Use of elliptic curves in cryptography
Lecture notes in computer sciences; 218 on Advances in cryptology---CRYPTO 85
A course in computational algebraic number theory
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Improving the parallelized Pollard lambda search on anomalous binary curves
Mathematics of Computation
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Mathematics of Computation
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Speeding up the Discrete Log Computation on Curves with Automorphisms
ASIACRYPT '99 Proceedings of the International Conference on the Theory and Applications of Cryptology and Information Security: Advances in Cryptology
Speeding Up Pollard's Rho Method for Computing Discrete Logarithms
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Information Sciences: an International Journal
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Information Sciences: an International Journal
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IEEE Transactions on Information Theory
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It is clear that the negation map can be used to speed up the computation of elliptic curve discrete logarithms with the Pollard rho method. However, the random walks defined on elliptic curve points equivalence class {+/-P} used by Pollard rho will always get trapped in fruitless cycles. We propose an efficient alternative approach to resolve fruitless cycles. Besides the theoretical analysis, we also examine the performance of the new algorithm in experiments with elliptic curve groups. The experiment results show that we can achieve the speedup by a factor extremely close to 2 using the new algorithm with the negation map, which is the best performance reported in the literature.