Argon2 is a
key derivation function that was selected as the winner of the 2015
Password Hashing Competition
The Password Hashing Competition was an open competition announced in 2013 to select one or more password hash functions that can be recognized as a recommended standard. It was modeled after the successful Advanced Encryption Standard process and ...
. It was designed by
Alex Biryukov, Daniel Dinu, and
Dmitry Khovratovich
Dmitry Khovratovich is a cryptographer, currently a Lead Cryptographer for the Dusk Network, researcher for the Ethereum Foundation, and member of the International Association for Cryptologic Research. He developed, together with Alex Biryu ...
from the
University of Luxembourg
The University of Luxembourg ( French: ''Université du Luxembourg''; German: ''Universität Luxemburg''; Luxembourgish: ''Universitéit Lëtzebuerg'') is a public research university in Luxembourg.
History
The University of Luxembourg was foun ...
. The reference implementation of Argon2 is released under a Creative Commons
CC0
A Creative Commons (CC) license is one of several public copyright licenses that enable the free distribution of an otherwise copyrighted "work".A "work" is any creative material made by a person. A painting, a graphic, a book, a song/lyric ...
license (i.e.
public domain
The public domain (PD) consists of all the creative work
A creative work is a manifestation of creative effort including fine artwork (sculpture, paintings, drawing, sketching, performance art), dance, writing (literature), filmmaking, ...
) or the
Apache License 2.0, and provides three related versions:
*Argon2d maximizes resistance to GPU cracking attacks. It accesses the memory array in a password dependent order, which reduces the possibility of
time–memory trade-off (TMTO) attacks, but introduces possible
side-channel attack
In computer security, a side-channel attack is any attack based on extra information that can be gathered because of the fundamental way a computer protocol or algorithm is implemented, rather than flaws in the design of the protocol or algori ...
s.
*Argon2i is optimized to resist side-channel attacks. It accesses the memory array in a password independent order.
*Argon2id is a hybrid version. It follows the Argon2i approach for the first half pass over memory and the Argon2d approach for subsequent passes. The RFC recommends using Argon2id if you do not know the difference between the types or you consider side-channel attacks to be a viable threat.
All three modes allow specification by three parameters that control:
*execution time
*memory required
*degree of parallelism
Cryptanalysis
While there is no public cryptanalysis applicable to Argon2d, there are two published attacks on the Argon2i function. The first attack is applicable only to the old version of Argon2i, while the second has been extended to the latest version (1.3).
The first attack shows that it is possible to compute a single-pass Argon2i function using between a quarter and a fifth of the desired space with no time penalty, and compute a multiple-pass Argon2i using only / (≈ /2.72) space with no time penalty. According to the Argon2 authors, this attack vector was fixed in version 1.3.
The second attack shows that Argon2i can be computed by an algorithm which has complexity O(
7/4 log()) for all choices of parameters (space cost), (time cost), and thread-count such that =∗.
The Argon2 authors claim that this attack is not efficient if Argon2i is used with three or more passes.
However, Joël Alwen and Jeremiah Blocki improved the attack and showed that in order for the attack to fail, Argon2i v1.3 needs more than 10 passes over memory.
Algorithm
Function Argon2
Inputs:
password (P): Bytes (0..2
32-1)
Password (or message) to be hashed
salt (S): Bytes (8..2
32-1)
Salt (16 bytes recommended for password hashing)
parallelism (p): Number (1..2
24-1)
Degree of parallelism (i.e. number of threads)
tagLength (T): Number (4..2
32-1)
Desired number of returned bytes
memorySizeKB (m): Number (8p..2
32-1)
Amount of memory (in kibibytes
The byte is a unit of digital information that most commonly consists of eight bits. Historically, the byte was the number of bits used to encode a single character of text in a computer and for this reason it is the smallest addressable uni ...
) to use
iterations (t): Number (1..2
32-1)
Number of iterations to perform
version (v): Number (0x13)
The current version is 0x13 (19 decimal)
key (K): Bytes (0..2
32-1)
Optional key (Errata: PDF says 0..32 bytes, RFC says 0..232 bytes)
associatedData (X): Bytes (0..2
32-1)
Optional arbitrary extra data
hashType (y): Number (0=Argon2d, 1=Argon2i, 2=Argon2id)
Output:
tag: Bytes (tagLength)
The resulting generated bytes, tagLength bytes long
''Generate initial 64-byte block H0.''
All the input parameters are concatenated and input as a source of additional entropy.
Errata: RFC says H0 is 64-bits; PDF says H0 is 64-bytes.
Errata: RFC says the Hash is H^, the PDF says it's ℋ (but doesn't document what ℋ is). It's actually Blake2b.
