Correctness of Li Generalization of RSA Cryptosystem.
Roman Popovych · IACR Cryptology ePrint Archive · 2009
For given N=pq with p and q different odd primes and natural m Banghe Li introduced the public key cryptosystem [1]. In the case m=1 the system is just the famous RSA public key cryptosystem [2]. The cryptosystem is more secure in general [2] than RSA system. But one has to solve a few problems connected with the introduced cryptosystem. The cryptosystem works with elements of the quotient ring ZN[x]/(h(x)). To construct the system it is necessary to calculate a number φ(N,h) of units of the ring. If polynomial h(x) is special to N, then formula for φ(N,h) is given in [1], but it is not simple to verify if h(x) is special. In general formulas for φ(N,h) are not known. For degree m=2 of the polynomial h(x) formulas for the number φ(N,h) are given in [1]. A question of correctness of the cryptosystem emerges even in the simplest case m=2. We answer positively the Li’s question about correctness of the system in this case.