Efficient and Universally Composable Protocols for Oblivious Transfer from the CDH Assumption

Oblivious Transfer (OT) is a simple, yet fundamental primitive which suffices to achieve almost every cryptographic application. In a recent work (Latincrypt `15), Chou and Orlandi (CO) present the most efficient, fully UC-secure OT protocol to date and argue its security under the CDH assumption. Unfortunately, a subsequent work by Genc et al. (Eprint `17) exposes a flaw in their proof which renders the CO protocol insecure. In this work, we make the following contributions: We first point out two additional, previously undiscovered flaws in the CO protocol and then show how to patch the proof with respect to static and malicious corruptions in the UC model under the stronger Gap Diffie-Hellman (GDH) assumption. With the proof failing for adaptive corruptions even under the GDH assumption, we then present a novel OT protocol which builds on ideas from the CO protocol and can be proven fully UC-secure under the CDH assumption. Interestingly, our new protocol is actually significantly more efficient (roughly by a factor of two) than the CO protocol. This improvement is made possible by avoiding costly redundancy in the symmetric encryption scheme used in the CO protocol. Our ideas can also be applied to the original CO protocol, which yields a similar gain in efficiency

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 and Round-Optimal Oblivious Transfer and Commitment with Adaptive Security

We construct the most efficient two-round adaptively secure bit-OT in the Common Random String (CRS) model. The scheme is UC secure under the Decisional Diffie-Hellman (DDH) assumption. It incurs O(1) exponentiations and sends O(1) group elements, whereas the state of the art requires O(k^2) exponentiations and communicates poly(k) bits, where k is the computational security parameter. Along the way, we obtain several other efficient UC-secure OT protocols under DDH : - The most efficient yet two-round adaptive string-OT protocol assuming programmable random oracle. Furthermore, the protocol can be made non-interactive in the simultaneous message setting, assuming random inputs for the sender. - The first two-round string-OT with amortized constant exponentiations and communication overhead which is secure in the observable random oracle model. - The first two-round receiver equivocal string-OT in the CRS model that incurs constant computation and communication overhead. We also obtain the first non-interactive adaptive string UC-commitment in the CRS model which incurs a sublinear communication overhead in the security parameter. Specifically, we commit to polylog(k) bits while communicating O(k) bits. Moreover, it is additively homomorphic in nature. We can also extend our results to the single CRS model where multiple sessions share the same CRS. As a corollary, we obtain a two-round adaptively secure MPC protocol in this model

Fast and Universally-Composable Oblivious Transfer and Commitment Scheme with Adaptive Security

Adaptive security embodies one of the strongest notions of security that allows an adversary to corrupt parties at any point during protocol execution and gain access to its internal state. Since it models real-life situations such as ``hacking , efficient adaptively-secure multiparty computation (MPC) protocols are desirable. Such protocols demand primitives such as oblivious transfer (OT) and commitment schemes that are adaptively-secure as building blocks. Efficient realizations of these primitives have been found to be challenging, especially in the no erasure model. We make progress in this direction and provide efficient constructions that are Universally-Composable in the random oracle model. Oblivious Transfer: We present the first round optimal framework for building adaptively-secure OT in the programmable random oracle (PRO) model, relying upon the framework of Peikert et al. (Crypto 2008). When instantiated with Decisional Diffie Hellman assumption, it incurs a minimal communication overhead of one k bit string and computational overhead of 5 random oracle queries over its static counterpart, where k is the security parameter. This computation overhead translates to 0.02% and 1% in the LAN and WAN setting. Additionally, we obtain a construction of adaptively-secure 1-out-of-N OT by extending the result of Naor et al. (Journal of Cryptology 2005) that transforms logN copies of 1-out-of-2 OTs to one 1-out-of-N OT in the PRO model. We complete the picture of efficient OT constructions by presenting the first adaptively secure OT Extension, extending the protocol of Asharov et al. (Eurocrypt 2015) for the adaptive setting using PRO. Our OT extension enables us to obtain adaptive OTs at an amortized cost of 3 symmetric key operations and communication of 3k bit strings. It incurs a runtime overhead of 2% and 11.95%, in the LAN and WAN setting and almost no communication overhead over the static OT extension protocol. In concrete terms, the cost is 2microsecs and 115 microsecs for each OT in LAN and WAN. Commitment Scheme: We present an adaptively secure commitment scheme in the Global Random Oracle model solely relying on observable random oracle (ORO). Our commitment scheme has a one-time offline setup phase, where a common reference string (crs) is generated between the parties using an ORO. In the online phase, the parties use the crs and ORO to generate commitments in a non-interactive fashion. Our construction incurs communication of 4k bit strings and computation of 4 exponentiations and 4 random oracle queries for committing to an arbitrary length message. Empirically, it takes around 0.18ms and 0.2 ms for committing to 128 bits and 2048 bits respectively. It finds applications in secure two-party computation (2PC) protocols that adopt offline-online paradigm, where the crs can be generated in the offline phase and the scheme can be used in the online phase

