Double-Moduli Gaussian Encryption/Decryption with Primary Residues and Secret Controls

Abstract

In this paper an encryption-decryption algorithm based on two moduli is described: one in the real field of integers and another in the field of complex integers. Also the proper selection of cryptographic system parameters is described. Several numeric illustrations explain step-by-step how to precondition a plaintext, how to select secret control parameters, how to ensure feasibility of all private keys and how to avoid ambiguity in the process of information recovery. The proposed cryptographic system is faster than most of known public key cryptosystems, since it requires a small number of multiplications and additions, and does not require exponentiations for its implementation

Primality Testing Using Complex Integers and Pythagorean Triplets

“…Yet, every real prime n that satisfies is the complex composite, [9]. A public key cryptographic algorithm based on complex moduli is described in [10]. mod 4 1 …”

Cryptanalysis of the Double-Moduli Cryptosystem

“…The cryptosystem introduced by Verkhovsky in [1], for which we construct an attack, is described in this section. We assume an a priori agreed large integer .…”

“…x . Using the last equality and computing , we obtain that 1 If we analyze the complexity of Algorithm 4.1, we easily see that each step is completed in polynomial time. By running Algorithm 4.1, an adversary is able to decrypt any message with a high probability.…”

“…In this article we present a lattice attack done on a NTRU-like scheme introduced by Verkhovsky in [1].…”

Computation of Complex Primes Using Elliptic Curves: Application for Cryptosystem Design

“…Finally, we provided a deterministic algorithm with polynomial time complexity that computes a complex prime (C, F) for every real prime p. In [9] is demonstrated how to implement the complex primes in cryptographic systems based on double moduli reduction, where one modulus is a real prime and another modulus is a complex prime.…”