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
A course in computational algebraic number theory
Improving the parallelized Pollard lambda search on anomalous binary curves
Mathematics of Computation
On random walks for Pollard's Rho method
Mathematics of Computation
Cybernetics and Systems Analysis
Faster Attacks on Elliptic Curve Cryptosystems
SAC '98 Proceedings of the Selected Areas in Cryptography
Elliptic Scalar Multiplication Using Point Halving
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
ANTS-III Proceedings of the Third International Symposium on Algorithmic Number Theory
On the efficiency of Pollard's rho method for discrete logarithms
CATS '08 Proceedings of the fourteenth symposium on Computing: the Australasian theory - Volume 77
CRYPTO '09 Proceedings of the 29th Annual International Cryptology Conference on Advances in Cryptology
On the correct use of the negation map in the Pollard rho method
PKC'11 Proceedings of the 14th international conference on Practice and theory in public key cryptography conference on Public key cryptography
Field inversion and point halving revisited
IEEE Transactions on Computers
New directions in cryptography
IEEE Transactions on Information Theory
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Pollard rho method and its parallelized variants are at present known as the best generic algorithms for computing elliptic curve discrete logarithms. We propose new iteration function for the rho method by exploiting the fact that point halving is more efficient than point addition for elliptic curves over binary fields. We present a careful analysis of the alternative rho method with new iteration function. Compared to the previous r-adding walk, generally the new method can achieve a significant speedup for computing elliptic curve discrete logarithms over binary fields. For instance, for certain NIST-recommended curves over binary fields, the new method is about 12---17% faster than the previous best methods.