Achievable Upper Bound for the Sup-Norm of the Product of Elements of the Ring of Truncated Polynomials and its Application to the Analysis of NTRU-Like Cryptosystems

Abstract

An answer is obtained to a question posed in 2008 by V. Lyubashevsky about an efficient algorithm for calculating the parameter θ(f) that characterizes the value of the sup-norm of the product of elements of the ring of truncated polynomials modulo a given unitary polynomial f (x) with real coefficients. The results are used to estimate the decryption failure probability in NTRU-like cryptosystems.