Use of elliptic curves in cryptography
Lecture notes in computer sciences; 218 on Advances in cryptology---CRYPTO 85
Look-Up Table-Based Large Finite Field Multiplication in Memory Constrained Cryptosystems
IEEE Transactions on Computers - Special issue on computer arithmetic
Elliptic Curve Public Key Cryptosystems
Elliptic Curve Public Key Cryptosystems
VLSI Designs for Multiplication over Finite Fields GF (2m)
AAECC-6 Proceedings of the 6th International Conference, on Applied Algebra, Algebraic Algorithms and Error-Correcting Codes
CM-Curves with Good Cryptographic Properties
CRYPTO '91 Proceedings of the 11th Annual International Cryptology Conference on Advances in Cryptology
A Super-Serial Galois Fields Multiplier for FPGAs and its Application to Public-Key Algorithms
FCCM '99 Proceedings of the Seventh Annual IEEE Symposium on Field-Programmable Custom Computing Machines
A Cellular-Array Multiplier for GF(2m)
IEEE Transactions on Computers
Customizable elliptic curve cryptosystems
IEEE Transactions on Very Large Scale Integration (VLSI) Systems
Design of flexible GF(2m) elliptic curve cryptography processors
IEEE Transactions on Very Large Scale Integration (VLSI) Systems
International Journal of Information and Computer Security
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We describe the implementation of an elliptic curve cryptographic (ECC) coprocessor over GF(2m) on an FPGA and also the result of simulations evaluating its LSI implementation. This coprocessor is suitable for server systems that require efficient ECC operations for various parameters. For speeding-up an elliptic scalar multiplication, we developed a novel configuration of a multiplier over GF(2m), which enables the multiplication of any bit length by using our data conversion method. The FPGA implementation of the coprocessor with our multiplier, operating at 3 MHz, takes 80 ms for 163-bit elliptic scalar multiplication on a pesudo-random curve and takes 45 ms on a Koblitz curve. The 0.25 µm ASIC implementation of the coprocessor, operating at 66 MHz and having a hardware size of 165 Kgates, would take 1.1 ms for 163-bit elliptic scalar multiplication on a pesudo-random curve and would take 0.65 ms on a Koblitz curve.