Cramer–Shoup cryptosystem

The definition of security achieved by Cramer–Shoup is formally termed "indistinguishability under adaptive chosen ciphertext attack" (IND-CCA2). This security definition is currently the strongest definition known for a public key cryptosystem: it assumes that the attacker has access to a decryption oracle which will decrypt any ciphertext using the scheme's secret decryption key. The "adaptive" component of the security definition means that the attacker has access to this decryption oracle both before and after he observes a specific target ciphertext to attack (though he is prohibited from using the oracle to simply decrypt this target ciphertext). The weaker notion of security against non-adaptive chosen ciphertext attacks (IND-CCA1) only allows the attacker to access the decryption oracle before observing the target ciphertext.

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