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Proposition One-wayness of ElGamal encryption holds under the Computational Diffie-Hellman (CDH), and conversely. CDH Problem (informally) Given $(P, [r]P, [s]P)$ find $[rs]P$. Let the public key be $Q = [s]P$ where $s$ is the corresponding secret key. Let also a ciphertext $C = (C_1, C_2)$ with $C_1 = [r]P$ and $C_2 = M + [r]Q$ for a message $M$ (...