International Association for Cryptologic Research

International Association
for Cryptologic Research

CryptoDB

Daniel Escudero

Publications

Year
Venue
Title
2020
CRYPTO
Improved Primitives for MPC over Mixed Arithmetic-Binary Circuits 📺
This work introduces novel techniques to improve the translation between arithmetic and binary data types in multi-party computation. To this end, we introduce a new approach to performing these conversions, using what we call \emph{extended doubly-authenticated bits} (edaBits), which correspond to shared integers in the arithmetic domain whose bit decomposition is shared in the binary domain. These can be used to considerably increase the efficiency of non-linear operations such as truncation, secure comparison and bit-decomposition. Our eDaBits are similar to the \emph{daBits} technique introduced by Rotaru et al.~(Indocrypt 2019). However, our main observations are that (1) applications that benefit from daBits can also benefit from edaBits in the same way, and (2) we can generate edaBits directly in a much more efficeint way than computing them directly from a set of DaBits. Technically, the second contribution is much more challenging, and involves a novel cut and choose technique that may be of independent interest, and requires taking advantage of natural tamper-resilient properties of binary circuits that occur in our construction to obtain the best level of efficiency. Finally, we show how our eDaBits can be applied to efficiently implement various non-linear protocols of interest, and we thoroughly analyze their correctness for both signed and unsigned integers. The results of this work can be applied to any corruption threshold, although they seem best suited to dishonest majority protocols such as SPDZ. We implement and benchmark our constructions, and experimentally verify that our technique yield a substantial increase in effiency. Our eDaBits save in communication by a factor that lies between $2$ and $170$ for secure comparisons with respect to a purely arithmetic approach, and between $2$ and $60$ with respect to using daBits. Improvements in throughput per second are more subdued but still as high as a factor of $47$. We also apply our novel machinery to the tasks of biometric matching and convolutional neural networks, obtaining a noticeable improvement as well.
2019
TCC
Efficient Information-Theoretic Secure Multiparty Computation over $\mathbb {Z}/p^k\mathbb {Z}$ via Galois Rings
At CRYPTO 2018, Cramer et al. introduced a secret-sharing based protocol called SPD$$\mathbb {Z}_{2^k}$$ that allows for secure multiparty computation (MPC) in the dishonest majority setting over the ring of integers modulo $$2^k$$, thus solving a long-standing open question in MPC about secure computation over rings in this setting. In this paper we study this problem in the information-theoretic scenario. More specifically, we ask the following question: Can we obtain information-theoretic MPC protocols that work over rings with comparable efficiency to corresponding protocols over fields? We answer this question in the affirmative by presenting an efficient protocol for robust Secure Multiparty Computation over $$\mathbb {Z}/p^{k}\mathbb {Z}$$ (for any prime p and positive integer k) that is perfectly secure against active adversaries corrupting a fraction of at most 1/3 players, and a robust protocol that is statistically secure against an active adversary corrupting a fraction of at most 1/2 players.
2018
CRYPTO
SPD$\mathbb {Z}_{2^k}$: Efficient MPC mod $2^k$ for Dishonest Majority 📺
Most multi-party computation protocols allow secure computation of arithmetic circuits over a finite field, such as the integers modulo a prime. In the more natural setting of integer computations modulo $$2^{k}$$, which are useful for simplifying implementations and applications, no solutions with active security are known unless the majority of the participants are honest.We present a new scheme for information-theoretic MACs that are homomorphic modulo $$2^k$$, and are as efficient as the well-known standard solutions that are homomorphic over fields. We apply this to construct an MPC protocol for dishonest majority in the preprocessing model that has efficiency comparable to the well-known SPDZ protocol (Damgård et al., CRYPTO 2012), with operations modulo $$2^k$$ instead of over a field. We also construct a matching preprocessing protocol based on oblivious transfer, which is in the style of the MASCOT protocol (Keller et al., CCS 2016) and almost as efficient.