Equivalences and Implications
Indistinguishability is an important property for maintaining the confidentiality of encrypted communications. However, the property of indistinguishability has in some cases been found to imply other, apparently unrelated security properties. Sometimes these implications go in both directions, making two definitions equivalent; for example, it is known that the property of indistinguishability under adaptive chosen ciphertext attack (IND-CCA2) is equivalent to the property of non-malleability under the same attack scenario (NM-CCA2). This equivalence is not immediately obvious, as non-malleability is a property dealing with message integrity, rather than confidentiality. In other cases, it has been demonstrated that indistinguishability can be combined with certain other definitions, in order to imply still other useful definitions, and vice versa. The following list summarizes a few known implications, though it is by no means complete.
The notation means that property A implies property B. means that properties A and B are equivalent. means that property A does not necessarily imply property B.
- IND-CPA semantic security under CPA.
- NM-CPA (non-malleability under chosen plaintext attack) IND-CPA.
- NM-CPA (non-malleability under chosen plaintext attack) IND-CCA2.
- NM-CCA2 (non-malleability under adaptive chosen ciphertext attack) IND-CCA2.
Read more about this topic: Ciphertext Indistinguishability
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