[Resource Topic] 2006/109: A Simpler Sieving Device: Combining ECM and TWIRL

Welcome to the resource topic for 2006/109

A Simpler Sieving Device: Combining ECM and TWIRL

Authors: Willi Geiselmann, Fabian Januszewski, Hubert Koepfer, Jan Pelzl, Rainer Steinwandt


A main obstacle in manufacturing the TWIRL device for realizing the sieving step of the Number Field Sieve is the sophisticated chip layout. Especially the logic for logging and recovering large prime
factors found during sieving adds significantly to the layout complexity. We describe a device building on the Elliptic Curve Method (ECM) that for parameters of interest enables the replacement of the complete logging part in TWIRL by an off-wafer postprocessing. The postprocessing is done in real time, leaving the total sieving time basically unchanged.

The proposed device is an optimized ECM implementation building on curves chosen to cope with factor sizes as expected in the output of
TWIRL. According to our preliminary analysis, for the relation collection step expected for a 1024-bit factorization our design is realizable with current fab technology at very moderate cost. The proposed ECM engine also finds the vast majority of the needed cofactor factorizations. In summary, we think the proposed device to enable a significant decrease of TWIRL’s layout complexity and therewith its cost.

ePrint: https://eprint.iacr.org/2006/109

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 .