Improved Routing-Based Linear Algebra for the Number Field Sieve

Recently, efficient custom-hardware designs were proposed for the linear algebra step of the Number Field Sieve integer factoring algorithm. These designs make use of a heuristic mesh routing algorithm, whose performance has been analyzed only experimentally. We show that the routing algorithm may in fact encounter livelocks, i.e., may never terminate. We propose a context-specific solution for this problem. We also show how efficiency can be improved by a factor of ≈ 4 through the use of a parallel tori topology and packet injection during routing.

• Type: Conference
• Year: 2005
• Where: ITCC
• Authors: Willi Geiselmann, Hubert Köpfer, Rainer Steinwandt, Eran Tromer
• Keywords: Information Technology, Integer Factoring Algorithm, ITCC 2005, Mesh Routing Algorithm, Routing Algorithm