Publicly Verifiable Zero-Knowledge and Post-Quantum Signatures From VOLE-in-the-Head
We present a new method for transforming zero-knowledge protocols in the designated verifier setting into public-coin protocols, which can be made non-interactive and publicly verifiable. Our transformation applies to a large class of ZK protocols based on oblivious transfer. In particular, we show that it can be applied to recent, fast protocols based on vector oblivious linear evaluation (VOLE), with a technique we call VOLE-in-the-head, upgrading these protocols to support public verifiability. Our resulting ZK protocols have linear proof size, and are simpler, smaller and faster than related approaches based on MPC-in-the-head. To build VOLE-in-the-head while supporting both binary circuits and large finite fields, we develop several new technical tools. One of these is a new proof of security for the SoftSpokenOT protocol (Crypto 2022), which generalizes it to produce certain types of VOLE correlations over large fields. Secondly, we present a new ZK protocol that is tailored to take advantage of this form of VOLE, which leads to a publicly verifiable VOLE-in-the-head protocol with only 2x more communication than the best, designated-verifier VOLE-based protocols. We analyze the soundness of our approach when made non-interactive using the Fiat-Shamir transform, using round-by-round soundness. As an application of the resulting NIZK, we present FAEST, a post-quantum signature scheme based on AES. FAEST is the first AES-based signature scheme to be smaller than SPHINCS+, with signature sizes between 5.6 and 6.6kB at the 128-bit security level. Compared with the smallest version of SPHINCS+ (7.9kB), FAEST verification is slower, but the signing times are between 8x and 40x faster.
MPC With Delayed Parties Over Star-Like Networks
This paper examines multi-party computation protocols in the presence of two major constraints present in deployed systems. Firstly, we consider the situation where the parties are connected not by direct point-to-point connections, but by a star-like topology with a few central post-office style relays. Secondly, we consider MPC protocols with a strong honest majority ($t \gg n/2$) in which we have stragglers (some parties are progressing slower than others). We model stragglers by allowing the adversary to delay messages to and from some parties for a given length of time. We first show that having only a single honest relay is enough to ensure consensus of the messages sent within a protocol; secondly, we show that special care must be taken to describe multiplication protocols in the case of relays and stragglers; thirdly, we present an efficient honest-majority MPC protocol which can be run ontop of the relays and which provides active-security with abort in the case of a strong honest majority, even when run with stragglers. We back up our protocol presentation with both experimental evaluations and simulations of the effect of the relays and delays on our protocol.
Four-Round Black-Box Non-Malleable Commitments from One-Way Permutations
We construct the first four-round non-malleable commitment scheme based solely on the black-box use of one-to-one one-way functions. Prior to our work, all non-malleable commitment schemes based on black-box use of polynomial-time cryptographic primitives require more than 16 rounds of interaction. A key tool for our construction is a proof system that satisfies a new definition of security that we call non-malleable zero-knowledge with respect to commitments. In a nutshell, such a proof system can be safely run in parallel with any (potentially interactive) commitment scheme. We provide an instantiation of this tool using the MPC-in-the-Head approach in combination with BMR. The resulting protocol makes black-box use of one-to-one one-way functions.
TinyKeys: A New Approach to Efficient Multi-Party Computation
We present a new approach to designing concretely efficient MPC protocols with semi-honest security in the dishonest majority setting. Motivated by the fact that within the dishonest majority setting the efficiency of most practical protocols does not depend on the number of honest parties , we investigate how to construct protocols which improve in efficiency as the number of honest parties increases. Our central idea is to take a protocol which is secure for $$n-1$$ n - 1 corruptions and modify it to use short symmetric keys, with the aim of basing security on the concatenation of all honest parties’ keys. This results in a more efficient protocol tolerating fewer corruptions, whilst also introducing an LPN-style syndrome decoding assumption. We first apply this technique to a modified version of the semi-honest GMW protocol, using OT extension with short keys, to improve the efficiency of standard GMW with fewer corruptions. We also obtain more efficient constant-round MPC, using BMR-style garbled circuits with short keys, and present an implementation of the online phase of this protocol. Our techniques start to improve upon existing protocols when there are around $$n=10$$ n = 10 parties with $$h=4$$ h = 4 honest parties, and as these increase we obtain up to a 13 times reduction (for $$n=400,h=120$$ n = 400 , h = 120 ) in communication complexity for our GMW variant, compared with the best-known GMW-based protocol modified to use the same threshold.
High-Performance Multi-party Computation for Binary Circuits Based on Oblivious Transfer
We present a unified view of the two-party and multi-party computation protocols based on oblivious transfer first outlined in Nielsen et al. (CRYPTO 2012) and Larraia et al. (CRYPTO 2014). We present a number of modifications and improvements to these earlier presentations, as well as full proofs of the entire protocol. Improvements include a unified pre-processing and online MAC methodology, mechanisms to pass between different MAC variants and fixing a minor bug in the protocol of Larraia et al. in relation to a selective failure attack. It also fixes a minor bug in Nielsen et al. resulting from using Jensen’s inequality in the wrong direction in an analysis.
