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This result is proven in the following research papers: Johan Hastad, Mats Naslund. The Security of all RSA and Discrete Log Bits. Journal of the ACM, Oct 2003, pp.1--45. W. Alexi, B. Chor, O. Goldrech, C. Schnorr. RSA and Rabin functions: Certain parts are as hard as the whole. SIAM Journal on Computing, vol 17 no 2, pp.194--209. They show that if ...

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It's hard to be sure without seeing a bit more context, but the paragraph you quoted looks like it's part of a definition of IND-CPA security (ciphertext indistinguishability under a chosen-plaintext attack) for public-key ciphers. Here's the corresponding definition from the Wikipedia article I linked to above: "For a probabilistic asymmetric key ...

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No there are not equivalent those two notions. Here is the explanation: The game in IND-CCA is the following: Setup: The challenger gives the public parameters to the adversary. Phase 1: The adversary is asking for as many encryptions of plaintexts through the encryption oracle. Phase 2: The adversary then is asking for as many decryptions of ciphertexts ...

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