Restricted Syndrome Decoding (ResSD) is a variant of linear code decoding problem where each of the error's entries must belong to a fixed small set of values. This problem underlies the security of CROSS, a post-quantum signature scheme that is one of the Round 2 candidates of NIST's ongoing additional signatures call. We show that solutions to this problem can be deduced from vectors of a particular structure and a small norm in newly constructed codes, in both Hamming and Euclidean metrics. This allows us to reduce Restricted Syndrome Decoding to both code-based (Regular Syndrome Decoding) and lattice-based problems (Closest Vector Problem, List of Short/Close Vectors), increasing the attack surface and providing new insights into the security of ResSD. We evaluate our attacks on CROSS instances both theoretically and experimentally on reduced parameters.

翻译：受限综合征译码（ResSD）是线性码译码问题的一个变体，其中每个错误项的取值必须属于一个固定的小值集合。该问题是CROSS方案安全性的理论基础——CROSS是一种后量子签名方案，目前正参与美国国家标准与技术研究院（NIST）第二轮附加签名征集。我们证明，此问题解可以从新构造码中具有特定结构的向量及其在汉明度量与欧几里得度量下的小范数推导得出。这使我们能够将受限综合征译码同时归约到基于编码的问题（正则综合征译码）和基于格的问题（最近向量问题、短/近向量列表问题），从而扩大攻击面并为ResSD的安全性提供新见解。我们针对缩减参数下的CROSS实例进行了理论与实验两方面的攻击评估。