Generation of pseudorandom sequence over elliptic curve group and their properties

Abstract

In this paper, the application of Elliptic Curves in the generation of pseudorandom sequences is discussed. An Elliptic Curve of the form y 2+xy=x 3+ax 2+b, over GF(28) is considered. A base point P of large order N, of elliptic curve has been found. Using Linear Feedback Shift Register (LFSR) for generating sequence of integers {k i } modulo p, a prime, where p≥N, from which random key sequence {k i P} is obtained. The details of randomness tests [9] performed on the binary form of the sequence {k i P} of Elliptic Curve points are discussed for a sample example. The generated sequences have passed most of the FIPS 140–2 statistical tests. Hamming Correlation of random sequences generated is determined and results are discussed. Such sequences find applications as key sequences in the Stream Cipher Systems. Some of the results obtained in such applications are also given in this paper.