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**2003/088**

**Title:**

Elliptic Curve Point Multiplication

**Authors:**
A. G. Rostovtsev, 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.

**ePrint:**
https://eprint.iacr.org/2003/088

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