Advances in Applied Mathematics
Use of elliptic curves in cryptography
Lecture notes in computer sciences; 218 on Advances in cryptology---CRYPTO 85
A course in computational algebraic number theory
A course in computational algebraic number theory
Speeding up Elliptic Cryptosystems by Using a Signed Binary Window Method
CRYPTO '92 Proceedings of the 12th Annual International Cryptology Conference on Advances in Cryptology
Optimal Extension Fields for Fast Arithmetic in Public-Key Algorithms
CRYPTO '98 Proceedings of the 18th Annual International Cryptology Conference on Advances in Cryptology
Efficient Elliptic Curve Exponentiation Using Mixed Coordinates
ASIACRYPT '98 Proceedings of the International Conference on the Theory and Applications of Cryptology and Information Security: Advances in Cryptology
Fast Implementation of Elliptic Curve Arithmetic in GF(pn)
PKC '00 Proceedings of the Third International Workshop on Practice and Theory in Public Key Cryptography: Public Key Cryptography
Fast Implementation of Public-Key Cryptography ona DSP TMS320C6201
CHES '99 Proceedings of the First International Workshop on Cryptographic Hardware and Embedded Systems
Efficient Implementation of Elliptic Curve Cryptosystems on an ARM7 with Hardware Accelerator
ISC '01 Proceedings of the 4th International Conference on Information Security
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In this paper, we propose fast finite field and elliptic curve (EC) algorithms useful for embedding cryptographic functions on high performance device such that most instructions take just one cycle. In such case, the integer multiplications and additions have the same computational cost so that the computational cost analyses that were previously done in traditional manner may be invalid and in some cases the new algorithms should be introduced for fast computation. In our implementation, column major method for field multiplication and BP inversion algorithm are used for fast field arithmetic, and mixed coordinates method is used for efficient EC exponentiation. We give here analyses on various algorithms that are useful for implementing EC exponentiation on CalmRISC microcontroller with MAC2424 coprocessor, as well as new exact analyses on BP (Bailey-Paar) inversion algorithm and EC exponentiation. Using techniques shown in this paper, we implemented EC exponentiation for various coordinate systems and the best result took 122ms, assuming 50ns clock cycle.