Zero Knowledge Protocols and Signatures from the Restricted Syndrome Decoding Problem

Marco Baldi; Sebastian Bitzer; Alessio Pavoni; Paolo Santini; Antonia Wachter-Zeh; Violetta Weger

Paper 2023/385

Zero Knowledge Protocols and Signatures from the Restricted Syndrome Decoding Problem

Marco Baldi

, Marche Polytechnic University

Sebastian Bitzer, Technical University of Munich

Alessio Pavoni, Marche Polytechnic University

Paolo Santini

, Marche Polytechnic University

Antonia Wachter-Zeh

, Technical University of Munich

Violetta Weger

, Technical University of Munich

Abstract

The Restricted Syndrome Decoding Problem (R-SDP) cor- responds to the Syndrome Decoding Problem (SDP) with the additional constraint that entries of the solution vector must live in a desired sub- set of a finite field. In this paper we study how this problem can be applied to the construction of signatures derived from Zero-Knowledge (ZK) proofs. First, we show that R-SDP appears to be well suited for this type of applications: almost all ZK protocols relying on SDP can be modified to use R-SDP, with important reductions in the communication cost. Then, we describe how R-SDP can be further specialized, so that solutions can be represented with a number of bits that is slightly larger than the security parameter (which clearly provides an ultimate lower bound), thus enabling the design of ZK protocols with tighter and rather competitive parameters. Finally, we show that existing ZK protocols can greatly benefit from the use of R-SDP, achieving signature sizes in the order of 7 kB, which are smaller than those of several other schemes ob- tained from ZK protocols. For instance, this beats all schemes based on the Permuted Kernel Problem (PKP), almost all schemes based on SDP and several schemes based on rank metric problems.

Metadata

Available format(s): PDF
Category: Public-key cryptography
Publication info: Preprint.
Keywords: Code-based Cryptography Signature Scheme
Contact author(s): m baldi @ staff univpm it
sebastian bitzer @ tum de
s1101018 @ studenti univpm it
p santini @ staff univpm it
antonia wachter-zeh @ tum de
violetta weger @ tum de
History: 2023-03-24: approved; 2023-03-17: received; See all versions
Short URL: https://ia.cr/2023/385
License: CC BY

BibTeX

@misc{cryptoeprint:2023/385,
      author = {Marco Baldi and Sebastian Bitzer and Alessio Pavoni and Paolo Santini and Antonia Wachter-Zeh and Violetta Weger},
      title = {Zero Knowledge Protocols and Signatures from the Restricted Syndrome Decoding Problem},
      howpublished = {Cryptology ePrint Archive, Paper 2023/385},
      year = {2023},
      note = {\url{https://eprint.iacr.org/2023/385}},
      url = {https://eprint.iacr.org/2023/385}
}