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.
Next sessions
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Polytopes in the Fiat-Shamir with Aborts Paradigm
Speaker : Hugo Beguinet - ENS Paris / Thales
The Fiat-Shamir with Aborts paradigm (FSwA) uses rejection sampling to remove a secret’s dependency on a given source distribution. Recent results revealed that unlike the uniform distribution in the hypercube, both the continuous Gaussian and the uniform distribution within the hypersphere minimise the rejection rate and the size of the proof of knowledge. However, in practice both these[…]-
Cryptography
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Asymmetric primitive
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Mode and protocol
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Post-quantum Group-based Cryptography
Speaker : Delaram Kahrobaei - The City University of New York