A Construction of Binary Sequences from Elliptic Curves

Constructions of binary lattices and of binary sequences with ldquogoodrdquo pseudorandomness are presented along elliptic curves defined over finite fields. To evaluate the pseudorandomness of the resulting sequences, the well-distribution measure and the correlation measure of order k are estimated by using certain exponential sums over finite fields and elliptic curves. A low bound on the linear complexity profile is presented in terms of the bound on the correlation measure of order k. Finally, the resulting sequences are applied to define a Boolean function, whose nonlinearity, an important cryptographic criteria for Boolean functions, is estimated.