Applications of Secure Multiparty Computation

We generate and gather a lot of data about ourselves and others, some of it highly confidential. The collection, storage and use of this data is strictly regulated by laws, but restricting the use of data often limits the benefits which could be obtained from its analysis. Secure multi-party computation (SMC), a cryptographic technology, makes it possible to execute specific programs on confidential data while ensuring that no other sensitive information from the data is leaked. SMC has been the subject of academic study for more than 30 years, but first attempts to use it for actual computations in the early 2000s – although theoretically efficient – were initially not practicable. However, improvements in the situation have made possible the secure solving of even relatively large computational tasks. This book describes how many different computational tasks can be solved securely, yet efficiently. It describes how protocols can be combined to larger applications, and how the security-efficiency trade-offs of different components of an SMC application should be chosen. Many of the results described in this book were achieved as part of the project Usable and Efficient Secure Multi-party Computation (UaESMC), which was funded by the European Commission. The book will be of interest to all those whose work involves the secure analysis of confidential data

Endemic Oblivious Transfer via Random Oracles, Revisited

The notion of Endemic Oblivious Transfer (EOT) was introduced by Masny and Rindal (CCS\u2719). EOT offers a weaker security guarantee than the conventional random OT; namely, the malicious parties can fix their outputs arbitrarily. The authors presented a 1-round UC-secure EOT protocol under a tailor-made and non-standard assumption, Choose-and-Open DDH, in the RO model. In this work, we systematically study EOT in the UC/GUC framework. We present a new 1-round UC-secure EOT construction in the RO model under the DDH assumption. Under the GUC framework, we propose the first 1-round EOT construction under the CDH assumption in the Global Restricted Observable RO (GroRO) model proposed by Canetti et al. (CCS\u2714). We also provide an impossibility result, showing there exist no 1-round GUC-secure EOT protocols in the Global Restricted Programmable RO (GrpRO) model proposed by Camenisch et al. (Eurocrypt\u2718). Subsequently, we provide the first round-optimal (2-round) EOT protocol with adaptive security under the DDH assumption in the GrpRO model. Finally, we investigate the relations between EOT and other cryptographic primitives. As side products, we present the first 2-round GUC-secure commitment in the GroRO model as well as a separation between the GroRO and the GrpRO models, which may be of independent interest

Blazing Fast OT for Three-Round UC OT Extension

Oblivious Transfer (OT) is an important building block for multi-party computation (MPC). Since OT requires expensive public-key operations, efficiency-conscious MPC protocols use an OT extension (OTE) mechanism [Beaver 96, Ishai et al. 03] to provide the functionality of many independent OT instances with the same sender and receiver, using only symmetric-key operations plus few instances of some base OT protocol. Consequently there is significant interest in constructing OTE friendly protocols, namely protocols that, when used as base-OT for OTE, result in extended OT that are both round-efficient and cost-efficient. We present the most efficient OTE-friendly protocol to date. Specifically: - Our base protocol incurs only 3 exponentiations per instance. - Our base protocol results in a 3 round extended OT protocol. - The extended protocol is UC secure in the Observable Random Oracle Model (ROM) under the CDH assumption. For comparison, the state of the art for base OTs that result in 3-round OTE are proven only in the programmable ROM, and require 4 exponentiations under Interactive DDH or 6 exponentiations under DDH [Masney-Rindal 19]. We also implement our protocol and benchmark it against the Simplest OT protocol [Chou and Orlandi, Latincrypt 2015], which is the most efficient and widely used OT protocol but not known to suffice for OTE. The computation cost is roughly the same in both cases. Interestingly, our base OT is also 3 rounds. However, we slightly modify the extension mechanism (which normally adds a round) so as to preserve the number of rounds in our case

A PKI-based Framework for Establishing Efficient MPC Channels

The Transport Layer Security (TLS) protocol is a fundamental building block for ensuring security on Internet. It provides an easy to use framework for the purposes of establishing an authenticated and secure channel between two parties that have never physically met. Nevertheless, TLS only provides a simple cryptographic functionality compared to more advanced protocols such as protocols for secure multiparty computation (MPC). In this work, we provide a framework for efficiently establishing channels for MPC over the Internet. We focus on MPC protocols in the oblivious transfer (OT) hybrid model such that it is sufficient to establish OT correlations for such a channel. We revisit and combine different notions of UC security proposed in both the MPC and authenticated key exchange settings. Through this work, we show how an OT protocol can be composed with a secure authenticator to ensure the authenticity of messages sent during the OT. In addition, we adapt and analyse non-interactive OTs based on dense key encapsulation mechanisms (KEMs) in the random oracle model, where the first message, i.e. public key, can be reused. These KEMs can be instantiated based on CDH, RSA and LWE and after a performance and security evaluation, it turns out that the resulting OT protocols are very competitive with the state of the art and are able to leverage existing PKIs

A Domain Transformation for Structure-Preserving Signatures on Group Elements

We present a generic transformation that allows us to use a large class of pairing-based signatures to construct schemes for signing group elements in a structure preserving way. As a result of our transformation we obtain a new efficient signature scheme for signing a vector of group elements that is based only on the well established decisional linear assumption (DLIN). Moreover, the public keys and signatures of our scheme consist of group elements only, and a signature is verified by evaluating a set of pairing-product equations. In combination with the Groth-Sahai proof system, such a signature scheme is an ideal building block for many privacy-enhancing protocols. To do this, we start by proposing a new stateful signature scheme for signing vectors of exponents that is F-unforgeable under weak chosen message attacks. This signature scheme is of independent interest as it is compatible with Groth-Sahai proofs and secure under a computational assumption implied by DLIN. Then we give a general transformation for signing group elements based on signatures (for signing exponents) with efficient non-interactive zero-knowledge proofs. This transform also removes any dependence on state in the signature used to sign exponents. Finally, we obtain our result by instantiating this transformation with the above signature scheme and Groth-Sahai proofs