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Progress in Multivariate Cryptography: Systematic Review, Challenges, and Research Directions
ACM Computing Surveys ( IF 16.6 ) Pub Date : 2023-03-03 , DOI: 10.1145/3571071
Jayashree Dey, Ratna Dutta

Multivariate Public Key Cryptosystem (MPKC) seem to be promising toward future digital security even in the presence of quantum adversaries. MPKCs derive their security from the difficulty of solving a random system of multivariate polynomial equations over a finite field, which is known to be an NP-hard problem. This article aims at presenting a comprehensive survey that covers multivariate public key encryption and signature schemes specifically targeting toward security, efficiency, and parameter choice. The survey starts by giving an overview of the existing security challenges which include structural attacks such as MinRank attack, differential attack, and finding Gröbner basis for direct attack, and so on. Additionally, it discusses the necessary algorithms for the implementation of the multivariate schemes. This study also compares the promising multivariate encryption and signature schemes. The critical open challenges that are reviewed in this survey will serve as a single comprehensive source of information on multivariate encryption and signature schemes and a ready reference for researchers working in this rising area of public key cryptography.



中文翻译:

多元密码学进展:系统综述、挑战和研究方向

即使在存在量子对手的情况下,多元公钥密码系统(MPKC) 似乎也有望实现未来的数字安全。MPKC 的安全性源于在有限域上求解随机多元多项式方程组的困难,这被称为 NP 难问题。本文旨在提出一个全面的调查,涵盖专门针对安全性、效率和参数选择的多变量公钥加密和签名方案。该调查首先概述了现有的安全挑战,其中包括结构性攻击,例如最小等级攻击、差分攻击、寻找直接攻击的 Gröbner 基础等。此外,它还讨论了实现多变量方案的必要算法。本研究还比较了有前途的多元加密和签名方案。本次调查中审查的关键开放挑战将作为多元加密和签名方案的单一综合信息来源,并为在公钥密码学这一新兴领域工作的研究人员提供现成的参考。

更新日期:2023-03-04
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