CFRG
Internet Research Task Force (IRTF) A. Biryukov
Internet-Draft
Request for Comments: 9106 D. Dinu
Intended status:
Category: Informational University of Luxembourg
Expires: September 12, 2021
ISSN: 2070-1721 D. Khovratovich
ABDK Consulting
S. Josefsson
SJD AB
March 11,
August 2021
The memory-hard
Argon2 password hash Memory-Hard Function for Password Hashing and proof-of-work function
draft-irtf-cfrg-argon2-13 Proof-of-Work
Applications
Abstract
This document describes the Argon2 memory-hard function for password
hashing and proof-of-work applications. We provide an implementer-
oriented description with test vectors. The purpose is to simplify
adoption of Argon2 for Internet protocols. This document is a
product of the Crypto Forum Research Group (CFRG) in the IRTF.
Status of This Memo
This Internet-Draft document is submitted in full conformance with not an Internet Standards Track specification; it is
published for informational purposes.
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(IRTF). The IRTF publishes the
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Table of Contents
1. Introduction . . . . . . . . . . . . . . . . . . . . . . . . 2
1.1. Requirements Language
2. Notation and Conventions . . . . . . . . . . . . . . . . . . 3
3. Argon2 Algorithm . . . . . . . . . . . . . . . . . . . . . . 4
3.1. Argon2 Inputs and Outputs . . . . . . . . . . . . . . . . 4
3.2. Argon2 Operation . . . . . . . . . . . . . . . . . . . . 5
3.3. Variable-length hash function Variable-Length Hash Function H' . . . . . . . . . . . . 7
3.4. Indexing . . . . . . . . . . . . . . . . . . . . . . . . 7
3.4.1. Computing the 32-bit values 32-Bit Values J_1 and J_2 . . . . . . . 8
3.4.2. Mapping J_1 and J_2 to reference block index Reference Block Index [l][z] . 9
3.5. Compression function Function G . . . . . . . . . . . . . . . . . 10
3.6. Permutation P . . . . . . . . . . . . . . . . . . . . . . 11
4. Parameter Choice . . . . . . . . . . . . . . . . . . . . . . 12
5. Test Vectors . . . . . . . . . . . . . . . . . . . . . . . . 14
5.1. Argon2d Test Vectors . . . . . . . . . . . . . . . . . . 14
5.2. Argon2i Test Vectors . . . . . . . . . . . . . . . . . . 15
5.3. Argon2id Test Vectors . . . . . . . . . . . . . . . . . . 16
6. IANA Considerations . . . . . . . . . . . . . . . . . . . . . 18
7. Security Considerations . . . . . . . . . . . . . . . . . . . 18
7.1. Security as hash function a Hash Function and KDF . . . . . . . . . . . . 18
7.2. Security against time-space tradeoff attacks . . . . . . 18 Time-Space Trade-off Attacks
7.3. Security for time-bounded defenders . . . . . . . . . . . 19 Time-Bounded Defenders
7.4. Recommendations . . . . . . . . . . . . . . . . . . . . . 19
8. Acknowledgements . . . . . . . . . . . . . . . . . . . . . . 19
9. References . . . . . . . . . . . . . . . . . . . . . . . . . 19
9.1.
8.1. Normative References . . . . . . . . . . . . . . . . . . 19
9.2.
8.2. Informative References . . . . . . . . . . . . . . . . . 20
Acknowledgements
Authors' Addresses . . . . . . . . . . . . . . . . . . . . . . . 20
1. Introduction
This document describes the Argon2 [ARGON2ESP] memory-hard function
for password hashing and proof-of-work applications. We provide an
implementer oriented
implementer-oriented description with 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.
Argon2 is a traditional memory-hard function [HARD]. It is a streamlined design.
It aims at the highest memory filling memory-filling rate and effective use of
multiple computing units, while still providing defense against tradeoff
trade-off attacks. Argon2 is optimized for the x86 architecture and
exploits the cache and memory organization of the recent Intel and
AMD processors. Argon2 has one primary variant:
Argon2id variant, Argon2id, and two
supplementary variants: variants, Argon2d and Argon2i. Argon2d uses data-dependent data-
dependent 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 password-based key derivation.
Argon2id works as Argon2i for the first half of the first pass over
the memory, memory and as Argon2d for the rest, thus providing both side-channel side-
channel attack protection and brute-force cost savings due to time-memory tradeoffs. time-
memory trade-offs. Argon2i makes more passes over the memory to
protect from tradeoff trade-off attacks [AB15].
