Wave: A New Family of Trapdoor One-Way Preimage Sampleable Functions Based on Codes

TL;DR

This paper introduces Wave-PSF, a new code-based trapdoor one-way function family with provable security assumptions, enabling a hash-and-sign signature scheme with practical parameters and security guarantees.

Contribution

The paper proposes Wave-PSF, a novel code-based trapdoor function family with a formal security proof and a practical signature scheme based on it.

Findings

Security relies on decoding hardness and code indistinguishability.

Signature size is approximately 15,000 bits for 128-bit security.

Public key size is around 4 megabytes, with low rejection rates.

Abstract

We present here a new family of trapdoor one-way Preimage Sampleable Functions (PSF) based on codes, the Wave-PSF family. The trapdoor function is one-way under two computational assumptions: the hardness of generic decoding for high weights and the indistinguishability of generalized $(U,U+V)$-codes. Our proof follows the GPV strategy [GPV08]. By including rejection sampling, we ensure the proper distribution for the trapdoor inverse output. The domain sampling property of our family is ensured by using and proving a variant of the left-over hash lemma. We instantiate the new Wave-PSF family with ternary generalized $(U,U+V)$-codes to design a "hash-and-sign" signature scheme which achieves existential unforgeability under adaptive chosen message attacks (EUF-CMA) in the random oracle model. For 128 bits of classical security, signature sizes are in the order of 15 thousand bits, the public key size in the order of 4 megabytes, and the rejection rate is limited to one rejection every 10 to 12 signatures.