Welcome to the resource topic for 2022/1588
Title:
Factoring using multiplicative relations modulo n: a subexponential algorithm inspired by the index calculus
Authors: Katherine E. Stange
Abstract:We demonstrate that a modification of the classical index calculus algorithm can be used to factor integers. More generally, we reduce the factoring problem to finding an overdetermined system of multiplicative relations in any factor base modulo n, where n is the integer whose factorization is sought. The algorithm has subexponential runtime \exp(O(\sqrt{\log n \log \log n})) (or \exp(O( (\log n)^{1/3} (\log \log n)^{2/3} )) with the addition of a number field sieve), but requires a rational linear algebra phase, which is more intensive than the linear algebra phase of the classical index calculus algorithm. The algorithm is certainly slower than the best known factoring algorithms, but is perhaps somewhat notable for its simplicity and its similarity to the index calculus.
ePrint: https://eprint.iacr.org/2022/1588
See all topics related to this paper.
Feel free to post resources that are related to this paper below.
Example resources include: implementations, explanation materials, talks, slides, links to previous discussions on other websites.
For more information, see the rules for Resource Topics .