On a class of pseudorandom sequences from elliptic curves over finite fields
Following the idea of Xing et al., we investigate a general method for constructing families of pseudorandom sequences with low correlation and large linear complexity from elliptic curves over fields in this correspondence. With the help of the tool of exponential sums on elliptic curves, we study their periods, linear complexities, linear complexity profiles, distributions of r-patterns, periodic correlation, partial period distributions, and aperiodic correlation in detail. The results show that they have nice randomness.
elliptic curve linear complexity exponential sum on elliptic curve periodic correlation aperiodic correlation least period pseudo-random sequence r-pattern