G - 16th workshop on Elliptic Curve Cryptography
G - 16th workshop on Elliptic Curve Cryptography
G - 16th workshop on Elliptic Curve Cryptography
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Kozaki-Kutsuma-Matsuo’s method<br />
• KKM (Kozaki-Kutsuma-Matsuo’s) method [KKM07]<br />
• Che<strong>on</strong>’s algorithm iterates scalar multiplicati<strong>on</strong>s for same point<br />
• In the case of ECDLP, KKM method is not required<br />
⇒next point is calculated by <strong>on</strong>ly <strong>on</strong>e group operati<strong>on</strong><br />
• sP = s 0 P + s 1 nP + s 2 n 2 P+s 3 n 3 P = T(s 0 ,0)+T(s 1 ,1)+T(s 2 ,2)+T(s 3 3)<br />
O( log r )-group operati<strong>on</strong>s A few group operati<strong>on</strong>s<br />
T(i,j) 1 2 ・・・ n-1<br />
0 P 2 P ・・・ (n-1) P<br />
1 n P 2n P ・・・ (n-1)n P<br />
2 n 2 P 2n 2 P ・・・ (n-1)n 2 P<br />
3 n 3 P 2n 3 P ・・・ (n-1)n 3 P<br />
12<br />
Copyright 2012 FUJITSU LABORATORIES Ltd.
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