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.

中文翻译：

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二元域上椭圆曲线标量乘法的并行和正则算法。

当人们谈论椭圆曲线密码系统时，加速标量乘法一直是一个重要的话题。为了达到这个目的，已经提出了许多方法。一个有趣的观点是，当今的计算机通常具有多核处理器，可用于以并行方式进行密码计算。受这个想法的启发，我们提出了一种新的并行高效算法来加速标量乘法。首先，我们介绍了一种新的常规半减法，该方法通过利用投影坐标非常有效。然后，我们比较了计算重复加法和减半加法的许多不同算法。最后，我们结合最佳的加法和减法来获得一种新的更快的并行算法，其成本约为少于以前的最好。此外，我们的算法是常规的，没有任何虚拟操作，因此自然可以提供针对简单边信道攻击的保护。