A Simpler Sieving Device: Combining ECM and TWIRL

W. Geiselmann, F. Januszewski, H. Koepfer, Jan Pelzl, R. Steinwandt

International Conference on Information Security and Cryptology - ICISC 2006, Busan, Korea, Proceedings. LNCS, Springer-Verlag, November 30 - December 1, 2006.


Abstract

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 signi?cantly 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 o?-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 ?nds the vast majority of the needed cofactor factorizations. In summary, we think the proposed device to enable a signi?cant decrease of TWIRL’s layout complexity and therewith its cost.

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tags: cryptanalytic hardwar, ECM, NFS, RSA