Expressiveness of Definitions and Efficiency of Constructions in Computational Cryptography

Title of dissertation: EXPRESSIVENESS OF DEFINITIONS AND EFFICIENCY OF CONSTRUCTIONS IN COMPUTATIONAL CRYPTOGRAPHY David Omer Horvitz Doctor of Philosophy, 2007 Dissertation directed by: Professor Virgil Gligor Department of Electrical and Computer Eng. Professor Jonathan Katz Department of Computer Science The computational treatment of cryptography, and indeed any scientific treatment of a problem, is marked by its definitional side and by it constructive side. Results in this thesis better our understanding of both: on one side, they characterize the extent to which computational definitions capture the security of the basic task of symmetric encryption; on the other, they provide explicit bounds on the efficiency of commitment and secure two-party computation constructions. Specifically: • We relate the formal and computational treatments of symmetric encryption, obtaining a precise characterization of computational schemes whose computational semantics imply their formal semantics. We prove that this characterization is strictly weaker than previously-identified notions, and show how it may be realized in a simpler, more efficient manner. • We provide lower-bounds on the number of times a one-way permutation needs to be invoked (as a “black-box”) in order to construct statistically-binding commitments. Our bounds are tight for the case of perfectly-binding schemes. • We show that the secure computation of any two-party functionality can be performed in an optimal two rounds of communication even in a setting that accounts for concurrent execution with other protocols (i.e., the Universal Composability framework). Here, we rely on the assumption that parties have access to a common reference string; some sort of setup is known to be necessary. EXPRESSIVENESS OF DEFINITIONS AND EFFICIENCY OF CONSTRUCTIONS IN COMPUTATIONAL CRYPTOGRAPHY