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Diffie-Hellman & ECC·medium·25 pts
Recover the Signing Key
A toy elliptic curve, a public key, and the private key that produced it — small enough to brute force by hand.
A signing scheme uses the curve y² = x³ + 2x + 2 (mod 17), with base point G = (5, 1). The signer's public key Q = kG has leaked. Recover their private key k.
Curve
y² = x³ + 2x + 2 (mod 17), G = (5, 1), curve order 19
Q
(9, 1)
Hints
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Background on this technique
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Wrap, Then Decrypt →A token's wrapping key was also given decrypt rights. That single misconfiguration is enough to extract a key that was never supposed to leave.