Universally composable zero-knowledge protocol using trusted platform modules

Cryptographic protocols that are established as secure in the Universally Composable (UC) model of security provide strong security assurances even when run in complex environments. Unfortunately, in order to achieve such strong security properties, UC protocols are often impractical, and most non-trivial two-party protocols cannot be secure in the UC model without some sort of external capability (or "setup assumption") being introduced. Recent work by Hofheinz et al provided an important breakthrough in designing realistic universally composable two party protocols, in which they use trusted, tamper proof hardware as a special type of helping functionality which they call a catalyst. Hofheinz et al. use government issued signature cards as a catalyst to design universally composable protocols for zero-knowledge proofs and commitments, but did not give a complete security proof for either protocol. In this thesis, we consider another form of security hardware, Trusted Platform Modules (TPMs), which are more widespread than signature cards and are currently shipped as a part of almost every business laptop or desktop. Trusted Module Platforms are tamper evident devices which support cryptographic functionalities including digital signatures, but have a different key management model from signature cards. In this thesis we consider TPMs as catalysts and describe a universally composable zero knowledge protocol using Trusted Platform Modules. We also present a complete security proof for both the Hofheinz's universally composable zero knowledge protocol from signature cards and our universally composable zero knowledge protocol using TPMs as a catalyst

A Framework for Efficient Adaptively Secure Composable Oblivious Transfer in the ROM

Oblivious Transfer (OT) is a fundamental cryptographic protocol that finds a number of applications, in particular, as an essential building block for two-party and multi-party computation. We construct a round-optimal (2 rounds) universally composable (UC) protocol for oblivious transfer secure against active adaptive adversaries from any OW-CPA secure public-key encryption scheme with certain properties in the random oracle model (ROM). In terms of computation, our protocol only requires the generation of a public/secret-key pair, two encryption operations and one decryption operation, apart from a few calls to the random oracle. In~terms of communication, our protocol only requires the transfer of one public-key, two ciphertexts, and three binary strings of roughly the same size as the message. Next, we show how to instantiate our construction under the low noise LPN, McEliece, QC-MDPC, LWE, and CDH assumptions. Our instantiations based on the low noise LPN, McEliece, and QC-MDPC assumptions are the first UC-secure OT protocols based on coding assumptions to achieve: 1) adaptive security, 2) optimal round complexity, 3) low communication and computational complexities. Previous results in this setting only achieved static security and used costly cut-and-choose techniques.Our instantiation based on CDH achieves adaptive security at the small cost of communicating only two more group elements as compared to the gap-DH based Simplest OT protocol of Chou and Orlandi (Latincrypt 15), which only achieves static security in the ROM

Efficient UC Commitment Extension with Homomorphism for Free (and Applications)

Homomorphic universally composable (UC) commitments allow for the sender to reveal the result of additions and multiplications of values contained in commitments without revealing the values themselves while assuring the receiver of the correctness of such computation on committed values. In this work, we construct essentially optimal additively homomorphic UC commitments from any (not necessarily UC or homomorphic) extractable commitment. We obtain amortized linear computational complexity in the length of the input messages and rate 1. Next, we show how to extend our scheme to also obtain multiplicative homomorphism at the cost of asymptotic optimality but retaining low concrete complexity for practical parameters. While the previously best constructions use UC oblivious transfer as the main building block, our constructions only require extractable commitments and PRGs, achieving better concrete efficiency and offering new insights into the sufficient conditions for obtaining homomorphic UC commitments. Moreover, our techniques yield public coin protocols, which are compatible with the Fiat-Shamir heuristic. These results come at the cost of realizing a restricted version of the homomorphic commitment functionality where the sender is allowed to perform any number of commitments and operations on committed messages but is only allowed to perform a single batch opening of a number of commitments. Although this functionality seems restrictive, we show that it can be used as a building block for more efficient instantiations of recent protocols for secure multiparty computation and zero knowledge non-interactive arguments of knowledge

Unconditionally Secure and Universally Composable Commitments from Physical Assumptions

We present a constant-round unconditional black-box compiler that transforms any ideal (i.e., statistically-hiding and statistically-binding) straight-line extractable commitment scheme, into an extractable and equivocal commitment scheme, therefore yielding to UC-security [9]. We exemplify the usefulness of our compiler by providing two (constant-round) instantiations of ideal straight-line extractable commitment based on (malicious) PUFs [36] and stateless tamper-proof hardware tokens [26], therefore achieving the first unconditionally UC-secure commitment with malicious PUFs and stateless tokens, respectively. Our constructions are secure for adversaries creating arbitrarily malicious stateful PUFs/tokens. Previous results with malicious PUFs used either computational assumptions to achieve UC- secure commitments or were unconditionally secure but only in the indistinguishability sense [36]. Similarly, with stateless tokens, UC-secure commitments are known only under computational assumptions [13, 24, 15], while the (not UC) unconditional commitment scheme of [23] is secure only in a weaker model in which the adversary is not allowed to create stateful tokens. Besides allowing us to prove feasibility of unconditional UC-security with (malicious) PUFs and stateless tokens, our compiler can be instantiated with any ideal straight-line extractable commitment scheme, thus allowing the use of various setup assumptions which may better fit the application or the technology available

Highly-Efficient Universally-Composable Commitments based on the DDH Assumption

Universal composability (or UC security) provides very strong security guarantees for protocols that run in complex real-world environments. In particular, security is guaranteed to hold when the protocol is run concurrently many times with other secure and possibly insecure protocols. Commitment schemes are a basic building block in many cryptographic constructions, and as such universally composable commitments are of great importance in constructing UC-secure protocols. In this paper, we construct highly efficient UC-secure commitments from the standard DDH assumption, in the common reference string model. Our commitment stage is non-interactive, has a common reference string with $O(1)$ group elements, and has complexity of $O(1)$ exponentiations for committing to a group element (to be more exact, the effective cost is that of $23\frac{1}{3}$ exponentiations overall, for both the commit and decommit stages). Our scheme is secure in the presence of static adversaries

Composability in quantum cryptography

In this article, we review several aspects of composability in the context of quantum cryptography. The first part is devoted to key distribution. We discuss the security criteria that a quantum key distribution protocol must fulfill to allow its safe use within a larger security application (e.g., for secure message transmission). To illustrate the practical use of composability, we show how to generate a continuous key stream by sequentially composing rounds of a quantum key distribution protocol. In a second part, we take a more general point of view, which is necessary for the study of cryptographic situations involving, for example, mutually distrustful parties. We explain the universal composability framework and state the composition theorem which guarantees that secure protocols can securely be composed to larger applicationsComment: 18 pages, 2 figure