IACR News item: 19 July 2024
Clémence Chevignard, Pierre-Alain Fouque, Guilhem Mureau, Alice Pellet-Mary, Alexandre Wallet
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 in particular 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).
In some particular cases, these elements can be computed in polynomial time, making the reduction uniform. This is in particular 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).
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