Argon2id MUST be supported by any implementation of this document,
whereas Argon2d and Argon2i MAY be supported.
Argon2 is also a mode of operation over a fixed-input-length
compression function G and a variable-input-length hash function H.
Even though Argon2 can be potentially used with an arbitrary function
H, as long as it provides outputs up to 64 bytes, the BLAKE2b
function [BLAKE2] is used in this document it
is BLAKE2b [BLAKE2]. document.
For further background and discussion, see the Argon2 paper [ARGON2].
This document represents the consensus of the Crypto Forum Research
Group (CFRG).
1.1. Requirements Language
The key words "MUST", "MUST NOT", "REQUIRED", "SHALL", "SHALL NOT",
"SHOULD", "SHOULD NOT", "RECOMMENDED", "NOT RECOMMENDED", "MAY", and
"OPTIONAL" in this document are to be interpreted as described in RFC 2119 [RFC2119].
This document represents the consensus of the Crypto Forum Research
Group (CFRG).
BCP 14 [RFC2119] [RFC8174] when, and only when, they appear in all
capitals, as shown here.
2. Notation and Conventions
x^y --- integer x multiplied by itself integer y times
a*b --- multiplication of integer a and integer b
c-d --- subtraction of integer d from integer c
E_f --- variable E with subscript index f
g / h --- integer g divided by integer h. The result is a
rational
number number.
I(j) --- function I evaluated at j
K || L --- string K concatenated with string L
a XOR b --- bitwise exclusive-or between bitstrings a and b
a mod b --- remainder of integer a modulo integer b, always in
range [0, b-1]
a >>> n --- rotation of 64-bit string a to the right by n bits
trunc(a) --- the 64-bit value, truncated to the 32 least
significant bits
floor(a) --- the largest integer not bigger than a
ceil(a) --- the smallest integer not smaller than a
extract(a, i) --- the i-th set of 32-bits 32 bits from bitstring a, starting
from 0-th
|A| --- the number of elements in set A
LE32(a) --- 32-bit integer a converted to a bytestring byte string in little
endian. Example:
endian (for example, 123456 (decimal) is 40 E2 01 00. 00)
LE64(a) --- 64-bit integer a converted to a bytestring byte string in little
endian. Example:
endian (for example, 123456 (decimal) is 40 E2 01 00
00 00 00 00. 00)
int32(s) --- 32-bit string s is converted to a non-negative integer
in little endian. endian
int64(s) --- 64-bit string s is converted to a non-negative integer
in little endian. endian
length(P) --- the bytelength byte length of string P expressed as 32-bit
integer
ZERO(P) --- the P-byte zero string
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. It MUST have a length not greater than 2^(32) - 1 2^(32)-1
bytes.
o
* Nonce S, which is a salt for password hashing applications. It
MUST have a length not greater than 2^(32)-1 bytes. 16 bytes is
RECOMMENDED for password hashing. Salt The salt SHOULD be unique for
each password.
o
* Degree of parallelism p determines how many independent (but
synchronizing) computational chains (lanes) can be run. It MUST
be an integer value from 1 to 2^(24)-1.
o
* Tag length T MUST be an integer number of bytes from 4 to 2^(32)-
1.
o
* Memory size m MUST be an 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 passes t (used to tune the running time independently of
the memory size) MUST be an integer number from 1 to 2^(32)-1.
o
* Version number v MUST be one byte 0x13.
o
* Secret value K is OPTIONAL. If used, it MUST have a length not
greater than 2^(32)-1 bytes.
o
* Associated data X is OPTIONAL. If used, it MUST have a length not
greater than 2^(32)-1 bytes.
o
* Type y of Argon2: MUST be 0 for Argon2d, 1 for Argon2i, or 2 for Argon2id.
The Argon2 output, or "tag" "tag", is a string T bytes long.
3.2. Argon2 Operation
Argon2 uses an internal compression function G with two 1024-byte
inputs and
inputs, a 1024-byte output, and an internal hash function H^x() H^x(), with
x being its output length in bytes. Here Here, H^x() applied to string A
is the BLAKE2b (Section ([BLAKE2], Section 3.3) [BLAKE2] function, which takes
(d,ll,kk=0,nn=x) as parameters parameters, where d is A padded to a multiple of
128 bytes and ll is the length of d in bytes. The compression
function G is based on its internal permutation. A variable-length
hash function H' built upon H is also used. G is described in
Section 3.5 3.5, and H' is described in Section 3.3.
