MPCitH-based Signatures from Restricted Decoding Problems

2025-10-13

AI Summary

This work addresses the large signature size and low efficiency of MPC-in-the-Head (MPCitH)-based digital signatures. We systematically integrate the Restricted Decoding Problem (RDP) into the TCitH and VOLEitH frameworks for the first time. A unified modeling approach is proposed, enabling the first reduction of the computational assumptions underlying CROSS and WAVE to RDP—thereby establishing theoretical consistency across these schemes. Leveraging binary and ternary fully-weighted RDP instances, we construct lightweight signature schemes. Compared to NIST Post-Quantum Cryptography standardization candidates, our signatures are over twice as compact: the ternary variant achieves the smallest signature size to date under the MPCitH paradigm (<10 KB), while preserving quantum resistance and efficient verification.

Technology Category

• Machine Learning: Quantum Machine Learning
• Constraint Satisfaction and Optimization: Satisfiability Modulo Theories
• Knowledge Representation and Reasoning: Computational Complexity of Reasoning

Application Category

• Security and Privacy: Applications of cryptography
• Responsible Web: Data and user privacy-enhancing technologies for the Web
• Economics, Online Markets and Human Computation: Economic aspects of blockchain and cryptocurrencies

Abstract

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 in this framework. In this note, we embed 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.

Problem

• Embedding restricted decoding problems into MPCitH frameworks
• Reducing signature sizes by over 50% compared to NIST submission
• Achieving compact signatures using ternary full-weight decoding

Innovation

• Embedded restricted decoding in MPCitH frameworks
• Used ternary full-weight decoding assumption
• Achieved competitive signature sizes efficiently