How easy is collision search? Application to DES
EUROCRYPT '89 Proceedings of the workshop on the theory and application of cryptographic techniques on Advances in cryptology
The art of computer programming, volume 2 (3rd ed.): seminumerical algorithms
The art of computer programming, volume 2 (3rd ed.): seminumerical algorithms
The art of computer programming, volume 3: (2nd ed.) sorting and searching
The art of computer programming, volume 3: (2nd ed.) sorting and searching
Improving the parallelized Pollard lambda search on anomalous binary curves
Mathematics of Computation
On random walks for Pollard's Rho method
Mathematics of Computation
Faster Attacks on Elliptic Curve Cryptosystems
SAC '98 Proceedings of the Selected Areas in Cryptography
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
ANTS-III Proceedings of the Third International Symposium on Algorithmic Number Theory
Information Processing Letters
A computational introduction to number theory and algebra
A computational introduction to number theory and algebra
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
An Improvement to the Gaudry-Schost Algorithm for Multidimensional Discrete Logarithm Problems
Cryptography and Coding '09 Proceedings of the 12th IMA International Conference on Cryptography and Coding
International Journal of Applied Cryptography
International Journal of Applied Cryptography
| Hi-index | 0.00 |
We propose a method to speed up the r -adding walk on multiplicative subgroups of the prime field. The r -adding walk is an iterating function used with the Pollard rho algorithm and is known to require less iterations than Pollard's original iterating function in reaching a collision. Our main idea is to follow through the r -adding walk with only partial information about the nodes reached. The trail traveled by the proposed method is a normal r -adding walk, but with significantly reduced execution time for each iteration. While a single iteration of most r -adding walks on F p require a multiplication of two integers of logp size, the proposed method requires an operation of complexity only linear in logp , using a pre-computed table of size O ((logp ) r + 1·loglogp ). In practice, our rudimentary implementation of the proposed method increased the speed of Pollard rho with r -adding walks by a factor of more than 10 for 1024-bit random primes p .