The Argon2 operation is as follows.
1. Establish H_0 as the 64-byte value as shown below. If K, X, or S
has zero length length, it is just absent absent, but its length field remains.
H_0 = H^(64)(LE32(p) || LE32(T) || LE32(m) || LE32(t) ||
LE32(v) || LE32(y) || LE32(length(P)) || P ||
LE32(length(S)) || S || LE32(length(K)) || K ||
LE32(length(X)) || X)
Figure 1: H_0 generation Generation
2. Allocate the memory as m' 1024-byte blocks blocks, where m' is derived
as:
m' = 4 * p * floor (m / 4p)
Figure 2: Memory allocation Allocation
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'^(1024)(H_0 || LE32(0) || LE32(i))
Figure 3: Lane starting blocks Starting Blocks
4. Compute B[i][1] for all i ranging from (and including) 0 to (not
including) p.
B[i][1] = H'^(1024)(H_0 || LE32(1) || LE32(i))
Figure 4: Second lane blocks Lane Blocks
5. Compute B[i][j] for all i ranging from (and including) 0 to (not
including) p, p and for all j ranging from (and including) 2) 2 to (not
including) q. The computation MUST proceed slicewise
(Section 3.4): first first, blocks from slice 0 are computed for all
lanes (in an arbitrary order of lanes), then blocks from slice 1
are computed computed, etc. The block indices l and z are determined for
each i, j differently for Argon2d, Argon2i, and Argon2id.
B[i][j] = G(B[i][j-1], B[l][z])
Figure 5: Further block generation Block Generation
6. If the number of passes t is larger than 1, we repeat the steps.
However step 5. We
compute B[i][0] and B[i][j] for all i raging from (and including)
0 to (not including) p and for all j ranging from (and including)
1 to (not including) q. However, blocks are computed differently
as the old value is XORed with the new one:
B[i][0] = G(B[i][q-1], B[l][z]) XOR B[i][0];
B[i][j] = G(B[i][j-1], B[l][z]) XOR B[i][j].
Figure 6: Further passes Passes
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]
Figure 7: Final block Block
8. The output tag is computed as H'^T(C).
3.3. Variable-length hash function Variable-Length Hash Function H'
Let V_i be a 64-byte block, block and W_i be its first 32 bytes. Then we
define:
define function H' as follows:
if T <= 64
H'^T(A) = H^T(LE32(T)||A)
else
r = ceil(T/32)-2
V_1 = H^(64)(LE32(T)||A)
V_2 = H^(64)(V_1)
...
V_r = H^(64)(V_{r-1})
V_{r+1} = H^(T-32*r)(V_{r})
H'^T(X) = W_1 || W_2 || ... || W_r || V_{r+1}
Figure 8: Function H' for tag Tag and initial block computations Initial Block Computations
3.4. Indexing
To enable parallel block computation, we further partition the memory
matrix into SL = 4 vertical slices. The intersection of a slice and
a lane is called a segment, which has a length of q/SL. Segments of
the same slice can be computed in parallel and do 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
Figure 9: Single-Pass Argon2 with p lanes Lanes and 4 slices Slices
3.4.1. Computing the 32-bit values 32-Bit Values 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], while J_2 is
given by the next 32-bits 32 bits of block B[i][j-1]:
J_1 = int32(extract(B[i][j-1], 0))
J_2 = int32(extract(B[i][j-1], 1))
Figure 10: Deriving J1,J2 in Argon2d
3.4.1.2. Argon2i
For each segment segment, we do the following. First First, we compute the value Z
as
as:
Z= ( LE64(r) || LE64(l) || LE64(sl) || LE64(m') ||
LE64(t) || LE64(y) ), )
Figure 11: Input to Compute J1,J2 in Argon2i
where
r --
r: the pass number
l --
l: the lane number
sl --
sl: the slice number
m' --
m': the total number of memory blocks
t --
t: the total number of passes
y --
y: the Argon2 type (0 for Argon2d, 1 for Argon2i, 2 for Argon2id)
Input to compute J1,J2 in Argon2i
Then we compute compute:
q/(128*SL) 1024-byte values
G(ZERO(1024),G(ZERO(1024),
Z || LE64(1) || ZERO(968) )),
G(ZERO(1024),G(ZERO(1024),
Z || LE64(2) || ZERO(968) )),... ,
G(ZERO(1024),G(ZERO(1024),
Z || LE64(q/(128*SL)) || ZERO(968) )),
which are partitioned into q/(SL) 8-byte values X, which are viewed
as X1||X2 and converted to J_1=int32(X1) and J_2=int32(X2).
