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. / Graduate / 0984
| Identifer | oai:union.ndltd.org:uvic.ca/oai:dspace.library.uvic.ca:1828/7454 |
| Date | 17 August 2016 |
| Creators | Hajiabadi, Mohammad |
| Contributors | Kapron, Bruce M. (Bruce Michael) |
| Source Sets | University of Victoria |
| Language | English, English |
| Detected Language | English |
| Type | Thesis |
| Rights | Available to the World Wide Web |
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