Paper 2023/377

FuLeeca: A Lee-based Signature Scheme

Abstract

In this work we introduce a new code-based signature scheme, called \textsf{FuLeeca}, based on the NP-hard problem of finding codewords of given Lee-weight. The scheme follows the Hash-and-Sign approach applied to quasi-cyclic codes. Similar approaches in the Hamming metric have suffered statistical attacks, which revealed the small support of the secret basis. Using the Lee metric, we are able to thwart such attacks. We use existing hardness results on the underlying problem and study adapted statistical attacks. We propose parameters for \textsf{FuLeeca}~and compare them to an extensive list of proposed post-quantum secure signature schemes including the ones already standardized by NIST. This comparison reveals that \textsf{FuLeeca}~is competitive. For example, for NIST category I, i.e., 160 bit of classical security, we obtain an average signature size of 1100 bytes and public key sizes of 1318 bytes. Comparing the total communication cost, i.e., the sum of the signature and public key size, we see that \textsf{FuLeeca} is only outperformed by Falcon while the other standardized schemes Dilithium and SPHINCS+ show larger communication costs than \textsf{FuLeeca}.

Note: Compared to the previous version of this eprint-paper the parameters of the scheme have changed. This is because we take the conservative approach of considering lattice based attacks in comparison to the previous version. For more information see also Section 4.3.