Use of elliptic curves in cryptography
Lecture notes in computer sciences; 218 on Advances in cryptology---CRYPTO 85
A remark concerning m-divisibility and the discrete logarithm in the divisor class group of curves
Mathematics of Computation
Improving the parallelized Pollard lambda search on anomalous binary curves
Mathematics of Computation
Handbook of Applied Cryptography
Handbook of Applied Cryptography
Faster Attacks on Elliptic Curve Cryptosystems
SAC '98 Proceedings of the Selected Areas in Cryptography
Identity-Based Encryption from the Weil Pairing
CRYPTO '01 Proceedings of the 21st Annual International Cryptology Conference on Advances in Cryptology
Supersingular Curves in Cryptography
ASIACRYPT '01 Proceedings of the 7th International Conference on the Theory and Application 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
Short Signatures from the Weil Pairing
Journal of Cryptology
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
A subexponential algorithm for the discrete logarithm problem with applications to cryptography
SFCS '79 Proceedings of the 20th Annual Symposium on Foundations of Computer Science
Subset-Restricted Random Walks for Pollard rho Method on ${\mathbf{F}_{p^m}}$
Irvine Proceedings of the 12th International Conference on Practice and Theory in Public Key Cryptography: PKC '09
New directions in cryptography
IEEE Transactions on Information Theory
An improved algorithm for computing logarithms over and its cryptographic significance (Corresp.)
IEEE Transactions on Information Theory
A public key cryptosystem and a signature scheme based on discrete logarithms
IEEE Transactions on Information Theory
Reducing elliptic curve logarithms to logarithms in a finite field
IEEE Transactions on Information Theory
| Hi-index | 7.29 |
It is clear that the distinctive feature of the normal basis representations, namely, the p-th power of an element is just the cyclic shift of its normal basis representation where p is the characteristic of the underlying field, can be used to speed up the computation of discrete logarithms over finite extension fields F"p"^"m. We propose a variant of the Pollard rho method to take advantage of this feature, and achieve the speedup by a factor of m, rather than 3p-34p-3m, the previous result reported in the literature. Besides the theoretical analysis, we also compare the performances of the new method with the previous algorithm in experiments, and the result confirms our analysis. Due to the MOV reduction, our method can be applied to paring-based cryptosystems over binary or ternary fields.