Algebraic Cryptanalysis on Ntru-HPS and Ntru-HRSS

Abstract

NTRU is a lattice-based public-key cryptosystem designed by Hoffstein, Pipher, and Silverman in 1996. NTRU published on Algorithmic Number Theory Symposium (ANTS) in 1998. The ANTS’98 NTRU became the IEEE standard for public key cryptographic techniques based on hard problems over lattices in 2008. NTRU was later redeveloped by NTRU Inc. in 2018 and became one of the finalists in round 3 of the PQC (Post-Quantum Cryptography) standardization process organized by NIST in 2020. There are two types of NTRU algorithms proposed by NTRU Inc., which are classified based on parameter determination, NTRU-HPS (Hoffstein, Pipher, Silverman) and NTRU-HRSS (Hulsing, Rijnveld, Schanck, Schwabe). Algebraic cryptanalysis on ANTS’98 NTRU had previously been carried out in 2009 and 2012. In this paper, algebraic cryptanalysis is performed on NTRU-HPS with q=2048, n=509 (ntruhps2048509) and NTRU-HRSS with n=701 (ntruhrss701). This research aims to evaluate the resistance of NTRU-HPS and NTRU-HRSS algorithms against algebraic cryptanalysis by reconstructing the private key value. As a result, NTRU-HPS and NTRU-HRSS resistance to algebraic cryptanalysis.