(i) (20 pts) Consider the following public-key encryption scheme. The public key is (G,q, g, h = gª), and the private ke

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I 20 Pts Consider The Following Public Key Encryption Scheme The Public Key Is G Q G H Ga And The Private Ke 1 (171.06 KiB) Viewed 21 times

(i) (20 pts) Consider the following public-key encryption scheme. The public key is (G,q, g, h = gª), and the private key is x (generated the same way as in the El Gamal encryption scheme). In order to encrypt a bit b, the sender does the following: ● If b=0, choose uniform y € Z, and compute c₁ = gº and c₂ = h'. Set the ciphertext to be (C₁, C₂). • If b = 1, choose independent and uniform y, z € Zą, and compute c₁ = gº and C₂ = g². Set the ciphertext to be (C₁, C₂). (b) (12 Points) Prove that this encryption scheme is CPA secure if the decisional Diffie-Hellman problem is hard relative to the group G.