扭曲戈普沙码的密码学应用
Cryptographic Applications of Twisted Goppa Codes
AI总结：
本文提出多扭曲戈普沙码及其在尼德里特公钥密码系统中的应用，展示了其在纠错和安全性方面的贡献。
摘要：
本文定义了多扭曲戈普沙（MTG）码作为多扭曲里德-所罗门（MTRS）码对偶的子域子码，并研究其性质。我们证明，如果MTG多项式定义的MTG码的次数为t，则在其特定条件下，其最小距离至少为t+1。在扩展先前仅限于最后一个位置单扭曲的方法基础上，我们利用扩展欧几里得算法高效解码具有任意位置单扭曲的MTG码，可纠正多达⌊t/2⌋个错误。这种解码方法突显了这些码在尼德里特公钥密码系统（PKC）中的实际潜力。此外，我们还证明基于MTG码的尼德里特PKC对部分密钥恢复攻击具有安全性。此外，我们还通过使用非平凡自同构群构造准循环MTG码，从而减少了公钥大小。
英文摘要：
This article defines multi-twisted Goppa (MTG) codes as subfield subcodes of duals of multi-twisted Reed-Solomon (MTRS) codes and examines their properties. We show that if $t$ is the degree of the MTG polynomial defining an MTG code, its minimum distance is at least $t + 1$ under certain conditions. Extending earlier methods limited to single twist at last position, we use the extended Euclidean algorithm to efficiently decode MTG codes with a single twist at any position, correcting up to $\left\lfloor \tfrac{t}{2} \right\rfloor$ errors. This decoding method highlights the practical potential of these codes within the Niederreiter public key cryptosystem (PKC). Furthermore, we establish that the Niederreiter PKC based on MTG codes is secure against partial key recovery attacks. Additionally, we also reduce the public key size by constructing quasi-cyclic MTG codes using a non-trivial automorphism group.
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