Threshold-Computation-in-the-Head (TCitH) and VOLE-in-the-Head (VOLEitH), two recent developments of the MPC-in-the-Head (MPCitH) paradigm, have significantly improved the performance of digital signature schemes. This work embeds the restricted decoding problem within these frameworks: we propose a structurally simple modeling that achieves competitive signature sizes. Specifically, by instantiating the restricted decoding problem with the same hardness assumption underlying CROSS, we reduce sizes by more than a factor of two compared to the NIST submission. Moreover, we observe that ternary full-weight decoding, closely related to the hardness assumption underlying WAVE, is a restricted decoding problem. Using ternary full-weight decoding, we obtain signature sizes comparable to the smallest MPCitH-based candidates in the NIST competition.

翻译：阈值计算在首（TCitH）与向量不经意线性评估在首（VOLEitH）作为MPC在首（MPCitH）范式的两项最新进展，显著提升了数字签名方案的性能。本研究将受限解码问题嵌入上述框架：我们提出了一种结构简洁的建模方法，实现了具有竞争力的签名尺寸。具体而言，通过采用与CROSS方案相同的底层硬度假设来实例化受限解码问题，相比NIST提交方案，我们将签名尺寸缩减了超过两倍。此外，我们观察到与WAVE方案硬度假设密切相关的三元全重解码问题同样属于受限解码范畴。基于三元全重解码构造的方案，我们获得了与NIST竞赛中基于MPCitH的最小尺寸候选方案相当的签名大小。