Deterministic and efficiently searchable encryption
CRYPTO'07 Proceedings of the 27th annual international cryptology conference on Advances in cryptology
Better security for deterministic public-key encryption: the auxiliary-input setting
CRYPTO'11 Proceedings of the 31st annual conference on Advances in cryptology
TCC'12 Proceedings of the 9th international conference on Theory of Cryptography
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The symmetric encryption problem which manifests itself when two parties must securely transmit a message m with a short shared secret key is considered in conjunction with a computationally unbounded adversary. As the adversary is unbounded, any encryption scheme must leak information about m; in particular, the mutual information between m and its ciphertext cannot be zero. Despite this, a family of encryption schemes is presented that guarantee that for any message space in {0,1}n with minimum entropy n-lscr and for any Boolean function h:{0,1}n rarr {0,1}, no adversary can predict h(m) from the ciphertext of m with more than 1/nomega(1) advantage; this is achieved with keys of length lscr+omega(logn). In general, keys of length lscr+s yield a bound of 2-Theta(s) on the advantage. These encryption schemes rely on no unproven assumptions and can be implemented efficiently. Applications of this to cryptosystems based on complexity-theoretic assumptions are discussed and, in addition, a simplified proof of a fundamental "elision lemma" of Goldwasser and Micali is provided