Claudio Orlandi

Oblivious Transfer (OT) is a fundamental cryptographic primitive and a core building block for many multiparty cryptographic protocols. While existing OT extension techniques achieve excellent asymptotic efficiency for very large batches, their performance degrades when the total number of OTs is only moderate, since the cost of generating the required base OTs is no longer effectively amortized. In this work, we close this gap by presenting OT constructions that achieve square-root communication complexity for batched OT generation. Concretely, our most efficient protocol generates ell random OTs using O(lambda sqrt(ell)) bits of communication, where lambda is the security parameter. Our constructions are inspired by recent advances in homomorphic secret sharing and techniques for distributed discrete logarithm computation, and explore complementary points in the design space. The first construction is based on the Damgård-Jurik cryptosystem and standard assumptions, at the cost of a one-time trusted setup. The second eliminates the need for trusted setup, relying instead on a power-DDH assumption over prime-order groups. For 128-bit security, our schemes require approximately 2.6 KiB and 1.25 KiB of communication, respectively, to generate 128 random OTs, including the hash key in the power-DDH construction. Our best construction outperforms existing OT extension techniques for batch sizes of up to 32,768 OTs.

Given a collection of vectors \boldsymbolx ^(1), \dots,\boldsymbolx ^(n) \in \0,1\ ^d, the selection problem asks to report the index of an "approximately largest'' entry in \boldsymbolx =\sum_j=1 ^n \boldsymbolx ^(j) . Selection abstracts a host of problems, for example: Recommendation of a popular item based on user feedback; releasing statistics on the most popular web sites; hyperparameter tuning and feature selection in machine learning. We study selection under differential privacy, where a released index guarantees privacy for individual vectors. Though selection can be solved with an excellent utility guarantee in the central model of differential privacy, the distributed setting where no single entity is trusted to aggregate the data lacks solutions. Specifically, strong privacy guarantees with high utility are offered in high trust settings, but not in low trust settings. For example, in the popular shuffle model of distributed differential privacy, there are strong lower bounds suggesting that the utility of the central model cannot be obtained. In this paper we design a protocol for differentially private selection in a trust setting similar to the shuffle model---with the crucial difference that our protocol tolerates corrupted servers while maintaining privacy. Our protocol uses techniques from secure multi-party computation (MPC) to implement a protocol that: (i) has utility on par with the best mechanisms in the central model, (ii) scales to large, distributed collections of high-dimensional vectors, and (iii) uses k\geq 3 servers that collaborate to compute the result, where the differential privacy guarantee holds assuming an honest majority. Since general-purpose MPC techniques are not sufficiently scalable, we propose a novel application of integer secret sharing, and evaluate the utility and efficiency of our protocol both theoretically and empirically. Our protocol improves on previous work by Champion, shelat and Ullman (CCS '19) by significantly reducing the communication costs, demonstrating that large-scale differentially private selection with information-theoretical guarantees is feasible in a distributed setting.

Secure distributed generation of RSA moduli (e.g., generating N=pq where none of the parties learns anything about p or q) is an important cryptographic task, that is needed both in threshold implementations of RSA-based cryptosystems and in other, advanced cryptographic protocols that assume that all the parties have access to a trusted RSA modulo. In this paper, we provide a novel protocol for secure distributed RSA key generation based on the Miller-Rabin test. Compared with the more commonly used Boneh-Franklin test (which requires many iterations), the Miller-Rabin test has the advantage of providing negligible error after even a single iteration of the test for large enough moduli (e.g., 4096 bits). From a technical point of view, our main contribution is a novel divisibility test which allows to perform the primality test in an efficient way, while keeping p and q secret. Our semi-honest RSA generation protocol uses any underlying secure multiplication protocol in a black-box way, and our protocol can therefore be instantiated in both the honest or dishonest majority setting based on the chosen multiplication protocol. Our semi-honest protocol can be upgraded to protect against active adversaries at low cost using existing compilers. Finally, we provide an experimental evaluation showing that for the honest majority case, our protocol is much faster than Boneh-Franklin.