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Diffie-Hellman & ECC·medium·35 pts

A Suspicious Generator

An active attacker swapped the generator before the exchange completed. The shared secret only has two possible values now.

A man-in-the-middle intercepted a Diffie-Hellman exchange and substituted a malicious generator with order exactly 2, before either side computed a shared secret. Whatever secret resulted, it can only be one of two possible values — regardless of either party's actual private exponent.

The flag below was XORed with that shared secret (reduced to a single byte). Try both candidate keys.

p

1000000007

g (the substituted generator, = p − 1)

1000000006

ciphertext (hex)

6565727d756b326a6a59757364617436737659653668603768636b6368727b

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Background on this technique

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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.