Speeding up elliptic scalar multiplication using multidoubling
Y Sakai, K Sakurai - IEICE transactions on fundamentals of …, 2002 - search.ieice.org
Y Sakai, K Sakurai
IEICE transactions on fundamentals of electronics, communications and …, 2002•search.ieice.orgWe discuss multidoubling methods for efficient elliptic scalar multiplication. The methods
allows computation of 2 k P directly from P without computing the intermediate points, where
P denotes a randomly selected point on an elliptic curve. We introduce algorithms for elliptic
curves with Montgomery form and Weierstrass form defined over finite fields with
characteristic greater than 3 in terms of affine coordinates. These algorithms are faster than k
repeated doublings. Moreover, we apply the algorithms to scalar multiplication on elliptic …
allows computation of 2 k P directly from P without computing the intermediate points, where
P denotes a randomly selected point on an elliptic curve. We introduce algorithms for elliptic
curves with Montgomery form and Weierstrass form defined over finite fields with
characteristic greater than 3 in terms of affine coordinates. These algorithms are faster than k
repeated doublings. Moreover, we apply the algorithms to scalar multiplication on elliptic …
We discuss multidoubling methods for efficient elliptic scalar multiplication. The methods allows computation of 2k P directly from P without computing the intermediate points, where P denotes a randomly selected point on an elliptic curve. We introduce algorithms for elliptic curves with Montgomery form and Weierstrass form defined over finite fields with characteristic greater than 3 in terms of affine coordinates. These algorithms are faster than k repeated doublings. Moreover, we apply the algorithms to scalar multiplication on elliptic curves and analyze computational complexity. As a result of our implementation with respect to the Montgomery and Weierstrass forms in terms of affine coordinates, we achieved running time reduced by 28% and 31%, respectively, in the scalar multiplication of an elliptic curve of size 160-bit over finite fields with characteristic greater than 3.
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