BI-NTRU Encryption Schemes: Two New Secure Variants of NTRU

Abstract

NTRU is one of the first public key cryptosystems not based on factorization or discrete logarithmic problems and is also considered secure even against quantum computer attacks. In 2011, Stehle and Steinfeld proposed a variant of the classical NTRU that is IND-CPA secure but for the key generation algorithm, they use Gaussian distribution with a large standard deviation to prove the uniformity of the public key by assuming the hardness of Ring Learning With Error (Ring-LWE) problem. In this paper, we present two variants of NTRUEncrypt called BI-NTRU-Product and BI-NTRU-LPR which are IND-CPA secure assuming the hardness of Ring-LWE problem. We also show how one can design an IND-CCA2 secure key encapsulation mechanism from our encryption schemes by using a variant of the Fujisaki-Okamoto Transformation (CRYPTO 1999 and Journal of Cryptology 2013).