Encryption security against key-dependent-message attacks: applications, realizations and separations

Date

2016-08-17

Authors

Hajiabadi, Mohammad

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Abstract

In this thesis we study the notion of circular security for bit-encryption schemes. Informally speaking, a bit-encryption scheme is circular secure if it remains secure even if the key of the system is used to encrypt its own individual bits. This notion (or slight extensions thereof) has foundational applications, most notably in the context of fully-homomorphic encryption and amplification techniques for key dependent- message security. We explore the notion of circular security from three different perspectives, stemming from (1) assumptions sufficient to realize this notion, (2) minimal black-box assumptions on which this notion can be based and (c) applications of this notion when combined with other properties. Our main results are as follows: We give a construction of circular-secure public-key bit encryption based on any public-key encryption scheme that satisfies two special properties. We show that our constructed scheme besides circular security also offers two forms of key-leakage resilience. Our construction unifies two existing specific constructions of circular-secure schemes in the literature and also gives rise to the first construction based on homomorphic hash proof systems. We show that seed-circular-secure public-key bit-encryption schemes cannot be based on semantically-secure public-key encryption schemes in a fully-blackbox way. A scheme is seed-circular-secure if it allows for the bits of the seed (used to generate the public/secret keys) to be securely encrypted under the corresponding public key. We then extend this result to rule out a large and non-trivial class of constructions for circular security that we call key-isolating constructions. We give generic constructions of several fundamental cryptographic primitives based on a public-key bit-encryption scheme that combines circular security with a structural property called reproducibility. The main primitives that we build include families of trapdoor functions with strong security properties (i.e., one-wayness under correlated inputs), adaptive-chosen-ciphertext (CCA2) secure encryption schemes and deterministic encryption schemes.

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Keywords

Data encryption (Computer science), Public key cryptography

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