Abstract
We propose a general construction of deterministic encryption schemes that unifies prior work and gives novel schemes. Specifically, its instantiations provide:
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A construction from any trapdoor function that has sufficiently many hardcore bits.
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A construction that provides “bounded” multi-message security from lossy trapdoor functions.
The security proofs for these schemes are enabled by three tools that are of broader interest:
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A weaker and more precise sufficient condition for semantic security on a high-entropy message distribution. Namely, we show that to establish semantic security on a distribution M of messages, it suffices to establish indistinguishability for all conditional distribution M|E, where E is an event of probability at least 1/4. (Prior work required indistinguishability on all distributions of a given entropy.)
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A result about computational entropy of conditional distributions. Namely, we show that conditioning on an event E of probability p reduces the quality of computational entropy by a factor of p and its quantity by log2 1/p.
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A generalization of leftover hash lemma to correlated distributions.
We also extend our result about computational entropy to the average case, which is useful in reasoning about leakage-resilient cryptography: leaking λ bits of information reduces the quality of computational entropy by a factor of 2λ and its quantity by λ.
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Fuller, B., O’Neill, A., Reyzin, L. (2012). A Unified Approach to Deterministic Encryption: New Constructions and a Connection to Computational Entropy. In: Cramer, R. (eds) Theory of Cryptography. TCC 2012. Lecture Notes in Computer Science, vol 7194. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-28914-9_33
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