Paper 2016/940

Fast Actively Secure OT Extension for Short Secrets

Arpita Patra, Pratik Sarkar, and Ajith Suresh

Abstract

Oblivious Transfer (OT) is one of the most fundamental cryptographic primitives with wide-spread application in general secure multi-party computation (MPC) as well as in a number of tailored and special-purpose problems of interest such as private set intersection (PSI), private information retrieval (PIR), contract signing to name a few. Often the instantiations of OT require prohibitive communication and computation complexity. OT extension protocols are introduced to compute a very large number of OTs referred as extended OTs at the cost of a small number of OTs referred as seed OTs. We present a fast OT extension protocol for small secrets in active setting. Our protocol when used to produce $1$-out-of-$n$ OTs outperforms all the known actively secure OT extensions. Our protocol is built on the semi-honest secure extension protocol of Kolesnikov and Kumaresan of CRYPTO'13 (referred as KK13 protocol henceforth) which is the best known OT extension for short secrets. At the heart of our protocol lies an efficient consistency checking mechanism that relies on the linearity of Walsh-Hadamard (WH) codes. Asymptotically, our protocol adds a communication overhead of $O(\mu \log{\kappa})$ bits over KK13 protocol irrespective of the number of extended OTs, where $\kappa$ and $\mu$ refer to computational and statistical security parameter respectively. Concretely, our protocol when used to generate a large enough number of OTs adds only $0.011-0.028\%$ communication overhead and $4-6\%$ runtime overhead both in LAN and WAN over KK13 extension. The runtime overheads drop below $2\%$ when in addition the number of inputs of the sender in the extended OTs is large enough. As an application of our proposed extension protocol, we show that it can be used to obtain the most efficient PSI protocol secure against a malicious receiver and a semi-honest sender.