Abstract
This study presents a high performance GF(2 m ) Elliptic Curve Crypto-processor architecture. The proposed architecture exploits parallelism at the projective coordinate level to perform parallel field multiplications. In the proposed architecture, normal basis representation is used. Comparisons between the Projective, Jacobian and Mixed coordinate systems using sequential and parallel designs are presented. Results show that parallel designs using normal basis gives better area- time complexity (AT 2 ) than sequential designs by 33-252% which leads to a wide range of design tradeoffs. The results also show that mixed coordinate system is the best in both sequential and parallel designs and gives the least number of multiplications levels when using 3 multipliers and the best AT 2 when using only 2 multipliers.
Highlights
Elliptic Curves Cryptosystems (ECC)[1,2] has attracted many researchers and has been included in many standards[3,4,5,6,7,8]
One solution for meeting this requirement is to exploit the inherent parallelism within Elliptic curve point operations in projective coordinate
In this study we presented a high performance GF(2m) Elliptic Curve Crypto processor
Summary
Elliptic Curves Cryptosystems (ECC)[1,2] has attracted many researchers and has been included in many standards[3,4,5,6,7,8]. Inversion operations, which are needed in point addition over Elliptic Curves are the most expensive operation over Finite Fields[9,10,11,12]. The approach adopted in the literature is to represent Elliptic Curve points in projective coordinate in order to replace the inversion operations with repetitive multiplications[9,10,11,12,13,14,15]. The selection of a projective coordinate is based on the number of arithmetic operations, mainly multiplications. One solution for meeting this requirement is to exploit the inherent parallelism within Elliptic curve point operations in projective coordinate.
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