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Lecture notes in computer science

An Efficient Lattice-Based Signature Scheme with Provably Secure Instantiation

Sedat Akleylek, Nina Bindel, Johannes A Buchmann, Juliane Krämer, Giorgia Azzurra Marson

Published Jan 1, 2016• 71 citations
Publisher
DOI
10.1007/978-3-319-31517-1_3

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Recently, lattice signatures based on the Fiat‐Shamir framework have seen a lot of improvements which are efficient in practice. The security of these signature schemes depends mainly on the hardness of solving short integer solutions (SIS) and/or learning with errors problem in the random oracle model. The authors propose an alternative lattice‐based signature scheme on the Fiat‐Shamir framework over the ring . The key generation in the signature scheme is based on the combination of NTRU and Ring SIS like key generation. Both the signature and the verification are done efficiently by doing polynomial convolutions in the ring . The proposed signature scheme is provably secure based on the hardness of the Ring SIS problem in the random oracle model. The scheme is also efficient up to constant factors as the highly practical schemes which have provable secure instantiation.
Abstract. We provide an alternative method for constructing lattice-based digital signatures which does not use the “hash-and-sign ” methodology of Gentry, Peikert, and Vaikuntanathan (STOC 2008). Our resulting signature scheme is secure, in the random oracle model, based on the worst-case hardness of the Õ(n1.5)-SIVP problem in general lattices. The secret key, public key, and the signature size of our scheme are smaller than in all previous instantiations of the hash-and-sign signature, and our signing algorithm is also quite simple, requiring just a few matrix-vector multiplications and rejection samplings. We then also show that by slightly changing the parameters, one can get even more efficient signatures that are based on the hardness of the Learning With Errors problem. Our construction naturally transfers to the ring setting, where the size of the public and secret keys can be significantly shrunk, which results in the most practical to-date provably secure signature scheme based on lattices. 1
Blind signatures are fundamental cryptographic primitives enabling privacy-preserving authentication and have seen renewed interest in the post-quantum literature. Existing efficient constructions predominantly rely on Fischlin’s generic paradigm instantiated over lattice assumptions, while blinding techniques for Σ-protocol-based blind signatures remain sparse beyond lattices. Moreover, achieving provable concurrent security under polynomially many sessions has been a longstanding open challenge for this approach in the post-quantum literature as evidenced by the recent attacks in EC’24 and PKC’24. This work broadens the landscape of post-quantum blind signatures by introducing novel techniques and proposing four frameworks based on general cryptographic group actions, without requiring commutativity. Our constructions admit instantiations under diverse post-quantum assumptions, including CSIDH (isogeny-based), LESS (code-based, NIST round-two), and more. These frameworks offer flexible trade-offs in assumptions (from interactive one-more to the standard inversion problem) and key/signature sizes, and culminate in a construction that achieves security under polynomially many concurrent sessions. This enables the first efficient blind signatures from isogenies and codes with provable concurrent security with 4.5 and 64.7 KB respectively. We also outline several directions for optimization and further instantiations for future work.