Low-Energy Digit-Serial/Parallel Finite Field Multipliers
Journal of VLSI Signal Processing Systems - Special issue on application specific systems, architectures and processors
Mastrovito Multiplier for General Irreducible Polynomials
IEEE Transactions on Computers
Elliptic curves in cryptography
Elliptic curves in cryptography
Elliptic curve cryptography on smart cards without coprocessors
Proceedings of the fourth working conference on smart card research and advanced applications on Smart card research and advanced applications
Performance analysis of elliptic curve cryptography for SSL
WiSE '02 Proceedings of the 1st ACM workshop on Wireless security
Generic implementations of elliptic curve cryptography using partial reduction
Proceedings of the 9th ACM conference on Computer and communications security
Reconfigurable Implementation of Elliptic Curve Crypto Algorithms
IPDPS '02 Proceedings of the 16th International Parallel and Distributed Processing Symposium
Fast Multiplication on Elliptic Curves over GF(2m) without Precomputation
CHES '99 Proceedings of the First International Workshop on Cryptographic Hardware and Embedded Systems
An End-to-End Systems Approach to Elliptic Curve Cryptography
CHES '02 Revised Papers from the 4th International Workshop on Cryptographic Hardware and Embedded Systems
An FPGA implementation of an elliptic curve processor GF(2m)
Proceedings of the 14th ACM Great Lakes symposium on VLSI
FPGA implementation of point multiplication on koblitz curves using kleinian integers
CHES'06 Proceedings of the 8th international conference on Cryptographic Hardware and Embedded Systems
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We describe a cryptographic processor for Elliptic Curve Cryptography (ECC). ECC is evolving as an attractive alternative to other public-key cryptosystems such as the Rivest-Shamir- Adleman algorithm (RSA) by offering the smallest key size and the highest strength per bit. The cryptographic processor performs point multiplication for elliptic curves over binary polynomial fields GF(2m). In contrast to other designs that only support one curve at a time, our processor is capable of handling arbitrary curves without requiring reconfiguration. More specifically, it can handle both named curves as standardized by the National Institute for Standards and Technology (NIST) as well as any other generic curves up to a field degree of 255. Efficient support for arbitrary curves is particularly important for the targeted server applications that need to handle requests for secure connections generated by a multitude of heterogeneous client devices. Such requests may specify curves which are infrequently used or not even known at implementation time. We have implemented the cryptographic processor in a field-programmable gate array (FPGA) running at a clock frequency of 66.4 MHz. Its performance is 6955 point multiplications per second for named curves over GF(2163) and 3308 point multiplications per second for generic curves over GF(2163). We have integrated the cryptographic processor into the open source toolkit OpenSSL, which implements the Secure Sockets Layer (SSL) which is today's dominant Internet security protocol. This report is an extended version of a paper presented at the IEEE 14th International Conference on Application-specific Systems, Architectures and Processors, The Hague, June 2003 where it received the "Best Paper Award".