An Identification Scheme Based on Sparse Polynomials

This paper gives a new example of exploiting the idea of using polynomials with restricted coefficients over finite fields and rings to construct reliable cryptosystems and identification schemes. 1 Overview The recently discovered idea of using polynomials with restricted coefficients in cryptography has already found several cryptographic applications such as the NTRU cryptosystem [7], the ENROOT cryptosystem [4] and the PASS identification scheme [6]; see also [5]. In contrast to the constructions of NTRU and PASS, which consider classes of polynomials of low degree with many "small" non-zero coefficients, ENROOT introduced a public key cryptosystem where the polynomials are of high degree, but extremely sparse. In this paper, we give a new application of this idea to the design of a fast and reliable identification scheme. Let q be a prime power and let IFq be the finite field of q elements. Given a set S IFq, we say that a polynomial G(X) IFq[X] is an Spolynomial if ev...

• Type: Conference
• Year: 2000
• Where: PKC
• Authors: William D. Banks, Daniel Lieman, Igor Shparlinski
• Keywords: Cryptology, Cryptosystem, Identification Scheme, PKC 2000, Polynomial