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My question is about symmetric randomized encryption. Let c=E(k,m,r) be a randomized block encryption function where r denotes a random input chosen for each message block m. k and c denote the symmetric key and ciphertext respectively. If E has indistinguishability of m0, m1 for any chosen plaintexts by an adversary given a chphertext c of mb for a randomly chosen bit b, how does this translate to security of key k given ci for any chosen plaintexts mi by allowing oracle access to the adversary? In the deterministic encryption there is the security condition that the computation of k given p,c is infeasible. How is this property assured by indistinguishability?

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If you could guess the key, you could decrypt the challenge ciphertexts and figure out what which plaintext is which.

Conversely, if the cryptosystem has ciphertext indistinguishability in this attack model, then you obviously can't figure out which plaintext is which, so you can't guess the key.

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