argon2

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 {{mvar|N}}/{{mvar|e}} (≈ {{mvar|N}}/2.72) space with no time penalty.{{cite report |author1=Henry |author2=Corrigan-Gibbs |author3=Dan Boneh |author4=Stuart Schechter |date=2016-01-14 |title=Balloon Hashing: Provably Space-Hard Hash Functions with Data-Independent Access Patterns |url=https://eprint.iacr.org/2016/027.pdf }} According to the Argon2 authors, this attack vector was fixed in version 1.3.{{Cite web|url=https://www.ietf.org/mail-archive/web/cfrg/current/msg07948.html|title=[Cfrg] Argon2 v.1.3|website=www.ietf.org|access-date=2016-10-30}}

The second attack shows that Argon2i can be computed by an algorithm which has complexity O({{mvar|n}}^7/4 log({{mvar|n}})) for all choices of parameters {{mvar|σ}} (space cost), {{mvar|τ}} (time cost), and thread-count such that {{mvar|n}}={{mvar|σ}}∗{{mvar|τ}}.{{cite report |author1=Joël Alwen |author2=Jeremiah Blocki |date=2016-02-19 |title=Efficiently Computing Data-Independent Memory-Hard Functions |url=https://eprint.iacr.org/2016/115.pdf }} 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.{{cite report |author1=Joël Alwen |author2=Jeremiah Blocki |date=2016-08-05 |title=Towards Practical Attacks on Argon2i and Balloon Hashing |url=https://eprint.iacr.org/2016/759.pdf }}

To address these concerns, RFC9106 recommends using Argon2id to largely mitigate such attacks. {{Cite IETF |title=Argon2 Memory-Hard Function for Password Hashing and Proof-of-Work Applications |rfc=9106 |sectionname=Recommendations |section=7.4 |date=September 2021 |publisher=IETF |access-date=12 July 2023}}

Source:

Function Argon2

Inputs:

password (P): Bytes (0..2³²-1) Password (or message) to be hashed

salt (S): Bytes (8..2³²-1) Salt (16 bytes recommended for password hashing)

parallelism (p): Number (1..2²⁴-1) Degree of parallelism (i.e. number of threads)

tagLength (T): Number (4..2³²-1) Desired number of returned bytes

memorySizeKB (m): Number (8p..2³²-1) Amount of memory (in kibibytes) to use

iterations (t): Number (1..2³²-1) Number of iterations to perform

version (v): Number (0x13) The current version is 0x13 (19 decimal)

key (K): Bytes (0..2³²-1) Optional key (Errata: PDF says 0..32 bytes, RFC says 0..2³² bytes)

associatedData (X): Bytes (0..2³²-1) 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

H₀ ← 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

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[0] ← Hash(H₀ ∥ 0 ∥ i, 1024) //Generate a 1024-byte digest

B_i[1] ← Hash(H₀ ∥ 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[j] = G(B_i[j-1], B_i′[j′]) //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[0] = B_i[0] xor G(B_i[columnCount-1], B_i′[j′])

else

B_i[j] = B_i[j] xor G(B_i[j-1], B_i′[j′])

Compute final block C as the XOR of the last column of each row

C ← B₀[columnCount-1]

for i ← 1 to parallelism-1 do

C ← C xor B_i[columnCount-1]

Compute output tag

return Hash(C, tagLength)

Argon2 makes use of a hash function capable of producing digests up to 2³² bytes long. This hash function is internally built upon Blake2.

{{pre|style=font-size:95%|1=

Function Hash(message, digestSize)

Inputs:

message: Bytes (0..2³²-1) Message to be hashed

digestSize: Integer (1..2³²) 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)-2;

Generate r whole blocks.

Initial block is generated from message

V₁ ← 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 V_i

(except the possibly partial last block, which we take the whole thing)

Let A_i represent the lower 32-bytes of block V_i

return A₁ ∥ A₂ ∥ ... ∥ A_r ∥ V_r+1

}}

As of May 2023, OWASP's Password Storage Cheat Sheet recommends that people "use Argon2id with a minimum configuration of 19 MiB of memory, an iteration count of 2, and 1 degree of parallelism."{{cite web|url=https://cheatsheetseries.owasp.org/cheatsheets/Password_Storage_Cheat_Sheet.html | title=Password Storage Cheat Sheet | work=OWASP Cheat Sheet Series |publisher=OWASP |accessdate=2023-05-17}}

OWASP recommends that Argon2id should be preferred over Argon2d and Argon2i because it provides a balanced resistance to both GPU-based attacks and side-channel attacks.

OWASP further notes that the following Argon2id options provide equivalent cryptographic strength and simply trade off memory usage for compute workload:

• Memory: 46 MiB, Iterations: 1, Parallelism: 1
• Memory: 19 MiB, Iterations: 2, Parallelism: 1
• Memory: 12 MiB, Iterations: 3, Parallelism: 1
• Memory: 9 MiB, Iterations: 4, Parallelism: 1
• Memory: 7 MiB, Iterations: 5, Parallelism: 1

{{reflist}}

• [https://github.com/p-h-c/phc-winner-argon2 Argon2 source code repository on Github]
• [https://www.cryptolux.org/images/0/0d/Argon2.pdf Argon2 specification]
• [https://password-hashing.net/ Password Hashing Competition]
• [https://www.cryptolux.org/index.php/Argon2 Uni.Lu Argon2 Page]
• [https://eprint.iacr.org/2016/027.pdf Balloon Hashing: A Memory-Hard Function Providing Provable Protection Against Sequential Attacks]
• {{IETF RFC|9106|link=no}} Argon2 Memory-Hard Function for Password Hashing and Proof-of-Work Applications

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