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Accelerating scalar multiplication has always been a significant topic when people talk about the elliptic curve cryptosystem. Many approaches have been come up with to achieve this aim. An interesting perspective is that computers nowadays usually have multicore processors which could be used to do cryptographic computations in parallel style. Inspired by this idea, we present a new parallel and efficient algorithm to speed up scalar multiplication. First, we introduce a new regular halve-and-add method which is very efficient by utilizing projective coordinate. Then, we compare many different algorithms calculating double-and-add and halve-and-add. Finally, we combine the best double-and-add and halve-and-add methods to get a new faster parallel algorithm which costs around less than the previous best. Furthermore, our algorithm is regular without any dummy operations, so it naturally provides protection against simple side-channel attacks.

Parallel and Regular Algorithm of Elliptic Curve Scalar Multiplication over Binary Fields