Large Scale, Actively Secure Computation from LPN and Free-XOR Garbled Circuits 📺
Whilst secure multiparty computation (MPC) based on garbled circuits is concretely efficient for a small number of parties $n$, the gap between the complexity of practical protocols, which is $O(n^2)$ per party, and the theoretical complexity, which is $O(n)$ per party, is prohibitive for large values of $n$. In order to bridge this gap, Ben-Efraim, Lindell and Omri (ASIACRYPT 2017) introduced a garbled-circuit-based MPC protocol with an almost-practical pre-processing, yielding $O(n)$ complexity per party. However, this protocol is only passively secure and does not support the free-XOR technique by Kolesnikov and Schneider (ICALP 2008), on which almost all practical garbled-circuit-based protocols rely on for their efficiency. In this work, to further bridge the gap between theory and practice, we present a new $n$-party garbling technique based on a new variant of standard LPN-based encryption. Using this approach we can describe two new garbled-circuit based protocols, which have practical evaluation phases. Both protocols are in the preprocessing model, have $O(n)$ complexity per party, are actively secure and support the free-XOR technique. The first protocol tolerates full threshold corruption and ensures the garbled circuit contains no adversarially introduced errors, using a rather expensive garbling phase. The second protocol assumes that at least $n/c$ of the parties are honest (for an arbitrary fixed value $c$) and allows a significantly lighter preprocessing, at the cost of a small sacrifice in online efficiency. We demonstrate the practicality of our approach with an implementation of the evaluation phase using different circuits. We show that like the passively-secure protocol of Ben-Efraim, Lindell and Omri, our approach starts to improve upon other practical protocols with $O(n^2)$ complexity when the number of parties is around $100$.
Banquet: Short and Fast Signatures from AES 📺
In this work we introduce Banquet, a digital signature scheme with post-quantum security, constructed using only symmetric-key primitives. The design is based on the MPC-in-head paradigm also used by Picnic (CCS 2017) and BBQ (SAC 2019). Like BBQ, Banquet uses only standardized primitives, namely AES and SHA-3, but signatures are more than 50\% shorter, making them competitive with Picnic (which uses a non-standard block cipher to improve performance). The MPC protocol in Banquet uses a new technique to verify correctness of the AES S-box computations, which is efficient because the cost is amortized with a batch verification strategy. Our implementation and benchmarks also show that both signing and verification can be done in under 10ms on a current x64 CPU. We also explore the parameter space to show the range of trade-offs that are possible with the Banquet design, and show that Banquet can nearly match the signature sizes possible with Picnic (albeit with slower, but still practical run times) or have speed within a factor of two of Picnic (at the cost of larger signatures).
Efficient Constant-Round MPC with Identifiable Abort and Public Verifiability 📺
Recent years have seen a tremendous growth in the interest in se- cure multiparty computation (MPC) and its applications. While much progress has been made concerning its efficiency, many current, state-of-the-art protocols are vulnerable to Denial of Service attacks, where a cheating party may prevent the honest parties from learning the output of the computation, whilst remaining anonymous. The security model of identifiable abort aims to prevent these at- tacks, by allowing honest parties to agree upon the identity of a cheating party, who can then be excluded in the future. Several existing MPC protocols offer security with identifiable abort against a dishonest majority of corrupted parties. However, all of these protocols have a round complexity that scales linearly with the depth of the circuit (and are therefore unsuitable for use in high latency net- works) or use cryptographic primitives or techniques that have a high computa- tional overhead. In this work, we present the first efficient MPC protocols with identifiable abort in the dishonest majority setting, which run in a constant number of rounds and make only black-box use of cryptographic primitives. Our main construction is built from highly efficient primitives in a careful way to achieve identifiability at a low cost. In particular, we avoid the use of public-key operations outside of a setup phase, incurring a relatively low overhead on top of the fastest currently known constant-round MPC protocols based on garbled circuits. Our construction also avoids the use of adaptively secure primitives and heavy zero-knowledge machinery, which was inherent in previous works. In addition, we show how to upgrade our protocol to achieve public verifiability using a public bulletin board, allowing any external party to verify correctness of the computation or identify a cheating party.
TinyKeys: A New Approach to Efficient Multi-Party Computation 📺
We present a new approach to designing concretely efficient MPC protocols with semi-honest security in the dishonest majority setting. Motivated by the fact that within the dishonest majority setting the efficiency of most practical protocols does not depend on the number of honest parties, we investigate how to construct protocols which improve in efficiency as the number of honest parties increases. Our central idea is to take a protocol which is secure for $$n-1$$ n-1 corruptions and modify it to use short symmetric keys, with the aim of basing security on the concatenation of all honest parties’ keys. This results in a more efficient protocol tolerating fewer corruptions, whilst also introducing an LPN-style syndrome decoding assumption.We first apply this technique to a modified version of the semi-honest GMW protocol, using OT extension with short keys, to improve the efficiency of standard GMW with fewer corruptions. We also obtain more efficient constant-round MPC, using BMR-style garbled circuits with short keys, and present an implementation of the online phase of this protocol. Our techniques start to improve upon existing protocols when there are around $$n=20$$ n=20 parties with $$h=6$$ h=6 honest parties, and as these increase we obtain up to a 13 times reduction (for $$n=400, h=120$$ n=400,h=120) in communication complexity for our GMW variant, compared with the best-known GMW-based protocol modified to use the same threshold.
Concretely Efficient Large-Scale MPC with Active Security (or, TinyKeys for TinyOT)
In this work we develop a new theory for concretely efficient, large-scale MPC with active security. Current practical techniques are mostly in the strong setting of all-but-one corruptions, which leads to protocols that scale badly with the number of parties. To work around this issue, we consider a large-scale scenario where a small minority out of many parties is honest and design scalable, more efficient MPC protocols for this setting. Our results are achieved by introducing new techniques for information-theoretic MACs with short keys and extending the work of Hazay et al. (CRYPTO 2018), which developed new passively secure MPC protocols in the same context. We further demonstrate the usefulness of this theory in practice by analyzing the concrete communication overhead of our protocols, which improve upon the most efficient previous works.
- Eurocrypt 2023
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- Carsten Baum (4)
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