SPANSE: Combining sparsity with density for efficient one-time code-based digital signatures

Abstract

The use of codes defined by sparse characteristic matrices, like QC-LDPC and QC-MDPC codes, has become an established solution to design secure and efficient code-based public-key encryption schemes, as also witnessed by the ongoing NIST post-quantum cryptography standardization process. However, similar approaches have been less fortunate in the context of code-based digital signatures, since no secure and efficient signature scheme based on these codes is available to date. The main limitation of previous attempts in this line of research has been the use of sparse signatures, which produces some leakage of information about the private key. In this paper, we propose a new code-based digital signature scheme that overcomes such a problem by publishing signatures that are abnormally dense, rather than sparse. This eliminates the possibility of deducing information from the sparsity of signatures, and follows a recent trend in code-based cryptography exploiting the hardness of the decoding problem for large-weight vectors, instead of its classical version based on small-weight vectors. We focus on one-time use and provide a first parameterization of the new scheme, the main advantages of which are very fast signature generation and verification, and public keys that are not too large for a code-based signature scheme.