In this paper we present a variant of the McEliece cryptosystem that possesses several interesting properties, including a reduction of the public key for a given security level. In contrast to the classical McEliece cryptosystems, where block codes are used, we propose the use of a convolutional encoder to be part of the public key. The permutation matrix is substituted by a polynomial matrix whose coefficient matrices have columns with weight zero or at least weight two. This allows the use of Generalized Reed-Solomon (GRS) codes which translates into shorter keys for a given security level. Hence, the private key is constituted by a generator matrix of a GRS code and two polynomial matrices containing large parts generated completely at random. In this setting the message is a sequence of messages instead of a single block message and the errors are added throughout the sequence. We discuss possible structural and ISD attacks to this scheme. We conclude presenting the key sizes obtained for different parameters and estimating the computational cost of encryption and decryption process.

翻译：本文提出一种具有多种优良性质的McEliece密码体制变体，包括在给定安全等级下实现公钥尺寸缩减。不同于采用分组码的经典McEliece密码体制，我们建议将卷积编码器作为公钥组成部分。置换矩阵被替换为系数矩阵的列权重为零或至少为二的系数矩阵多项式矩阵。这使得通用里德-所罗门(GRS)码得以应用，从而在给定安全等级下转化为更短的密钥。由此，私钥由GRS码的生成矩阵和两个包含完全随机生成的大规模分量的多项式矩阵构成。在该设定中，消息为消息序列而非单个分组消息，错误则贯穿整个序列添加。我们讨论针对该方案的结构性攻击与信息集解码(ISD)攻击，最终给出不同参数下的密钥尺寸，并估算加密解密过程的计算开销。