Year: 2026
Type: article
Abstract: The Restricted Syndrome Decoding Problem (RSDP) is a variant of the well-known syndrome decoding problem. It has recently been turned into a post-quantum signature scheme named CROSS by Baldi et al.. It is a scheme highlighted for being computationally friendly and providing a compact signature and public key size. This paper investigates an Oracle-based definition of the RSDP that has already proved useful in constructing other cryptographic primitives. We propose a new solving algorithm for this novel and interesting problem. Our approach is to first introduce a new weight definition for vectors over $$\mathbb {F}_{p}$$ F p and then develop a solving algorithm similar to the BKW algorithm that includes finding many such low-weight vectors in a dual space. We make use of several advanced techniques, such as Covering codes and Subspace Hypothesis Testing . We show that when there are many samples, our algorithm can be more advantageous than prior work based on information-set decoding adaptations for RSDP or algebraic approaches.
Source: Cryptography and Communications
Authors: Thomas Johansson, Qian Guo, Vu Nguyen
Institution: Lund University
Language: English
Subfield: Artificial Intelligence
Field: Computer Science
Domain: Physical Sciences
Open Access status: hybrid
Estimated APC paid: $3,190
OpenAlex ID: W4413440370