On the equivalence of two post-quantum cryptographic families

被引：1

作者：

Meneghetti, Alessio ^{[1
]}

Pellegrini, Alex ^{[2
]}

Sala, Massimiliano ^{[1
]}

机构：

[1] Univ Trento, Dept Math, Trento, Italy

[2] Eindhoven Univ Technol, Dept Math & Comp Sci, Eindhoven, Netherlands

来源：

ANNALI DI MATEMATICA PURA ED APPLICATA | 2023年 / 202卷 / 02期

关键词：

Maximum likelihood decoding; Quadratic multivariate systems; Polynomial-time reductions; Code-based cryptography; Multivariate-based cryptography; INTRACTABILITY; ISOMORPHISMS; POLYNOMIALS; HARDNESS; CODES; NP;

D O I：

10.1007/s10231-022-01267-x

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

The maximum likelihood decoding problem (MLD) is known to be NP-hard and its complexity is strictly related to the security of some post-quantum cryptosystems, that is, the so-called code-based primitives. Analogously, the multivariate quadratic system problem (MQ) is NP-hard and its complexity is necessary for the security of the so-called multivariate-based primitives. In this paper we present a closed formula for a polynomial-time reduction from any instance of MLD to an instance of MQ, and viceversa. We also show a polynomial-time isomorphism between MQ and MLD, thus demonstrating the direct link between the two post-quantum cryptographic families.

引用

页码：967 / 991

页数：25

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