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Wiki definition :
A cryptosystem is considered secure in terms of indistinguishability if no adversary, given an encryption of a message randomly chosen from a two-element message space determined by the adversary, can identify the message choice with probability significantly better than that of random guessing (1⁄2). If any adversary can succeed in distinguishing the chosen ciphertext with a probability significantly greater than 1⁄2, then this adversary is considered to have an "advantage" in distinguishing the ciphertext, and the scheme is not considered secure in terms of indistinguishability. This definition encompasses the notion that in a secure scheme, the adversary should learn no information from seeing a ciphertext. Therefore, the adversary should be able to do no better than if it guessed randomly.
I understood the meaning of this but what do you mean by
Indistinguishability under chosen-plaintext attack and
Indistinguishability under chosen ciphertext attack ? Could anyone give me an example, and answer in easy understanding language.