## CryptoDB

### Ignacio Cascudo

#### Publications

**Year**

**Venue**

**Title**

2021

PKC

Flexible and Efficient Verifiable Computation on Encrypted Data
📺
Abstract

We consider the problem of verifiable and private delegation of computation [Gennaro et al. CRYPTO'10] in which a client stores private data on an untrusted server and asks the server to compute functions over this data. In this scenario we aim to achieve three main properties: the server should not learn information on inputs and outputs of the computation (privacy), the server cannot return wrong results without being caught (integrity), and the client can verify the correctness of the outputs faster than running the computation (efficiency). A known paradigm to solve this problem is to use a (non-private) verifiable computation (VC) to prove correctness of a homomorphic encryption (HE) evaluation on the ciphertexts. Despite the research advances in obtaining efficient VC and HE, using these two primitives together in this paradigm is concretely expensive. Recent work [Fiore et al. CCS'14, PKC'20] addressed this problem by designing specialized VC solutions that however require the HE scheme to work with very specific parameters; notably HE ciphertexts must be over $\mathbb{Z}_q$ for a large prime $q$.
In this work we propose a new solution that allows a flexible choice of HE parameters, while staying modular (based on the paradigm combining VC and HE) and efficient (the VC and the HE schemes are both executed at their best efficiency). At the core of our new protocol are new homomorphic hash functions for Galois rings. As an additional contribution we extend our results to support non-deterministic computations on encrypted data and an additional privacy property by which verifiers do not learn information on the inputs of the computation.

2020

TCC

A Secret-Sharing Based MPC Protocol for Boolean Circuits with Good Amortized Complexity
📺
Abstract

We present a new secure multiparty computation protocol in the preprocessing model that allows for the evaluation of a number of instances of a boolean circuit in parallel, with a small online communication complexity per instance of $10$ bits per party and multiplication gate. Our protocol is secure against an active dishonest majority, and can also be transformed, via existing techniques, into a protocol for the evaluation of a single “well-formed” boolean circuit with the same complexity per multiplication gate at the cost of some overhead that depends on the topology of the circuit.
Our protocol uses an approach introduced recently in the setting of honest majority and information-theoretical security which, using an algebraic notion called reverse multiplication friendly embeddings, essentially transforms a batch of evaluations of an arithmetic circuit over a small ?eld into one evaluation of another arithmetic circuit over a larger ?eld. To obtain security against a dishonest majority we combine this approach with the well-known SPDZ protocol that operates over a large ?eld. Structurally our protocol is most similar to MiniMAC, a protocol which bases its security on the use of error-correcting codes, but our protocol has a communication complexity which is half of that of MiniMAC when the best available binary codes are used. With respect to certain variant of MiniMAC that utilizes codes over larger ?elds, our communication complexity is slightly worse; however, that variant of MiniMAC needs a much larger preprocessing than ours. We also show that our protocol also has smaller amortized communication complexity than Committed MPC, a protocol for general ?elds based on homomorphic commitments, if we use the best available constructions for those commitments. Finally, we construct a preprocessing phase from oblivious transfer based on ideas from MASCOT and Committed MPC.

2020

ASIACRYPT

ALBATROSS: publicly AttestabLe BATched Randomness based On Secret Sharing
📺
Abstract

In this paper we present ALBATROSS, a family of multiparty randomness generation protocols with guaranteed output delivery and public verification that allows to trade off corruption tolerance for a much improved amortized computational complexity. Our basic stand alone protocol is based on publicly verifiable secret sharing (PVSS) and is secure under in the random oracle model under the decisional Diffie-Hellman (DDH) hardness assumption. We also address the important issue of constructing Universally Composable randomness beacons, showing two UC versions of Albatross: one based on simple UC NIZKs and another one based on novel efficient ``designated verifier'' homomorphic commitments. Interestingly this latter version can be instantiated from a global random oracle under the weaker Computational Diffie-Hellman (CDH) assumption. An execution of ALBATROSS with $n$ parties, out of which up to $t=(1/2-\epsilon)\cdot n$ are corrupt for a constant $\epsilon>0$, generates $\Theta(n^2)$ uniformly random values, requiring in the worst case an amortized cost per party of $\Theta(\log n)$ exponentiations per random value. We significantly improve on the SCRAPE protocol (Cascudo and David, ACNS 17), which required $\Theta(n^2)$ exponentiations per party to generate one uniformly random value. This is mainly achieved via two techniques: first, the use of packed Shamir secret sharing for the PVSS; second, the use of linear $t$-resilient functions (computed via a Fast Fourier Transform-based algorithm) to improve the randomness extraction.

