MinRank is an NP-complete problem in linear algebra whose characteristics make it attractive to build post-quantum cryptographic primitives. Several MinRank-based digital signature schemes have been proposed. In particular, two of them, MIRA and MiRitH, have been submitted to the NIST Post-Quantum Cryptography Standardization Process. In this paper, we propose a key-generation algorithm for MinRank-based schemes that reduces the size of the public key to about 50% of the size of the public key generated by the previous best (in terms of public-key size) algorithm. Precisely, the size of the public key generated by our algorithm sits in the range of 328-676 bits for security levels of 128-256 bits. We also prove that our algorithm is as secure as the previous ones.

翻译：MinRank是线性代数中一个NP完全问题，其特性使其成为构建后量子密码学原语的有力候选。目前已有多种基于MinRank的数字签名方案被提出，其中MIRA和MiRitH两种方案已提交至NIST后量子密码学标准化流程。本文提出了一种针对MinRank方案的新型密钥生成算法，该算法可将公钥规模缩减至此前最优算法（以公钥尺寸为指标）生成公钥规模的约50%。具体而言，本算法生成的公钥在128-256比特安全等级下，其规模范围约为328-676比特。同时，我们证明了该算法与先前算法具有同等级别的安全性。