The values r, l, sl, m', t, y, and i are represented as 8 bytes in little-
little endian.
3.4.1.3. Argon2id
If the pass number is 0 and the slice number is 0 or 1, then compute
J_1 and J_2 as for Argon2i, else compute J_1 and J_2 as for Argon2d.
3.4.2. Mapping J_1 and J_2 to reference block index Reference Block Index [l][z]
The value of l = 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
(sl=0)
(sl=0), the block is taken from the current lane.
The set W contains the indices that are referenced according to the
following rules:
1. If l is the current lane, then W includes the indices of all
blocks in the last SL - 1 = 3 segments computed and finished, as
well as the blocks computed in the current segment in the current
pass excluding B[i][j-1].
2. If l is not the current lane, then W includes the indices of all
blocks in the last SL - 1 = 3 segments computed and finished in
lane l. If B[i][j] is the first block of a segment, then the
very last index from W is excluded.
Then take a block from W with a non-uniform nonuniform distribution over [0, |W|)
using the mapping following mapping:
J_1 -> |W|(1 - J_1^2 / 2^(64))
Figure 12: Computing J1
To avoid floating point computation, the following approximation is
used:
x = J_1^2 / 2^(32)
y = (|W| * x) / 2^(32)
zz = |W| - 1 - y
Figure 13: Computing J1, part Part 2
Then take the zz-th index from W, W; it will be the z value for the
reference block index [l][z].
3.5. Compression function Function G
The compression function G is built upon the BLAKE2b-based
transformation P. P operates on the 128-byte input, which can be
viewed as 8 eight 16-byte registers:
P(A_0, A_1, ... ,A_7) = (B_0, B_1, ... ,B_7)
Figure 14: Blake round function Round Function P
The 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 an 8x8
matrix of 16-byte registers R_0, R_1, ... , R_63. Then P is first
applied to each row, and then to each column 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)
Figure 15: Core of compression function Compression Function G
Finally, G outputs Z XOR R:
G: (X, Y) -> R -> Q -> Z -> Z XOR R
+---+ +---+
| X | | Y |
+---+ +---+
| |
---->XOR<----
--------|
| \ /
| +---+
| | R |
| +---+
| |
| \ /
| P rowwise
| |
| \ /
| +---+
| | Q |
| +---+
| |
| \ /
| P columnwise
| |
| \ /
| +---+
| | Z |
| +---+
| |
| \ /
------>XOR
|
\ /
Figure 16: Argon2 compression function G. Compression Function G
3.6. Permutation P
Permutation P is based on the round function of BLAKE2b. The 8 eight
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
Figure 17: Matrix element labeling Element Labeling
It works as follows:
GB(v_0, v_4, v_8, v_12)
GB(v_1, v_5, v_9, v_13)
GB(v_2, v_6, v_10, v_14)
GB(v_3, v_7, v_11, v_15)
GB(v_0, v_5, v_10, v_15)
GB(v_1, v_6, v_11, v_12)
GB(v_2, v_7, v_8, v_13)
GB(v_3, v_4, v_9, v_14)
Figure 18: Feeding matrix elements Matrix Elements to GB
GB(a, b, c, d) is defined as follows:
a = (a + b + 2 * trunc(a) * trunc(b)) mod 2^(64)
d = (d XOR a) >>> 32
c = (c + d + 2 * trunc(c) * trunc(d)) mod 2^(64)
b = (b XOR c) >>> 24
a = (a + b + 2 * trunc(a) * trunc(b)) mod 2^(64)
d = (d XOR a) >>> 16
c = (c + d + 2 * trunc(c) * trunc(d)) mod 2^(64)
b = (b XOR c) >>> 63
Figure 19: Details of GB
The modular additions in GB are combined with 64-bit multiplications.
Multiplications are the only difference to from 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 i.e., they cannot run side-
channel attacks based on the timing information, nor he can they recover
the password much faster using garbage collection. These settings
are more typical for backend servers and cryptocurrency minings. For
practice
practice, we suggest the following settings:
o
* Cryptocurrency mining, that which takes 0.1 seconds on a 2 Ghz GHz CPU
using 1 core -- Argon2d with 2 lanes and 250 MB of RAM.
