CryptoDB
A reduction from Hawk to the principal ideal problem in a quaternion algebra
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| Conference: | EUROCRYPT 2025 |
| Abstract: | In this article we present a non-uniform reduction from rank-2 module-LIP over Complex Multiplication fields, to a variant of the Principal Ideal Problem, in some fitting quaternion algebra. This reduction is classical deterministic polynomial-time in the size of the inputs. The quaternion algebra in which we need to solve the variant of the principal ideal problem depends on the parameters of the module-LIP problem, but not on the problem's instance. Our reduction requires the knowledge of some special elements of this quaternion algebras, which is why it is non-uniform. In some particular cases, these elements can be computed in polynomial time, making the reduction uniform. This is the case for the Hawk signature scheme: we show that breaking Hawk is no harder than solving a variant of the principal ideal problem in a fixed quaternion algebra (and this reduction is uniform). |
BibTeX
@inproceedings{eurocrypt-2025-34984,
title={A reduction from Hawk to the principal ideal problem in a quaternion algebra},
publisher={Springer-Verlag},
author={Clémence Chevignard and Guilhem Mureau and Thomas Espitau and Alice Pellet-Mary and Heorhii Pliatsok and Alexandre Wallet},
year=2025
}