Cryptographic Applications of Sparse Polynomials over Finite Rings

Abstract. This paper gives new examples that exploit the idea of using sparse polynomials with restricted coefficients over a finite ring for designing fast, reliable cryptosystems and identification schemes. 1 Overview The idea of using polynomials with restricted coefficients in cryptography, though fairly new, has already found several cryptographic applications such as the NTRU cryptosystem [10], the ENROOT cryptosystem [6], the PASS identification scheme [9, 11], and the SPIFI identification scheme [2]; see also [8]. In contrast to the constructions of NTRU and PASS, which consider classes of low-degree polynomials with many "small" nonzero coefficients, ENROOT and SPIFI are based on the use of polynomials of high degree that are extremely sparse. Although these latter constructions were originally considered only over finite fields, in this paper we improve and extend the ideas of [2, 6] and show that both ENROOT and SPIFI can be generalized to the setting of an arbitra...

• Type: Conference
• Year: 2000
• Where: ICISC
• Authors: William D. Banks, Daniel Lieman, Igor Shparlinski, Van Thuong To
• Keywords: ICISC 2000, ICISC 2007, Identification Scheme, Polynomial, Restricted Coefficients