Argon2id is optimized for more realistic settings, where the
adversary possibly can possibly access the same machine, use its CPU CPU, or mount
cold-boot attacks. We suggest the following settings:
o
* Backend server authentication, that which takes 0.5 seconds on a 2 GHz
CPU using 4 cores -- Argon2id with 8 lanes and 4 GiB of RAM.
o
* Key derivation for hard-drive encryption, that which takes 3 seconds on
a 2 GHz CPU using 2 cores - -- Argon2id with 4 lanes and 6 GiB of
RAM.
o
* Frontend server authentication, that which takes 0.5 seconds on a 2 GHz
CPU using 2 cores - -- Argon2id with 4 lanes and 1 GiB of RAM.
We recommend the following procedure to select the type and the
parameters for practical use of Argon2.
1. If you are OK with a uniformly safe option, but option that is not tailored to your
application or hardware, hardware is acceptable, select Argon2id with t=1
iteration, p=4 lanes and lanes, m=2^(21) (2 GiB of RAM), 128-bit salt, and
256-bit tag size. This is the FIRST RECOMMENDED option.
2. If much less memory is available, a uniformly safe option is
Argon2id with t=3 iterations, p=4 lanes and lanes, m=2^(16) (64 MiB of
RAM), 128-bit salt, and 256-bit tag size. This is the SECOND
RECOMMENDED option.
3. Otherwise, start with selecting the type y. If you do not know
the difference between them the types or you consider side-channel
attacks
as to be a viable threat, choose Argon2id.
4. Select p=4 lanes.
5. Figure out the maximum amount of memory that each call can
afford and translate it to the parameter m.
6. Figure out the maximum amount of time (in seconds) that each
call can afford.
7. Select the salt length. A length of 128 bits is sufficient for
all
applications, applications but can be reduced to 64 bits in the case of
space constraints.
8. Select the tag length. A length of 128 bits is sufficient for
most applications, including key derivation. If longer keys are
needed, select longer tags.
9. If side-channel attacks are a viable threat, threat or if you're
uncertain, enable the memory wiping memory-wiping option in the library call.
10. Run the scheme of type y, memory m m, and p lanes, lanes using a
different number of passes t. Figure out the maximum t such
that the running time does not exceed the affordable time. If
it exceeds even exceeds for t = 1, reduce m accordingly.
11. Use Argon2 with determined values m, p, and t.
5. Test Vectors
This section contains test vectors for Argon2.
5.1. Argon2d Test Vectors
We provide test vectors with complete outputs (tags). For the
convenience of developers, we also provide some interim variables, variables --
concretely, the first and last memory blocks of each pass.
=======================================
Argon2d version number 19
=======================================
Memory: 32 KiB
Passes: 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
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
5.2. Argon2i Test Vectors
=======================================
Argon2i version number 19
=======================================
Memory: 32 KiB
Passes: 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
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
5.3. Argon2id Test Vectors
=======================================
Argon2id version number 19
=======================================
Memory: 32 KiB, Passes: 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: 28 89 de 48 7e b4 2a e5 00 c0 00 7e d9 25 2f
10 69 ea de c4 0d 57 65 b4 85 de 6d c2 43 7a 67 b8 54 6a 2f 0a
cc 1a 08 82 db 8f cf 74 71 4b 47 2e 94 df 42 1a 5d a1 11 2f fa
11 43 43 70 a1 e9 97
After pass 0:
Block 0000 [ 0]: 6b2e09f10671bd43
Block 0000 [ 1]: f69f5c27918a21be
Block 0000 [ 2]: dea7810ea41290e1
Block 0000 [ 3]: 6787f7171870f893
...
Block 0031 [124]: 377fa81666dc7f2b
Block 0031 [125]: 50e586398a9c39c8
Block 0031 [126]: 6f732732a550924a
Block 0031 [127]: 81f88b28683ea8e5
After pass 1:
Block 0000 [ 0]: 3653ec9d01583df9
Block 0000 [ 1]: 69ef53a72d1e1fd3
Block 0000 [ 2]: 35635631744ab54f
Block 0000 [ 3]: 599512e96a37ab6e
...
