ECM at Work
The performance of the Elliptic Curve Method (ECM) for integer factorization plays an important role in the security assessment of RSA-based protocols as a co-factorization tool inside the number field sieve. The efficient arithmetic for Edwards curves found an application by speeding up ECM. The authors propose techniques based on generating and combining addition chains to optimize Edwards ECM in terms of both performance and memory requirements. This makes their approach very suitable for memory-constrained devices such as graphics processing units. For commonly used ECM parameters they are able to lower the required memory up to a factor 55 compared to the state-of-the-art Edwards ECM approach.