Construction of an elliptic curve over finite fields to combine with convolutional code for cryptography

Abstract

The construction of an efficient cryptographic system, based on the combination of the ElGamal elliptic curve algorithm and convolutional codes using the Viterbi decoding algorithm over the Gaussian channel, is proposed. The originality is based on the construction of the mapping of encryption and coding at the channel level and the constraints imposed on the construction of the elliptic curve. When using elliptic curves and codes for cryptography it is necessary to construct elliptic curves with a given or known number of points over a given finite field with a range of constraint lengths, in order to represent the input alphabet and produce channel gain, respectively. The results show that the benefit of coding with encryption increases the security and coding gain and reduces the expansion factor, but at the expense of higher complexity.