Improving the parallelized Pollard lambda search on anomalous binary curves. (English) Zbl 1101.14325
Summary: The best algorithm known for finding logarithms on an elliptic curve \((E)\) is the (parallelized) Pollard lambda collision search. We show how to apply a Pollard lambda search on a set of equivalence classes derived from \(E\), which requires fewer iterations than the standard approach. In the case of anomalous binary curves over \(\mathbb{F}_{2^m}\), the new approach speeds up the standard algorithm by a factor of \(\sqrt{2m}\).
MSC:
14Q05 | Computational aspects of algebraic curves |
14G50 | Applications to coding theory and cryptography of arithmetic geometry |
94A60 | Cryptography |
11Y16 | Number-theoretic algorithms; complexity |
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