Dissertation/Thesis Abstract

Efficient Cryptographic Primitives for Non-Interactive Zero-Knowledge Proofs and Applications
by Haralambiev, Kristiyan, Ph.D., New York University, 2011, 157; 3466893
Abstract (Summary)

Non-interactive zero-knowledge (NIZK) proofs have enjoyed much interest in cryptography since they were introduced more than twenty years ago by Blum et al. [BFM88]. While quite useful when designing modular cryptographic schemes, until recently NIZK could be realized efficiently only using certain heuristics. However, such heuristic schemes have been widely criticized. In this work we focus on designing schemes which avoid them. In [GS08], Groth and Sahai presented the first efficient (and currently the only) NIZK proof system in the standard model. The construction is based on bilinear maps and is limited to languages of certain satisfiable system of equations. Given this expressibility limitation of the system of equations, we are interested in cryptographic primitives that are “compatible” with it. Equipped with such primitives and the Groth-Sahai proof system, we show how to construct cryptographic schemes efficiently in a modular fashion.

In this work, we describe properties required by any cryptographic scheme to mesh well with Groth-Sahai proofs. Towards this, we introduce the notion of “structure-preserving” cryptographic scheme. We present the first constant-size structure-preserving signature scheme for messages consisting of general bilinear group elements. This allows us (for the first time) to instantiate efficiently a modular construction of round-optimal blind signature based on the framework of Fischlin [Fis06].

Our structure-preserving homomorphic trapdoor commitment schemes yield the first efficient leakage-resilient signatures (in the bounded leakage model) which satisfy the standard security requirements and additionally tolerate any amount of leakage.

Furthermore, we build a structure-preserving encryption scheme which satisfies the standard CCA security requirements. While resembling the notion of verifiable encryption, it provides better properties and yields the first efficient two-party protocol for joint ciphertext computation. Note that the efficient realization of such a protocol was not previously possible even using the heuristics mentioned above.

Lastly, we revisit the notion of simulation extractability and define “true-simulation extractable” NIZK proofs. Although quite similar to the notion of simulation-sound extractable NIZK proofs, there is a subtle but rather important difference which makes it weaker and easier to instantiate efficiently. As it turns out, in many scenarios this new notion is sufficient.

Indexing (document details)
Advisor: Shoup, Victor
Commitee: Abe, Masayuki, Camenisch, Jan, Dodis, Yevgeniy, Khot, Subhash, Shoup, Victor
School: New York University
Department: Computer Science
School Location: United States -- New York
Source: DAI-B 72/10, Dissertation Abstracts International
Subjects: Computer science
Keywords: Cryptography, Non-interactive proofs, Structure-preserving, Zero-knowledge proofs
Publication Number: 3466893
ISBN: 9781124807942
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