A fast algorithm for computing multiplicative inverses in GF(2m) using normal bases
Information and Computation
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
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
Fast Key Exchange with Elliptic Curve Systems
CRYPTO '95 Proceedings of the 15th Annual International Cryptology Conference on Advances in Cryptology
From Euclid's GCD to Montgomery Multiplication to the Great Divide
From Euclid's GCD to Montgomery Multiplication to the Great Divide
Secure Hash Standard - SHS: Federal Information Processing Standards Publication 180-4
Secure Hash Standard - SHS: Federal Information Processing Standards Publication 180-4
A Formal Framework for Expressing Trust Negotiation in the Ubiquitous Computing Environment
UIC '08 Proceedings of the 5th international conference on Ubiquitous Intelligence and Computing
Workload Characterization of a Lightweight SSL Implementation Resistant to Side-Channel Attacks
CANS '08 Proceedings of the 7th International Conference on Cryptology and Network Security
Implementation and analysis of stream ciphers based on the elliptic curves
Computers and Electrical Engineering
On parallelization of high-speed processors for elliptic curve cryptography
IEEE Transactions on Very Large Scale Integration (VLSI) Systems
A cryptographic processor for arbitrary elliptic curves over GF(2m)
A cryptographic processor for arbitrary elliptic curves over GF(2m)
Generic GF(2m) arithmetic in software and its application to ECC
ACISP'03 Proceedings of the 8th Australasian conference on Information security and privacy
Customizable elliptic curve cryptosystems
IEEE Transactions on Very Large Scale Integration (VLSI) Systems
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Elliptic Curve Cryptography (ECC) is evolving as an attractive alternative to other public-key schemes such as RSA by offering the smallest key size and the highest strength per bit. The importance of ECC has been recognized by the US government and the standards bodies NIST and SECG. Standards for preferred elliptic curves over prime fields GF(p) and binary polynomial fields GF(2m) as well as the Elliptic Curve Digital Signature Algorithm (ECDSA) have been created. A security protocol based on ECC requires support for different curves representing different security levels. This is particularly true for server applications that are exposed to requests for secure connections with different parameters generated by a multitude of client devices. Reported implementations of ECC over GF(2m) typically choose to implement each curve as a special case so that modular reduction can be optimized, thus improving the overall performance. In contrast, this paper focuses on generic implementations of ECC point multiplication for arbitrary curves over GF(2m). We present a novel reduction algorithm that allows hardware and software implementations for variable field degrees m. Though not as high in performance as an implementation optimized for a specific curve, it offers an attractive solution to supporting infrequently used curves or curves not known at the time of the implementation.