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Efficient elliptic curve exponentiation using mixed coordinates. (English) Zbl 0939.11039
Ohta, Kazuo (ed.) et al., Advances in cryptology - ASIACRYPT ’98. International conference on the Theory and application of cryptology and information security, Beijing, China, October 18-22, 1998. Proceedings. Berlin: Springer. Lect. Notes Comput. Sci. 1514, 51-65 (1998).

Elliptic curve cryptosystems are becoming increasingly used in practical applications since they offer improved performance and reduced bandwidth and memory. Central to this industrial interest is the fact that a number of ways exist to significantly improve the performance of such systems. This paper describes another such way.

The authors describe four coordinate systems for points on an elliptic curve, namely Affine, Projective, Jacobian and Chudnovsky. Then using these coordinate systems they describe ways to implement the essential cryptographic operation of point multiplication. This is done using a novel combination of the four coordinate systems, which they dub “mixed coordinates”.

The paper is well written and gives a number of examples and explicit formulae which will be useful to engineers working in this area who often find the mathematics in some papers quite duanting. Overall the authors report an improvement of twenty five percent in the performance of the final system. Although the paper describes the details in terms of curves over finite fields of large prime characteristic, it is clear that a similar mixed coordinate system works in fields of even characteristic as well.

MSC:
11Y16Algorithms; complexity (number theory)
11G05Elliptic curves over global fields
94A60Cryptography
14H50Plane and space curves