772 Block 0031 [127]: 0b012846a40f346a 773 Tag: 0d 64 0d f5 8d 78 76 6c 08 c0 37 a3 4a 8b 53 c9 d0 774 1e f0 45 2d 75 b6 5e b5 25 20 e9 6b 01 e6 59 776 6. IANA Considerations 778 None. 780 7. Security Considerations 782 7.1. Security as hash function and KDF 784 The collision and preimage resistance levels of Argon2 are equivalent 785 to those of the underlying BLAKE2b hash function. To produce a 786 collision, 2^(256) inputs are needed. To find a preimage, 2^(512) 787 inputs must be tried. 789 The KDF security is determined by the key length and the size of the 790 internal state of hash function H'. To distinguish the output of 791 keyed Argon2 from random, minimum of (2^(128),2^length(K)) calls to 792 BLAKE2b are needed. 794 7.2. Security against time-space tradeoff attacks 796 Time-space tradeoffs allow computing a memory-hard function storing 797 fewer memory blocks at the cost of more calls to the internal 798 comression function. The advantage of tradeoff attacks is measured 799 in the reduction factor to the time-area product, where memory and 800 extra compression function cores contribute to the area, and time is 801 increased to accomodate the recomputation of missed blocks. A high 802 reduction factor may potentially speed up preimage search. 804 The best known attacks on the 1-pass and 2-pass Argon2i is the low- 805 storage attack described in [CBS16], which reduces the time-area 806 product (using the peak memory value) by the factor of 5. The best 807 attack on 3-pass and more Argon2i is [AB16] with reduction factor 808 being a function of memory size and the number of passes. For 1 809 gibibyte of memory: 3 for 3 passes, 2.5 for 4 passes, 2 for 6 passes. 810 The reduction factor grows by about 0.5 with every doubling the 811 memory size. To completely prevent time-space tradeoffs from [AB16], 812 the number of passes MUST exceed binary logarithm of memory minus 26. 813 Asymptotically, the best attack on 1-pass Argon2i is given in [BZ17] 814 with maximal advantage of the adversary upper bounded by O(m^(0.233)) 815 where m is the number of blocks. This attack is also asymptotically 816 optimal as [BZ17] also prove the upper bound on any attack of 817 O(m^(0.25)). 819 The best tradeoff attack on t-pass Argon2d is the ranking tradeoff 820 attack, which reduces the time-area product by the factor of 1.33. 822 The best attack on Argon2id can be obtained by complementing the best 823 attack on the 1-pass Argon2i with the best attack on a multi-pass 824 Argon2d. Thus the best tradeoff attack on 1-pass Argon2id is the 825 combined low-storage attack (for the first half of the memory) and 826 the ranking attack (for the second half), which bring together the 827 factor of about 2.1. The best tradeoff attack on t-pass Argon2id is 828 the ranking tradeoff attack, which reduces the time-area product by 829 the factor of 1.33. 831 7.3. Security for time-bounded defenders 833 A bottleneck in a system employing the password-hashing function is 834 often the function latency rather than memory costs. A rational 835 defender would then maximize the bruteforce costs for the attacker 836 equipped with a list of hashes, salts, and timing information, for 837 fixed computing time on the defender's machine. The attack cost 838 estimates from [AB16] imply that for Argon2i, 3 passes is almost 839 optimal for the most of reasonable memory sizes, and that for Argon2d 840 and Argon2id, 1 pass maximizes the attack costs for the constant 841 defender time. 843 7.4. Recommendations 845 The Argon2id variant with t=1 and maximum available memory is 846 RECOMMENDED as a default setting for all environments. This setting 847 is secure against side-channel attacks and maximizes adversarial 848 costs on dedicated bruteforce hardware. 850 8. Acknowledgements 852 We thank greatly the following authors who helped a lot in preparing 853 and reviewing this document: Jean-Philippe Aumasson, Samuel Neves, 854 Joel Alwen, Jeremiah Blocki, Bill Cox, Arnold Reinhold, Solar 855 Designer, Russ Housley, Stanislav Smyshlyaev, Kenny Paterson, Alexey 856 Melnikov, Gwynne Raskind. 858 9. References 860 9.1. Normative References 862 [BLAKE2] Saarinen, M-J., Ed. and J-P. Aumasson, "The BLAKE2 863 Cryptographic Hash and Message Authentication Code (MAC)", 864 RFC 7693, November 2015, 865 . 867 [RFC2119] Bradner, S., "Key words for use in RFCs to Indicate 868 Requirement Levels", RFC 2119, March 1997, 869 . 871 9.2. Informative References 873 [AB15] Biryukov, A. and D. Khovratovich, "Tradeoff Cryptanalysis 874 of Memory-Hard Functions", Asiacrypt 2015, December 2015, 875 . 877 [AB16] Alwen, J. and J. Blocki, "Efficiently Computing Data- 878 Independent Memory-Hard Functions", Crypto 2016, December 879 2015, . 881 [ARGON2] Biryukov, A., Dinu, D., and D. Khovratovich, "Argon2: the 882 memory-hard function for password hashing and other 883 applications", WWW www.cryptolux.org, October 2015, 884 . 886 [ARGON2ESP] 887 Biryukov, A., Dinu, D., and D. Khovratovich, "Argon2: New 888 Generation of Memory-Hard Functions for Password Hashing 889 and Other Applications", Euro SnP 2016, March 2016, 890 . 892 [BZ17] Blocki, J. and S. Zhou, "On the Depth-Robustness and 893 Cumulative Pebbling Cost of Argon2i", TCC 2017, May 2017, 894 . 896 [CBS16] Corrigan-Gibbs, H., Boneh, D., and S. Schechter, "Balloon 897 Hashing: Provably Space-Hard Hash Functions with Data- 898 Independent Access Patterns", Asiacrypt 2016, January 899 2016, . 901 [HARD] Alwen, J. and V. Serbinenko, "High Parallel Complexity 902 Graphs and Memory-Hard Functions", STOC 2015, 2014, 903 . 905 Authors' Addresses 907 Alex Biryukov 908 University of Luxembourg 910 Email: alex.biryukov@uni.lu 912 Daniel Dinu 913 University of Luxembourg 915 Email: dumitru-daniel.dinu@uni.lu 917 Dmitry Khovratovich 918 ABDK Consulting 920 Email: khovratovich@gmail.com 921 Simon Josefsson 922 SJD AB 924 Email: simon@josefsson.org 925 URI: http://josefsson.org/