Cost-effective design for binary Edwards elliptic curves crypto-processor over GF (2^N) using parallel multipliers and architectures
by Qasem Abu Al-Haija; Ahmad Al Badawi
International Journal of Information and Computer Security (IJICS), Vol. 5, No. 3, 2013

Abstract: Arithmetic operations involved in ECC computation suffer from modular inversion operation. Modular inversion is known to be the most time consuming operation performed by the ECC crypto-processor. Inversion operations can be replaced by several simpler multiplication operations using projective coordinates system instead of the classical affine coordinates system. Based on this notion, new elliptic curve cryptographic processor architecture is presented here which results in significant reduction in execution time and gives a range of trade-off between speed and area. This is achieved by exploiting the inherent parallelism that exists in elliptic curve arithmetic computations. In this work, the binary Edwards's projective coordinates system over GF (2ⁿ) is presented to perform ECC arithmetic computations using parallel multipliers to obtain maximum parallelism. The projection X/Z, Y/Z when applied to the binary Edwards curves using the best number of parallel multipliers and adders reduces the computation time by 20% less than the use of affine coordinates with full utilisation of multiplier units. Our proposed processor enhances the addition operation time by 1.75 factor compared to the standard curves and four times scale up compared to the serial design of our processor.

Online publication date: Wed, 30-Jul-2014

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