Use of elliptic curves in cryptography
Lecture notes in computer sciences; 218 on Advances in cryptology---CRYPTO 85
Elliptic curves in cryptography
Elliptic curves in cryptography
Handbook of Applied Cryptography
Handbook of Applied Cryptography
Speeding Up Pollard's Rho Method for Computing Discrete Logarithms
ANTS-III Proceedings of the Third International Symposium on Algorithmic Number Theory
Guide to Elliptic Curve Cryptography
Guide to Elliptic Curve Cryptography
Attacking elliptic curve cryptosystems with special-purpose hardware
Proceedings of the 2007 ACM/SIGDA 15th international symposium on Field programmable gate arrays
Collision Search for Elliptic Curve Discrete Logarithm over GF(2m) with FPGA
CHES '07 Proceedings of the 9th international workshop on Cryptographic Hardware and Embedded Systems
Breaking ciphers with COPACOBANA –a cost-optimized parallel code breaker
CHES'06 Proceedings of the 8th international conference on Cryptographic Hardware and Embedded Systems
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
MicroEliece: McEliece for Embedded Devices
CHES '09 Proceedings of the 11th International Workshop on Cryptographic Hardware and Embedded Systems
Constructing cluster of simple FPGA boards for cryptologic computations
ARC'12 Proceedings of the 8th international conference on Reconfigurable Computing: architectures, tools and applications
Towards one cycle per bit asymmetric encryption: code-based cryptography on reconfigurable hardware
CHES'12 Proceedings of the 14th international conference on Cryptographic Hardware and Embedded Systems
A hardware-accelerated ECDLP with high-performance modular multiplication
International Journal of Reconfigurable Computing - Special issue on Selected Papers from the 2011 International Conference on Reconfigurable Computing and FPGAs (ReConFig 2011)
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The resistance against powerful index-calculus attacks makes Elliptic Curve Cryptosystems (ECC) an interesting alternative to conventional asymmetric cryptosystems, like RSA. Operands in ECC require significantly less bits at the same level of security, resulting in a higher computational efficiency compared to RSA. With growing computational capabilities and continuous technological improvements over the years, however, the question of the security of ECC against attacks based on special-purpose hardware arises. In this context, recently emerged low-cost FPGAs demand for attention in the domain of hardware-based cryptanalysis: the extraordinary efficiency of modern programmable hardware devices allow for a low-budget implementation of hardware-based ECC attacks---without the requirement of the expensive development of ASICs. With focus on the aspect of cost-efficiency, this contribution presents and analyzes an FPGA-based architecture of an attack against ECC over prime fields. A multi-processing hardware architecture for Pollard's Rho method is described. We provide results on actually used key lengths of ECC (128 bits and above) and estimate the expected runtime for a successful attack. As a first result, currently used elliptic curve cryptosystems with a security of 160 bit and above turn out to be infeasible to break with available computational and financial resources. However, some of the security standards proposed by the Standards for Efficient Cryptography Group (SECG) become subject to attacks based on low-cost FPGAs.