What a lovely hat

Paper 2017/1165

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

Megha Byali, Arpita Patra, Divya Ravi, and Pratik Sarkar

Abstract

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.