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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Che<strong>on</strong>’s Algorithm<br />
• Input: G, G 1 =xG, G d =x d G ∈ G, d|(r-1)<br />
• Output: x ∈ Z/rZ<br />
• Approach<br />
• Instead of finding x directly, find an integer k such that x = ζ k for a<br />
generator ζ∈ (Z/rZ)*<br />
• Che<strong>on</strong>’s algorithm finds k1, k2 such that k = k1 + k2 (r-1)/d in two steps<br />
• Procedures<br />
• Find k1 such that G d = ζ d<br />
k1<br />
G (for ζ d = ζ d )<br />
• Set e ← (r-1)/d, G e ← ζ -k1 G 1<br />
• Find k2 such that G e = ζ e<br />
k2<br />
G for (for ζ e = ζ e )<br />
• Output x = ζ k for k = k1 + k2×e<br />
Step 1<br />
Step 2<br />
8<br />
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