Abstract
We propose a new method to compute x-coordinate of kP + lQ simultaneously on the elliptic curve with Montgomery form over IFp without precomputed points. To compute x-coordinate of kP +lQ is required in ECDSA signature verification. The proposed method is about 25% faster than the method using scalar multiplication and the recovery of Y-coordinate of kP and lQ on the elliptic curve with Montgomery form over \( \mathbb{F}_p \) and also slightly faster than the simultaneous scalar multiplication on the elliptic curve with Weierstrass form over \( \mathbb{F}_p \) using NAF and mixed coordinates. Furthermore, our methodis applicable to Montgomery method on elliptic curves over \( \mathbb{F}_{2^n } \).
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Akishita, T. (2001). Fast Simultaneous Scalar Multiplication on Elliptic Curve with Montgomery Form. In: Vaudenay, S., Youssef, A.M. (eds) Selected Areas in Cryptography. SAC 2001. Lecture Notes in Computer Science, vol 2259. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-45537-X_20
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DOI: https://doi.org/10.1007/3-540-45537-X_20
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