Elliptic Curve Point Multiplication.
Alexander Rostovtsev, Elena Makhovenko · 2003
New type of elliptic curve point multiplication is proposed, where complex multiplication by - 2 or by (1 _+ x/)/2 is used instead of point duplication. This allows speeding up multiplication about 1.34 times. Us- ing higher radix makes it possible to use one point duplication instead of two and to speed-up computation about 1.6 times. The method takes prime group order factorization: r = p and integer exponent reduction modulo quadratic prime p in the Euclidean imaginary quadratic ring.