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.
Keywords RSA - NFS - ECM - cryptanalytic hardware