FuLeeca: A Lee-Based Signature Scheme.

In this work, we introduce a new code-based signature scheme, called 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 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 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 FuLeeca is only outperformed by Falcon while the other standardized schemes Dilithium and SPHINCS+ show higher communication costs than FuLeeca.