**Elliptic Curve Point Multiplication**

*A.G.Rostovtsev and E.B.Makhovenko*

**Abstract: **A method for elliptic curve point multiplication is proposed with complex multiplication by Sqrt[-2] or by (1+Sqrt[-7])/2 instead of point duplication, speeding up multiplication about 1.34 times. Higher radix makes it possible to use one point duplication instead of two and to speed up computation about 1.6 times. We employ prime group order factorization in corresponding quadratic order and integer exponent reduction modulo quadratic prime in the Euclidean imaginary quadratic ring.

**Category / Keywords: **implementation / elliptic curve cryptosystem; complex multiplication; fast algorithms

**Date: **received 5 May 2003

**Contact author: **rostovtsev at ssl stu neva ru

**Available format(s): **PDF | BibTeX Citation

**Version: **20030507:184213 (All versions of this report)

**Short URL: **ia.cr/2003/088

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