Abstract
Performing standard Weierstrass-form curves’ operations based on Edwards-form curves’ addition law, the overall security of elliptic curves can be strengthened while remain compatible with existing ECC system. We present a simplified algorithm for finding such dual-form elliptic curves over prime field F p with p ≡ 3 mod 4. Using the generated curves, algorithms for implementing dual-form operations on affine, projective and twisted coordinates are further discussed and optimized for the case of Weierstrass-form operations. The algorithms are implemented on FPGA and show competitive time and area performance both in Edwards form and Weierstrass form.
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Wang, J., Wang, X. (2012). Dual-form Elliptic Curves Simple Hardware Implementation. In: Huang, DS., Jiang, C., Bevilacqua, V., Figueroa, J.C. (eds) Intelligent Computing Technology. ICIC 2012. Lecture Notes in Computer Science, vol 7389. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-31588-6_67
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DOI: https://doi.org/10.1007/978-3-642-31588-6_67
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