Abstract
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 λ 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 12.0% less than the previous best. Furthermore, our algorithm is regular without any dummy operations, so it naturally provides protection against simple side-channel attacks.
Highlights
E efficiency of elliptic curve cryptosystem (ECC) is dominated by the speed of calculating scalar multiplication
Different power and time consumption of this two prominent building blocks can be detected by simple power analysis (SPA) [3] and timing attack—this naive implementation leads to information leakage of secret scalar k
Protecting against simple side-channel attacks (SSCA) can be achieved by recoding scalars in a regular manner, meaning that scalar multiplications are executed in the same instructions in the same order for any input value
Summary
We focus on elliptic curves E defined over binary fields F2m , by the Weierstrass equation: y2 + xy x3 + ax2 + b,. ALGORITHM 1: Regular ZSD halve-and-add (left-to-right) method
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