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
收藏
页码：967 / 991
页数：25
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