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.
CITATION STYLE
Roşca, M., Sakzad, A., Stehlé, D., & Steinfeld, R. (2017). Middle-product learning with errors. In Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) (Vol. 10403 LNCS, pp. 283–297). Springer Verlag. https://doi.org/10.1007/978-3-319-63697-9_10
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