Introduction to finite fields and their applications
Introduction to finite fields and their applications
A fast algorithm for computing multiplicative inverses in GF(2m) using normal bases
Information and Computation
Fast Arithmetic for Public-Key Algorithms in Galois Fields with Composite Exponents
IEEE Transactions on Computers
Elliptic curves in cryptography
Elliptic curves in cryptography
Low Complexity Bit-Parallel Finite Field Arithmetic Using Polynomial Basis
CHES '99 Proceedings of the First International Workshop on Cryptographic Hardware and Embedded Systems
Fast Multiplication on Elliptic Curves over GF(2m) without Precomputation
CHES '99 Proceedings of the First International Workshop on Cryptographic Hardware and Embedded Systems
Elliptic Curve Scalar Multiplier Design Using FPGAs
CHES '99 Proceedings of the First 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
Fast exponentiation with precomputation
EUROCRYPT'92 Proceedings of the 11th annual international conference on Theory and application of cryptographic techniques
Reconfigurable Implementation of Elliptic Curve Crypto Algorithms
IPDPS '02 Proceedings of the 16th International Parallel and Distributed Processing Symposium
IPDPS '02 Proceedings of the 16th International Parallel and Distributed Processing Symposium
Fully Parameterizable Elliptic Curve Cryptography Processor over GF(2)
FPL '02 Proceedings of the Reconfigurable Computing Is Going Mainstream, 12th International Conference on Field-Programmable Logic and Applications
Exploration of Design Space in ECDSA
FPL '02 Proceedings of the Reconfigurable Computing Is Going Mainstream, 12th International Conference on Field-Programmable Logic and Applications
A Scalable GF(p) Elliptic Curve Processor Architecture for Programmable Hardware
CHES '01 Proceedings of the Third International Workshop on Cryptographic Hardware and Embedded Systems
The Hessian Form of an Elliptic Curve
CHES '01 Proceedings of the Third International Workshop on Cryptographic Hardware and Embedded Systems
Enhancing Simple Power-Analysis Attacks on Elliptic Curve Cryptosystems
CHES '02 Revised Papers from the 4th International Workshop on Cryptographic Hardware and Embedded Systems
Genus Two Hyperelliptic Curve Coprocessor
CHES '02 Revised Papers from the 4th 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
Ultra High Performance ECC over NIST Primes on Commercial FPGAs
CHES '08 Proceeding sof the 10th international workshop on Cryptographic Hardware and Embedded Systems
High Speed Compact Elliptic Curve Cryptoprocessor for FPGA Platforms
INDOCRYPT '08 Proceedings of the 9th International Conference on Cryptology in India: Progress in Cryptology
Efficient key management FPGA-based cryptosystem using the RNS and iterative coding
International Journal of Information and Communication Technology
Optimized System-on-Chip Integration of a Programmable ECC Coprocessor
ACM Transactions on Reconfigurable Technology and Systems (TRETS)
Optimizing the HW/SW boundary of an ECC SoC design using control hierarchy and distributed storage
Proceedings of the Conference on Design, Automation and Test in Europe
Efficient time-area scalable ECC processor using µ-coding technique
WAIFI'10 Proceedings of the Third international conference on Arithmetic of finite fields
Scan-based attack against elliptic curve cryptosystems
Proceedings of the 2010 Asia and South Pacific Design Automation Conference
Customizable elliptic curve cryptosystems
IEEE Transactions on Very Large Scale Integration (VLSI) Systems
Superscalar coprocessor for high-speed curve-based cryptography
CHES'06 Proceedings of the 8th international conference on Cryptographic Hardware and Embedded Systems
Hyperelliptic curve coprocessors on a FPGA
WISA'04 Proceedings of the 5th international conference on Information Security Applications
Performance of HECC coprocessors using inversion-free formulae
ICCSA'06 Proceedings of the 2006 international conference on Computational Science and Its Applications - Volume Part III
Integration, the VLSI Journal
GF(2m) finite-field multipliers with reduced activity variations
WAIFI'12 Proceedings of the 4th international conference on Arithmetic of Finite Fields
Pushing the limits of high-speed GF(2m) elliptic curve scalar multiplication on FPGAs
CHES'12 Proceedings of the 14th international conference on Cryptographic Hardware and Embedded Systems
International Journal of Information and Computer Security
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This work proposes a processor architecture for elliptic curves cryptosystems over fields GF(2m). This is a scalable architecture in terms of area and speed that exploits the abilities of reconfigurable hardware to deliver optimized circuitry for different elliptic curves and finite fields. The main features of this architecture are the use of an optimized bit-parallel squarer, a digit-serial multiplier, and two programmable processors. Through reconfiguration, the squarer and the multiplier architectures can be optimized for any field order or field polynomial. The multiplier performance can also be scaled according to system's needs. Our results show that implementations of this architecture executing the projective coordinates version of the Montgomery scalar multiplication algorithmcan compute elliptic curve scalar multiplications with arbitrary points in 0.21 msec in the field GF(2167). A result that is at least 19 times faster than documented hardware implementations and at least 37 times faster than documented software implementations.