The fundamental operation in elliptic curve cryptographic schemes is the multiplication of an elliptic curve point by an integer. This paper describes a new method for accelerating this operation on classes of elliptic curves that have efficiently-computable endomorphisms. One advantage of the new method is that it is applicable to a larger class of curves than previous such methods. For this special class of curves, a speedup of up to 50% can be expected over the best general methods for point multiplication.
- Point Multiplication
- Elliptic Curve
- Elliptic Curf
- Point Doubling
- Discrete Logarithm Problem
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Gallant, R.P., Lambert, R.J., Vanstone, S.A. (2001). Faster Point Multiplication on Elliptic Curves with Efficient Endomorphisms. In: Kilian, J. (eds) Advances in Cryptology — CRYPTO 2001. CRYPTO 2001. Lecture Notes in Computer Science, vol 2139. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-44647-8_11
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