Use of elliptic curves in cryptography
Lecture notes in computer sciences; 218 on Advances in cryptology---CRYPTO 85
Fast Base Extension Using a Redundant Modulus in RNS
IEEE Transactions on Computers
Modulo Reduction in Residue Number Systems
IEEE Transactions on Parallel and Distributed Systems
An RNS Montgomery Modular Multiplication Algorithm
IEEE Transactions on Computers
Power Analysis Attacks of Modular Exponentiation in Smartcards
CHES '99 Proceedings of the First International Workshop on Cryptographic Hardware and Embedded Systems
Resistance against Differential Power Analysis for Elliptic Curve Cryptosystems
CHES '99 Proceedings of the First International Workshop on Cryptographic Hardware and Embedded Systems
Implementation of RSA Algorithm Based on RNS Montgomery Multiplication
CHES '01 Proceedings of the Third International Workshop on Cryptographic Hardware and Embedded Systems
The Montgomery Powering Ladder
CHES '02 Revised Papers from the 4th International Workshop on Cryptographic Hardware and Embedded Systems
A Scalable Dual-Field Elliptic Curve Cryptographic Processor
IEEE Transactions on Computers
High-speed hardware implementations of Elliptic Curve Cryptography: A survey
Journal of Systems Architecture: the EUROMICRO Journal
Ultra High Performance ECC over NIST Primes on Commercial FPGAs
CHES '08 Proceeding sof the 10th international workshop on Cryptographic Hardware and Embedded Systems
Exploiting the Power of GPUs for Asymmetric Cryptography
CHES '08 Proceeding sof the 10th international workshop on Cryptographic Hardware and Embedded Systems
High-Speed Elliptic Curve Cryptography Accelerator for Koblitz Curves
FCCM '08 Proceedings of the 2008 16th International Symposium on Field-Programmable Custom Computing Machines
An RNS implementation of an Fpelliptic curve point multiplier
IEEE Transactions on Circuits and Systems Part I: Regular Papers
Cox-Rower architecture for fast parallel montgomery multiplication
EUROCRYPT'00 Proceedings of the 19th international conference on Theory and application of cryptographic techniques
FPGA implementation of pairings using residue number system and lazy reduction
CHES'11 Proceedings of the 13th international conference on Cryptographic hardware and embedded systems
The CRNS framework and its application to programmable and reconfigurable cryptography
ACM Transactions on Architecture and Code Optimization (TACO) - Special Issue on High-Performance Embedded Architectures and Compilers
Improving modular inversion in RNS using the plus-minus method
CHES'13 Proceedings of the 15th international conference on Cryptographic Hardware and Embedded Systems
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We present a new hardware architecture to compute scalar multiplications in the group of rational points of elliptic curves defined over a prime field. We have made an implementation on Altera FPGA family for some elliptic curves defined over randomly chosen ground fields offering classic cryptographic security level. Our implementations show that our architecture is the fastest among the public designs to compute scalar multiplication for elliptic curves defined over a general prime ground field. Our design is based upon the Residue Number System, guaranteeing carry-free arithmetic and easy parallelism. It is SPA resistant and DPA capable.