Introduction to finite fields and their applications
Introduction to finite fields and their applications
Handbook of Applied Cryptography
Handbook of Applied Cryptography
Software Implementation of the NIST Elliptic Curves Over Prime Fields
CT-RSA 2001 Proceedings of the 2001 Conference on Topics in Cryptology: The Cryptographer's Track at RSA
Software Implementation of Elliptic Curve Cryptography over Binary Fields
CHES '00 Proceedings of the Second International Workshop on Cryptographic Hardware and Embedded Systems
A Scalable and Unified Multiplier Architecture for Finite Fields GF(p) and GF(2m)
CHES '00 Proceedings of the Second International Workshop on Cryptographic Hardware and Embedded Systems
A Bit-Serial Unified Multiplier Architecture for Finite Fields GF(p) and GF(2m)
CHES '01 Proceedings of the Third International Workshop on Cryptographic Hardware and Embedded Systems
High-speed hardware implementations of Elliptic Curve Cryptography: A survey
Journal of Systems Architecture: the EUROMICRO Journal
A unified architecture for a public key cryptographic coprocessor
Journal of Systems Architecture: the EUROMICRO Journal
A versatile Montgomery multiplier architecture with characteristic three support
Computers and Electrical Engineering
An RNS implementation of an Fpelliptic curve point multiplier
IEEE Transactions on Circuits and Systems Part I: Regular Papers
Flexible hardware processor for elliptic curve cryptography over NIST prime fields
IEEE Transactions on Very Large Scale Integration (VLSI) Systems
An efficient implementation of elliptic curve over finite fields
Proceedings of the International Conference and Workshop on Emerging Trends in Technology
A high-performance unified-field reconfigurable cryptographic processor
IEEE Transactions on Very Large Scale Integration (VLSI) Systems
Memory-constrained implementations of elliptic curve cryptography in co-Z coordinate representation
AFRICACRYPT'11 Proceedings of the 4th international conference on Progress in cryptology in Africa
A systematic evaluation of compact hardware implementations for the rijndael s-box
CT-RSA'05 Proceedings of the 2005 international conference on Topics in Cryptology
Arithmetic unit for computations in GF(p) with the left-shifting multiplicative inverse algorithm
ARCS'13 Proceedings of the 26th international conference on Architecture of Computing Systems
International Journal of Information and Computer Security
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In this article we present a hardware solution for finite field arithmetic with application in asymmetric cryptography. It supports calculation in GF(p) as well as in GF(2m). Addition and multiplication with interleaved modular reduction are the main functionality of the unit. Additional functions--like shift operations and integer incrementation--allow the calculation of the multiplicative inverse and covering all operations required to implement Elliptic Curve Cryptography. Redundant number representation and efficient modular reduction make it ready for future cryptographic bitlengths and allow operation at high clock frequency on moderate hardware resources.