The regular multivariate quadratic problem

📝 Original Info

• Title: The regular multivariate quadratic problem
• ArXiv ID: 2503.07342
• Date: 2025-03-10
• Authors: ** 정보가 제공되지 않았습니다. (논문에 저자 명단이 명시되지 않았습니다.) **

📝 Abstract

In this work, we introduce a novel variant of the multivariate quadratic problem, which is at the core of one of the most promising post-quantum alternatives: multivariate cryptography. In this variant, the solution of a given multivariate quadratic system must also be regular, i.e. if it is split into multiple blocks of consecutive entries with the same fixed length, then each block has only one nonzero entry. We prove the NP-completeness of this variant and show similarities and differences with other computational problems used in cryptography. Then we analyze its hardness by reviewing the most common solvers for polynomial systems over finite fields, derive asymptotic formulas for the corresponding complexities and compare the different approaches.

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