Variable length items are prepended with their length as 32-bit little-endian integers.
buffer ← parallelism ∥ tagLength ∥ memorySizeKB ∥ iterations ∥ version ∥ hashType
∥ Length(password) ∥ Password
∥ Length(salt) ∥ salt
∥ Length(key) ∥ key
∥ Length(associatedData) ∥ associatedData
H
0 ← Blake2b(buffer, 64)
''//default hash size of Blake2b is 64-bytes''
Calculate number of 1 KB blocks by rounding down memorySizeKB to the nearest multiple of 4*parallelism kibibytes
The byte is a unit of digital information that most commonly consists of eight bits. Historically, the byte was the number of bits used to encode a single character of text in a computer and for this reason it is the smallest addressable uni ...
blockCount ← Floor(memorySizeKB, 4*parallelism)
Allocate two-dimensional array of 1 KiB blocks (parallelism rows x columnCount columns)
columnCount ← blockCount / parallelism;
//In the RFC, columnCount is referred to as q
Compute the first and second block (i.e. column zero and one ) of each lane (i.e. row)
for i ← 0 to parallelism-1 do
for each row
B
i ← Hash(H
0 ∥ 0 ∥ i, 1024)
''//Generate a 1024-byte digest''
B
i ← Hash(H
0 ∥ 1 ∥ i, 1024)
''//Generate a 1024-byte digest''
Compute remaining columns of each lane
for i ← 0 to parallelism-1 do
//for each row
for j ← 2 to columnCount-1 do
//for each subsequent column
//i' and j' indexes depend if it's Argon2i, Argon2d, or Argon2id (See section 3.4)
i′, j′ ← GetBlockIndexes(i, j)
//the GetBlockIndexes function is not defined
B
i = G(B
i -1 B
i′ ′ //the G hash function is not defined
Further passes when iterations > 1
for nIteration ← 2 to iterations do
for i ← 0 to parallelism-1 do
for each row
for j ← 0 to columnCount-1 do
//for each subsequent column
//i' and j' indexes depend if it's Argon2i, Argon2d, or Argon2id (See section 3.4)
i′, j′ ← GetBlockIndexes(i, j)
if j 0 then
B
i = B
i xor G(B
i olumnCount-1 B
i′ ′
else
B
i = B
i xor G(B
i -1 B
i′ ′
Compute final block C as the XOR of the last column of each row
C ← B
0 olumnCount-1 for i ← 1 to parallelism-1 do
C ← C xor B
i olumnCount-1
Compute output tag
return Hash(C, tagLength)
Variable-length hash function
Argon2 makes use of a hash function capable of producing digests up to 2
32 bytes long. This hash function is internally built upon
Blake2
BLAKE is a cryptographic hash function based on Daniel J. Bernstein's ChaCha stream cipher, but a permuted copy of the input block, XORed with round constants, is added before each ChaCha round. Like SHA-2, there are two variants differing in t ...
.
Function Hash(message, digestSize)
Inputs:
message: Bytes (0..2
32-1)
Message to be hashed
digestSize: Integer (1..2
32)
Desired number of bytes to be returned
Output:
digest: Bytes (digestSize)
The resulting generated bytes, digestSize bytes long
Hash is a variable-length hash function, built using Blake2b, capable of generating
digests up to 232 bytes.
If the requested digestSize is 64-bytes or lower, then we use Blake2b directly
if (digestSize <= 64) then
return Blake2b(digestSize ∥ message, digestSize)
//concatenate 32-bit little endian digestSize with the message bytes
For desired hashes over 64-bytes (e.g. 1024 bytes for Argon2 blocks),
we use Blake2b to generate twice the number of needed 64-byte blocks,
and then only use 32-bytes from each block
Calculate the number of whole blocks (knowing we're only going to use 32-bytes from each)
r ← Ceil(digestSize/32)-1;
Generate r whole blocks.
Initial block is generated from message
V
1 ← Blake2b(digestSize ∥ message, 64);
Subsequent blocks are generated from previous blocks
for i ← 2 to r do
V
i ← Blake2b(V
i-1, 64)
Generate the final (possibly partial) block
partialBytesNeeded ← digestSize – 32*r;
V
r+1 ← Blake2b(V
r, partialBytesNeeded)
Concatenate the first 32-bytes of each block Vi
(except the possibly partial last block, which we take the whole thing)
Let Ai represent the lower 32-bytes of block Vi
return A
1 ∥ A
2 ∥ ... ∥ A
r ∥ V
r+1
References
External links
Argon2 source code repository on GithubArgon2 specificationPassword Hashing CompetitionUni.Lu Argon2 PageBalloon Hashing: A Memory-Hard Function Providing Provable Protection Against Sequential Attacks* Argon2 Memory-Hard Function for Password Hashing and Proof-of-Work Applications
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Key derivation functions
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