Code-based digital signatures suffer from two main drawbacks: large public key size and slow signature generation. Large public key size is inherent in almost all the code-based cryptosystems and other post-quantum alternatives; however, slow signature generation is due to their specific structure. Most of the current code-based signature schemes are constructed based on Courtois, Finiasz, and Sendrier (CFS) signature. CFS uses a counter to produce decodable syndromes or the complete decoding technique that imposes some extra computational cost to the signing algorithm for many choices of codes. In this study, the authors propose an efficient digital signature, PolarSig, which can reduce both public key size and signing time simultaneously. PolarSig uses some specific instances of polar codes that enable us to decode every random syndrome. Moreover, they apply puncturing and randomised omitting of frozen bits to protect the authors’ scheme from commonplace attacks targeting former cryptosystems based on polar codes. Besides, they prove that their signature is existentially unforgeable under a chosen message attack secure in the random oracle model.

中文翻译：

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PolarSig：基于极性代码的高效数字签名

基于代码的数字签名具有两个主要缺点：较大的公共密钥大小和较慢的签名生成。几乎所有基于代码的密码系统和其他后量子替代方案都具有较大的公共密钥大小。但是，签名生成速度慢是由于其特定的结构。当前大多数基于代码的签名方案都是基于Courtois，Finiasz和Sendrier（CFS）签名构建的。CFS使用计数器来产生可解码的校正子或完整的解码技术，从而对多种代码选择给签名算法造成了额外的计算成本。在这项研究中，作者提出了一种有效的数字签名PolarSig，它可以同时减少公共密钥的大小和签名时间。PolarSig使用极性代码的某些特定实例，这些实例使我们能够解码每个随机校验子。此外，他们采用打孔和对冻结位进行随机删除，以保护作者的方案免受基于极性代码的针对以前密码系统的普通攻击。此外，他们证明了在随机预言机模型中安全选择的消息攻击下，其签名在本质上是不可伪造的。