How to generate cryptographically strong sequences of pseudo-random bits
SIAM Journal on Computing
Computing logarithms in GF(2n)
Proceedings of CRYPTO 84 on Advances in cryptology
Discrete logarithms in finite fields and their cryptographic significance
Proc. of the EUROCRYPT 84 workshop on Advances in cryptology: theory and application of cryptographic techniques
The art of computer programming, volume 2 (3rd ed.): seminumerical algorithms
The art of computer programming, volume 2 (3rd ed.): seminumerical algorithms
Journal of Combinatorial Theory Series A
On an involution concerning pairs of polynomials over F2
Journal of Combinatorial Theory Series A
The index calculus method using non-smooth polynomials
Mathematics of Computation
The complete analysis of a polynomial factorization algorithm over finite fields
Journal of Algorithms
Theory of Information and Coding
Theory of Information and Coding
| Hi-index | 0.00 |
In this paper we are concerned with the Waterloo variant of the index calculus method for the discrete logarithm problem in {\Bbb F}_{2^n}. We provide a rigorous proof for the heuristic arguments for the running time of the Waterloo algorithm. This implies in studying the behavior of pairs of coprime smooth polynomials over finite fields. Our proof involves a double saddle point method, and it is in nature similar to the one of Odlyzko for the rigorous analysis of the basic index calculus.