A new cyclic cryptographic algorithm

Abstract

A new cryptographic algorithm based on a circle of arbitrary integer radius is presented in this research paper. This cryptographic algorithm performs phase modulation and integer modulation, using prime numbers. The algorithm shares some similar properties with the elliptic curves algorithm, but unlike the elliptic curves that have several points at infinity this algorithm has only one zero point. Encryption-decryption using this algorithm is straight forward. This algorithm is based on operations defined on the circumference of a circle of arbitrary radius and arbitrary center, modulo an arbitrary prime number large enough so that the cryptanalyst cannot break the code within a reasonable time. The operations around the circle provide the phase angle modulation while the modulo arithmetic with respect to the chosen prime number provide the integer modulation. This algorithm has no similarities with the phasemodulation transmission system for quantum cryptography, published in Physics journals. Based on its structure the algorithm should have the same complexity as the elliptic curve algorithm. Also based on an FPGA prototype using 8-bit prime numbers for modulation, FPGA implementation should be relatively easy.