The Athena Consortium

Tue, 30 Jun 2026 00:00:00 +0000

What is this Project About?

Arithmetization-oriented (AO) hash functions have proliferated rapidly over the past few years, driven by the demands of proof systems such as SNARKs and STARKs. Designing a hash function that is simultaneously efficient over a prime field and resistant to algebraic attacks is hard. Unfortunately, assessing whether a proposed design has actually achieved this isn’t any easier: our understanding of this topic remains limited.

The Athena consortium is a group of cryptographers coming together to rigorously examine the state of the art in the cryptanalysis of AO hash functions, with a particular focus on a regime of parameters that has received considerably less attention in the literature: small characteristic primes, meaning fields of size much smaller than the security parameter, such as KoalaBear ( $p = 2^{31} - 2^{24} + 1$ ) and Goldilocks ( $p = 2^{64} - 2^{32} + 1$ ).