Block 0031 [124]: 4d4b435cea35caa6
Block 0031 [125]: c582210d99ad1359
Block 0031 [126]: d087971b36fd6d77
Block 0031 [127]: a55222a93754c692
After pass 2:
Block 0000 [ 0]: 942363968ce597a4
Block 0000 [ 1]: a22448c0bdad5760
Block 0000 [ 2]: a5f80662b6fa8748
Block 0000 [ 3]: a0f9b9ce392f719f
...
Block 0031 [124]: d723359b485f509b
Block 0031 [125]: cb78824f42375111
Block 0031 [126]: 35bc8cc6e83b1875
Block 0031 [127]: 0b012846a40f346a
Tag: 0d 64 0d f5 8d 78 76 6c 08 c0 37 a3 4a 8b 53 c9 d0
1e f0 45 2d 75 b6 5e b5 25 20 e9 6b 01 e6 59
6. IANA Considerations
None.
This document has no IANA actions.
7. Security Considerations
7.1. Security as hash function a Hash Function and KDF
The collision and preimage resistance levels of Argon2 are equivalent
to those of the underlying BLAKE2b hash function. To produce a
collision, 2^(256) inputs are needed. To find a preimage, 2^(512)
inputs must be tried.
The KDF security is determined by the key length and the size of the
internal state of hash function H'. To distinguish the output of the
keyed Argon2 from random, a minimum of (2^(128),2^length(K)) calls to
BLAKE2b are needed.
7.2. Security against time-space tradeoff attacks Time-Space Trade-off Attacks
Time-space tradeoffs trade-offs allow computing a memory-hard function storing
fewer memory blocks at the cost of more calls to the internal
comression
compression function. The advantage of tradeoff trade-off attacks is measured
in the reduction factor to the time-area product, where memory and
extra compression function cores contribute to the area, area and time is
increased to accomodate accommodate the recomputation of missed blocks. A high
reduction factor may potentially speed up the preimage search.
The best known attacks best-known attack 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 3-pass and more Argon2i with 3 passes or more is [AB16] described in [AB16], with
the reduction factor being a function of memory size and the number
of passes. For passes (e.g., for 1 gibibyte of memory: memory, a reduction factor of 3
for 3 passes, 2.5 for 4 passes, 2 for 6 passes. passes). The reduction
factor grows by about 0.5 with every doubling of the memory size. To
completely prevent time-space tradeoffs trade-offs from [AB16], the number of
passes MUST exceed the binary logarithm of memory minus 26.
Asymptotically, the best attack on 1-pass Argon2i is given in [BZ17] [BZ17],
with maximal advantage of the adversary upper bounded by O(m^(0.233))
O(m^(0.233)), where m is the number of blocks. This attack is also
asymptotically optimal as [BZ17] also prove proves the upper bound on any
attack of is O(m^(0.25)).
The best tradeoff trade-off attack on t-pass Argon2d is the ranking tradeoff trade-off
attack, which reduces the time-area product by the factor of 1.33.
The best attack on Argon2id can be obtained by complementing the best
attack on the 1-pass Argon2i with the best attack on a multi-pass
Argon2d. Thus Thus, the best tradeoff trade-off attack on 1-pass Argon2id is the
combined low-storage attack (for the first half of the memory) and
the ranking attack (for the second half), which bring together generate the factor
of about 2.1. The best tradeoff trade-off attack on t-pass Argon2id is the
ranking tradeoff trade-off attack, which reduces the time-area product by the
factor of 1.33.
7.3. Security for time-bounded defenders Time-Bounded Defenders
A bottleneck in a system employing the password-hashing password hashing function is
often the function latency rather than memory costs. A rational
defender would then maximize the bruteforce brute-force costs for the attacker
equipped with a list of hashes, salts, and timing information, information for
fixed computing time on the defender's machine. The attack cost
estimates from [AB16] imply that for Argon2i, 3 passes is almost
optimal for the most of reasonable memory sizes, and that sizes; for Argon2d and Argon2id, 1
pass maximizes the attack costs for the constant defender time.
7.4. Recommendations
The Argon2id variant with t=1 and 2GiB 2 GiB memory is the FIRST
RECOMMENDED option and is suggested as a default setting for all
environments. This setting is secure against side-channel attacks
and maximizes adversarial costs on dedicated bruteforce brute-force hardware.
The Argon2id variant with t=3 and 64 MiB memory is the SECOND
RECOMMENDED option and is suggested as a default setting for memory-constrained memory-
constrained environments.
