Welcome to the resource topic for 2025/287
Title:
A reduction from Hawk to the principal ideal problem in a quaternion algebra
Authors: Clémence Chevignard, Guilhem Mureau, Thomas Espitau, Alice Pellet-Mary, Heorhii Pliatsok, Alexandre Wallet
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).
ePrint: https://eprint.iacr.org/2025/287
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