Lyubashevsky's Signature Has Multi-User Security under Adaptive Corruptions and Key Leakages

Abstract

We consider the multi-user security under the adaptive corruptions and key leakages (MU^c&l security) for lattice-based signatures. There already exists an MU^c&l secure signature based on a number-theoretic assumption, or a leakage-resilient lattice-based signature in the single-user setting. However, MU^c&l secure lattice-based signature is not known.

We examine the existing lattice-based signature schemes from the viewpoint of MU^c&l security. We find that the security of the Lyubashevsky's signature, which is proven to have the ordinary single-user security only, can be extended to the multiuser security even if we take into account the adaptive corruptions and the key leakages.

Our security proof in the multi-user setting makes use of the feature of the SIS problem so that a SIS instance is set to the public parameter and a reduction algorithm can set a public key with a secret key in order to answer a corruption query. We also show that the entropy of the secret key is kept under the bounded leakage with a high probability and then the leakage resilience of signature holds.