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Consider a scenario in which an adversary, attacking a certain public key encryption scheme, gains knowledge of several ciphertexts which underlying plaintext are meaningfully related with a given target ciphertext. This kind of related message attack has been proved successful against several public key encryption schemes; widely known is the Franklin-Reiter attack to RSA with low exponent and its subsequent improvement by Coppersmith. However, to the best of the knowledge no formal treatment of these type of attacks has to date been done, and as a result, it has not been rigorously studied which of the "Standard" security notions imply resilience to them.
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