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Elliptic curve pseudorandom sequence generators. (English) Zbl 0993.94547

Heys, Howard (ed.) et al., Selected areas in cryptography. 6th annual international workshop, SAC ’99. Kingston, Ontario, Canada, August 9-10, 1999. Proceedings. Berlin: Springer. Lect. Notes Comput. Sci. 1758, 34-48 (2000).
Summary: We introduce a new approach to the generation of binary sequences by applying trace functions to elliptic curves over \(\text{GF}(2^m)\). We call these sequences elliptic curve pseudorandom sequences (EC-sequence). We determine their periods, distribution of zeros and ones, and linear spans for a class of EC-sequences generated from supersingular curves. We exhibit a class of EC-sequences which has half period as a lower bound for their linear spans. EC-sequences can be constructed algebraically and can be generated efficiently in software or hardware by the same methods that are used for implementation of elliptic curve public-key cryptosystems.
For the entire collection see [Zbl 0933.00054].

MSC:

94A60 Cryptography
94A55 Shift register sequences and sequences over finite alphabets in information and communication theory
14G50 Applications to coding theory and cryptography of arithmetic geometry
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