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Argon2

2015 password-based key derivation function

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The Argon2 function uses a large, fixed-size memory region (often called the 'memory array' in documentation) to make brute-force attacks computationally expensive. The three variants differ in how they access this memory:

  • 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 attacks.
  • 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. RFC 9106 recommends using Argon2id if one does not know the difference between the types or if side-channel attacks are considered 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 N/e (≈ N/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(n7/4 log(n)) for all choices of parameters σ (space cost), τ (time cost), and thread-count such that n=σ∗τ. 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.

To address these concerns, RFC9106 recommends using Argon2id to largely mitigate such attacks.

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