An FFT extension of the elliptic curve method of factorization
An FFT extension of the elliptic curve method of factorization
Guide to Elliptic Curve Cryptography
Guide to Elliptic Curve Cryptography
Hardware Factorization Based on Elliptic Curve Method
FCCM '05 Proceedings of the 13th Annual IEEE Symposium on Field-Programmable Custom Computing Machines
SHARK: a realizable special hardware sieving device for factoring 1024-bit integers
CHES'05 Proceedings of the 7th international conference on Cryptographic hardware and embedded systems
CAIRN 2: An FPGA Implementation of the Sieving Step in the Number Field Sieve Method
CHES '07 Proceedings of the 9th international workshop on Cryptographic Hardware and Embedded Systems
EUROCRYPT '09 Proceedings of the 28th Annual International Conference on Advances in Cryptology: the Theory and Applications of Cryptographic Techniques
An optimized hardware architecture for the montgomery multiplication algorithm
PKC'08 Proceedings of the Practice and theory in public key cryptography, 11th international conference on Public key cryptography
Prime factorization using square root approximation
Computers & Mathematics with Applications
Cuteforce analyzer: implementing a heterogeneous bruteforce cluster with specialized coprocessors
CMS'12 Proceedings of the 13th IFIP TC 6/TC 11 international conference on Communications and Multimedia Security
ASIACRYPT'12 Proceedings of the 18th international conference on The Theory and Application of Cryptology and Information Security
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A novel portable hardware architecture for the Elliptic Curve Method of factoring, designed and optimized for application in the relation collection step of the Number Field Sieve, is described and analyzed. A comparison with an earlier proof-of-concept design by Pelzl, Šimka, et al. has been performed, and a substantial improvement has been demonstrated in terms of both the execution time and the area-time product. The ECM architecture has been ported across three different families of FPGA devices in order to select the family with the best performance to cost ratio. A timing comparison with a highly optimized software implementation, GMP-ECM, has been performed. Our results indicate that low-cost families of FPGAs, such as Xilinx Spartan 3, offer at least an order of magnitude improvement over the same generation of microprocessors in terms of the performance to cost ratio.