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Tesla: Tightly-secure efficient signatures from standard lattices
, 2015
"... Generally, lattice-based cryptographic primitives offer good performance and allow for strong security reductions. However, the most efficient current lattice-based sig-nature schemes sacrifice (part of its) security to achieve good performance: first, security is based on ideal lattice problems, ..."
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Generally, lattice-based cryptographic primitives offer good performance and allow for strong security reductions. However, the most efficient current lattice-based sig-nature schemes sacrifice (part of its) security to achieve good performance: first, security is based on ideal lattice problems, that might not be as hard as standard lattice problems. Secondly, the security reductions of the most efficient schemes are non-tight; hence, their choices of parameters offer security merely heuristically. Moreover, lattice-based signatures are instantiated for classical adversaries, although they are based on presumably quantum hard problems. Yet, it is not known how such schemes perform in a post-quantum world. We bridge this gap by proving the lattice-based signature scheme TESLA to be tightly se-cure based on the learning with errors problem over standard lattices in the random oracle model. As such, we improve the security of the original proposal by Bai and Galbraith (CT-RSA’14) twofold; we tighten the security reduction and we minimize the underlying security assumptions. Remarkably, by enhancing the security we can improve TESLA’s performance by a factor of two. Furthermore, we are first to propose parameters providing a security of 128 bits against both classical and quantum adversaries for a lattice-based signature scheme. Our implementation of TESLA competes well with state-of-the-art lattice-based signatures and SPHINCS (EUROCRYPT’15), the only signature scheme instantiated with quantum-hard parameters thus far.
Post-Quantum Zero-Knowledge and Signatures from Symmetric-Key Primitives *
"... Abstract We propose a new class of post-quantum digital signature schemes that: (a) derive their security entirely from the security of symmetric-key primitives, believed to be quantum-secure, and (b) have extremely small keypairs, and, (c) are highly parameterizable. In our signature constructions ..."
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Abstract We propose a new class of post-quantum digital signature schemes that: (a) derive their security entirely from the security of symmetric-key primitives, believed to be quantum-secure, and (b) have extremely small keypairs, and, (c) are highly parameterizable. In our signature constructions, the public key is an image y = f (x) of a one-way function f and secret key x. A signature is a non-interactive zero-knowledge proof of x, that incorporates a message to be signed. For this proof, we leverage recent progress of Giacomelli et al. (USENIX'16) in constructing an efficient Σ-protocol for statements over general circuits. We improve this Σ-protocol to reduce proof sizes by a factor of two, at no additional computational cost. While this is of independent interest as it yields more compact proofs for any circuit, it also decreases our signature sizes. We consider two possibilities for making the proof non-interactive, the Fiat-Shamir transform, and Unruh's transform (EUROCRYPT'12, We implement and benchmark both approaches and explore the possible choice of f , taking advantage of the recent trend to strive for practical symmetric ciphers with a particularly low number of multiplications and end up using LowMC. * This paper is a merge of
