Description
We introduce a new variant MP-LWE of the Learning With Errors problem (LWE) making use of the Middle Product between polynomials modulo an integer q. We exhibit a reduction from the Polynomial-LWE problem (PLWE) parametrized by a polynomial f, to MP-LWE which is defined independently of any such f. The reduction only requires f to be monic with constant coefficient coprime with q. It incurs a noise growth proportional to the so-called expansion factor of f. We also describe a public-key encryption scheme with quasi-optimal asymptotic efficiency (the bit-sizes of the keys and the run-times of all involved algorithms are quasi-linear in the security parameter), which is secure against chosen plaintext attacks under the MP-LWE hardness assumption. The scheme is hence secure under the assumption that PLWE is hard for at least one polynomial f of degree n among a family of f’s which is exponential in n.
Prochains exposés
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Oblivious Transfer from Zero-Knowledge Proofs (or how to achieve round-optimal quantum Oblivious Transfer without structure)
Orateur : Léo Colisson - Université Grenoble Alpes
We provide a generic construction to turn any classical Zero-Knowledge (ZK) protocol into a composable oblivious transfer (OT) protocol (the protocol itself involving quantum interactions), mostly lifting the round-complexity properties and security guarantees (plain-model/statistical security/unstructured functions…) of the ZK protocol to the resulting OT protocol. Such a construction is unlikely[…]-
Cryptography
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