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oai:drum.lib.umd.edu:1903/203172018-01-24T04:18:36Zcom_1903_2224com_1903_12com_1903_2col_1903_2756col_1903_3

Katz, Jonathan Apon, Daniel Christopher Digital Repository at the University of Maryland University of Maryland (College Park, Md.) Computer Science 2018-01-23T06:36:46Z 2018-01-23T06:36:46Z 2017 https://doi.org/10.13016/M23R0PV71 http://hdl.handle.net/1903/20317 In this dissertation, we explore the frontiers of theory of cryptography along two lines. In the first direction, we explore Lattice Cryptography, which is the primary sub-area of post-quantum cryptographic research. Our first contribution is the construction of a deniable attribute-based encryption scheme from lattices. A deniable encryption scheme is secure against not only eavesdropping attacks as required by semantic security, but also stronger coercion attacks performed after the fact. An attribute-based encryption scheme allows ``fine-grained'' access to ciphertexts, allowing for a decryption access policy to be embedded in ciphertexts and keys. We achieve both properties simultaneously for the first time from lattices. Our second contribution is the construction of a digital signature scheme that enjoys both short signatures and a completely tight security reduction from lattices. As a matter of independent interest, we give an improved method of randomized inversion of the G gadget matrix, which reduces the noise growth rate in homomorphic evaluations performed in a large number of lattice-based cryptographic schemes, without incurring the high cost of sampling discrete Gaussians. In the second direction, we explore Cryptographic Program Obfuscation. A program obfuscator is a type of cryptographic software compiler that outputs executable code with the guarantee that ``whatever can be hidden about the internal workings of program code, is hidden.'' Indeed, program obfuscation can be viewed as a ``universal and cryptographically-complete'' tool. Our third contribution is the first, full-scale implementation of secure program obfuscation in software. Our toolchain takes code written in a C-like programming language, specialized for cryptography, and produces secure, obfuscated software. Our fourth contribution is a new cryptanalytic attack against a variety of ``early'' program obfuscation candidates. We provide a general, efficiently-testable property for any two branching programs, called partial inequivalence, which we show is sufficient for launching an ``annihilation attack'' against several obfuscation candidates based on Garg-Gentry-Halevi multilinear maps. en Frontiers in Lattice Cryptography and Program Obfuscation Dissertation Mathematics Horticulture Cryptography Lattices Obfuscation open.access