Year: 2025
Type: article
Abstract: Bidoux and Gaborit introduced a new general technique to improve zero-knowledge ( ZK ) proof-of-knowledge ( PoK ) schemes for a large set of well-known post-quantum hard computational problems such as the syndrome decoding, the permuted kernel, the rank syndrome decoding, and the multivariate quadratic ( MQ ) problems. In particular, the authors’ idea in the study of Bidoux and Gaborit was to use the structure of these problems in the multi-instance setting to minimize the communication complexity of the resulting ZK PoK schemes. The security of the new schemes is then related to new hard problems. In this article, we focus on the new multivariate-based ZK PoK and the corresponding new underlying problem: the so-called DiffMQ H {{\mathtt{DiffMQ}}}_{{\rm{H}}} . We present a new efficient probabilistic algorithm for solving the DiffMQ H {{\mathtt{DiffMQ}}}_{{\rm{H}}} which is polynomial-time if m − n ∈ O ( 1 ) m-n\in O\left(1) . We also present experimental results showing that the algorithm is efficient in practice.
Language: English
Subfield: Artificial Intelligence
Field: Computer Science
Domain: Physical Sciences
Open Access status: gold
Estimated APC paid: $1,187
OpenAlex ID: W4409443854