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.
Cite
@article{arxiv.2510.11224,
title = {TCitH- and VOLEitH-based Signatures from Restricted Decoding},
author = {Sebastian Bitzer and Michele Battagliola and Antonia Wachter-Zeh and Violetta Weger},
journal= {arXiv preprint arXiv:2510.11224},
year = {2026}
}