Linear complexity of pseudorandom sequences generated by Fermat quotients and their generalizations
We use polynomial quotients modulo an odd prime p, which are generalized from the Fermat quotients, to define two families of d(>= 2)-ary sequences of period p(2). If d is a primitive element modulo p(2), we determine the minimal characteristic polynomials of the sequences and hence their linear complexities, which depend on whether p equivalent to 1 or 3 (mod 4). Moreover, we generalize the result to the polynomial quotients modulo a power of p. (C) 2011 Elsevier B.V. All rights reserved.
linear complexity pseudorandom sequences fermat quotients polynomial quotients cryptography finite fields