A Novel Method for Mapping Plaintext Characters to Elliptic Curve Affine points over Prime Field and Pseudorandom Number Generation

Abstract

Large number of active devices over the internet needs to manage huge amount of data. Demand for security of data stored in networked devices with limited computational power and battery life is challenging. Elliptic curve cryptography with smaller key size and less computational overheads protects data at lower cost. Elliptic curve cryptography requires the input to be encoded to the elliptic curve prior to encryption. This paper proposes a novel method for mapping plaintext characters as coordinates of elliptic curve in prime field. It is done by generating elliptic curve coordinates over the arithmetic operations performed on matrices built from ascii codes and its security is highly strengthened by scalar multiplication over base point G of the chosen elliptic curve. Choice of random number and private key for Elliptic curve cryptography can be further strengthened by the proposed novel cryptographically strong pseudorandom generator of 128 bits. It uses large space for choice of seed value to avoid brute force attacks and is built with permutation, substitution and x-or operations.