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Sequences with Almost Perfect Linear Complexity Profiles and Curves Over Finite Fields

For stream ciphers, we need to generate pseudorandom sequences which are of properties of unpredictability and randomness. A important measure of unpredictability and randomness is the linear complexity profile (l.c.p.) l/sub a/(n) of a sequence a. A sequence a is called almost perfect if the l.c.p. is l/sub a/(n)=n/2+O(1). Based on curves over finite fields, we present a method to construct almost perfect sequences. We also illustrate our construction by explicit examples from the projective line and elliptic curves over the binary field.