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.
Highlights
Introduction and Primary ResiduesThis paper describes and briefly analyzes a public key cryptographic (PKC) based on primary residues and Gaussian modulus
The proposed public key 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
Proposition 4.1: If W is a primary residue and private keys P, R and secret control S are selected in such a way that holds
Summary
This paper describes and briefly analyzes a public key cryptographic (PKC) based on primary residues and Gaussian modulus. The framework of the proposed PKC partially resembles NTRU PKC [1,2] {more details are provided in www.ntru.com} that was introduced in 1996 and later patented by three mathematicians from Brown University. Their PKC was analyzed in several papers [3,4,5]: in [3] it was pointed out that the decryption did not always recover the initial plaintext. In the proposed cryptosystem there is no necessity to consider polynomials with binary coefficients as it is done in papers [1] and [2]
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