8. Acknowledgements
We thank greatly the following authors who helped a lot in preparing
and reviewing this document: Jean-Philippe Aumasson, Samuel Neves,
Joel Alwen, Jeremiah Blocki, Bill Cox, Arnold Reinhold, Solar
Designer, Russ Housley, Stanislav Smyshlyaev, Kenny Paterson, Alexey
Melnikov, Gwynne Raskind.
9. References
9.1.
8.1. Normative References
[BLAKE2] Saarinen, M-J., Ed. and J-P. Aumasson, "The BLAKE2
Cryptographic Hash and Message Authentication Code (MAC)",
RFC 7693, DOI 10.17487/RFC7693, November 2015,
<https://www.rfc-editor.org/info/rfc7693>.
[RFC2119] Bradner, S., "Key words for use in RFCs to Indicate
Requirement Levels", BCP 14, RFC 2119,
DOI 10.17487/RFC2119, March 1997,
<http://www.rfc-editor.org/info/rfc2119>.
9.2.
<https://www.rfc-editor.org/info/rfc2119>.
[RFC8174] Leiba, B., "Ambiguity of Uppercase vs Lowercase in RFC
2119 Key Words", BCP 14, RFC 8174, DOI 10.17487/RFC8174,
May 2017, <https://www.rfc-editor.org/info/rfc8174>.
8.2. Informative References
[AB15] Biryukov, A. and D. Khovratovich, "Tradeoff Cryptanalysis
of Memory-Hard Functions", Asiacrypt ASIACRYPT 2015,
DOI 10.1007/978-3-662-48800-3_26, December 2015,
<https://eprint.iacr.org/2015/227.pdf>.
[AB16] Alwen, J. and J. Blocki, "Efficiently Computing Data-
Independent Memory-Hard Functions", Crypto CRYPTO 2016,
DOI 10.1007/978-3-662-53008-5_9, March 2016, December
2015,
<https://eprint.iacr.org/2016/115.pdf>.
[ARGON2] Biryukov, A., Dinu, D., and D. Khovratovich, "Argon2: the
memory-hard function for password hashing and other
applications", WWW www.cryptolux.org, October 2015, March 2017,
<https://www.cryptolux.org/images/0/0d/Argon2.pdf>.
[ARGON2ESP]
Biryukov, A., Dinu, D., and D. Khovratovich, "Argon2: New
Generation of Memory-Hard Functions for Password Hashing
and Other Applications", Euro SnP 2016,
DOI 10.1109/EuroSP.2016.31, March 2016,
<https://www.cryptolux.org/images/d/d0/Argon2ESP.pdf>.
[BZ17] Blocki, J. and S. Zhou, "On the Depth-Robustness and
Cumulative Pebbling Cost of Argon2i", TCC 2017,
DOI 10.1007/978-3-319-70500-2_15, May 2017,
<https://eprint.iacr.org/2017/442.pdf>.
[CBS16] Corrigan-Gibbs, H., Boneh, D., Corrigan-Gibbs, H., and S. Schechter, "Balloon
Hashing: Provably Space-Hard Hash Functions with Data-
Independent Access Patterns", Asiacrypt 2016, January A Memory-Hard Function Providing Provable
Protection Against Sequential Attacks", ASIACRYPT 2016,
DOI 10.1007/978-3-662-53887-6_8, May 2017,
<https://eprint.iacr.org/2016/027.pdf>.
[HARD] Alwen, J. and V. Serbinenko, "High Parallel Complexity
Graphs and Memory-Hard Functions", STOC '15,
DOI 10.1145/2746539.2746622, June 2015, 2014,
<https://eprint.iacr.org/2014/238.pdf>.
Acknowledgements
We greatly thank the following individuals who helped in preparing
and reviewing this document: Jean-Philippe Aumasson, Samuel Neves,
Joel Alwen, Jeremiah Blocki, Bill Cox, Arnold Reinhold, Solar
Designer, Russ Housley, Stanislav Smyshlyaev, Kenny Paterson, Alexey
Melnikov, and Gwynne Raskind.
The work described in this document was done before Daniel Dinu
joined Intel, while he was at the University of Luxembourg.
Authors' Addresses
Alex Biryukov
University of Luxembourg
Email: alex.biryukov@uni.lu
Daniel Dinu
University of Luxembourg
Email: daniel.dinu@intel.com
Dmitry Khovratovich
ABDK Consulting
Email: khovratovich@gmail.com
Simon Josefsson
SJD AB
Email: simon@josefsson.org
URI: http://josefsson.org/