Fast reduction and composition of binary quadratic forms
ISSAC '91 Proceedings of the 1991 international symposium on Symbolic and algebraic computation
The art of computer programming, volume 2 (3rd ed.): seminumerical algorithms
The art of computer programming, volume 2 (3rd ed.): seminumerical algorithms
A space efficient algorithm for group structure computation
Mathematics of Computation
Extending the GHS Weil Descent Attack
EUROCRYPT '02 Proceedings of the International Conference on the Theory and Applications of Cryptographic Techniques: Advances in Cryptology
The complexity of finding periods
STOC '79 Proceedings of the eleventh annual ACM symposium on Theory of computing
The Art of Computer Programming, Volume 4, Fascicle 2: Generating All Tuples and Permutations (Art of Computer Programming)
Lower bounds for discrete logarithms and related problems
EUROCRYPT'97 Proceedings of the 16th annual international conference on Theory and application of cryptographic techniques
New generic algorithms for hard knapsacks
EUROCRYPT'10 Proceedings of the 29th Annual international conference on Theory and Applications of Cryptographic Techniques
| Hi-index | 0.00 |
We describe a space-efficient algorithm for solving a generalization of the subset sum problem in a finite group G, using a Pollard-驴 approach. Given an element z and a sequence of elements S, our algorithm attempts to find a subsequence of S whose product in G is equal to z. For a random sequence S of length d log2 n, where n = #G and d 驴 2 is a constant, we find that its expected running time is $${O(\sqrt{n}\,{\rm log}\,n)}$$ group operations (we give a rigorous proof for d 4), and it only needs to store O(1) group elements. We consider applications to class groups of imaginary quadratic fields, and to finding isogenies between elliptic curves over a finite field.