2019

ASIACRYPT

Efficient UC Commitment Extension with Homomorphism for Free (and Applications)
Abstract

Homomorphic universally composable (UC) commitments allow for the sender to reveal the result of additions and multiplications of values contained in commitments without revealing the values themselves while assuring the receiver of the correctness of such computation on committed values. In this work, we construct essentially optimal additively homomorphic UC commitments from any (not necessarily UC or homomorphic) extractable commitment, while the previous best constructions require oblivious transfer. We obtain amortized linear computational complexity in the length of the input messages and rate 1. Next, we show how to extend our scheme to also obtain multiplicative homomorphism at the cost of asymptotic optimality but retaining low concrete complexity for practical parameters. Moreover, our techniques yield public coin protocols, which are compatible with the Fiat-Shamir heuristic. These results come at the cost of realizing a restricted version of the homomorphic commitment functionality where the sender is allowed to perform any number of commitments and operations on committed messages but is only allowed to perform a single batch opening of a number of commitments. Although this functionality seems restrictive, we show that it can be used as a building block for more efficient instantiations of recent protocols for secure multiparty computation and zero knowledge non-interactive arguments of knowledge.

2018

CRYPTO

Amortized Complexity of Information-Theoretically Secure MPC Revisited
📺
Abstract

A fundamental and widely-applied paradigm due to Franklin and Yung (STOC 1992) on Shamir-secret-sharing based general n-player MPC shows how one may trade the adversary thresholdt against amortized communication complexity, by using a so-called packed version of Shamir’s scheme. For e.g. the BGW-protocol (with active security), this trade-off means that if
$$t + 2k -2 < n/3$$
t+2k-2<n/3, then kparallel evaluations of the same arithmetic circuit on different inputs can be performed at the overall cost corresponding to a single BGW-execution.In this paper we propose a novel paradigm for amortized MPC that offers a different trade-off, namely with the size of the field of the circuit which is securely computed, instead of the adversary threshold. Thus, unlike the Franklin-Yung paradigm, this leaves the adversary threshold unchanged. Therefore, for instance, this paradigm may yield constructions enjoying the maximal adversary threshold
$$\lfloor (n-1)/3 \rfloor $$
⌊(n-1)/3⌋ in the BGW-model (secure channels, perfect security, active adversary, synchronous communication).Our idea is to compile an MPC for a circuit over an extension field to a parallel MPC of the same circuit but with inputs defined over its base field and with the same adversary threshold. Key technical handles are our notion of reverse multiplication-friendly embeddings (RMFE) and our proof, by algebraic-geometric means, that these are constant-rate, as well as efficient auxiliary protocols for creating “subspace-randomness” with good amortized complexity. In the BGW-model, we show that the latter can be constructed by combining our tensored-up linear secret sharing with protocols based on hyper-invertible matrices á la Beerliova-Hirt (or variations thereof). Along the way, we suggest alternatives for hyper-invertible matrices with the same functionality but which can be defined over a large enough constant size field, which we believe is of independent interest.As a demonstration of the merits of the novel paradigm, we show that, in the BGW-model and with an optimal adversary threshold
$$\lfloor (n-1)/3 \rfloor $$
⌊(n-1)/3⌋, it is possible to securely compute a binary circuit with amortized complexity O(n) of bits per gate per instance. Known results would give
$$n \log n$$
nlogn bits instead. By combining our result with the Franklin-Yung paradigm, and assuming a sub-optimal adversary (i.e., an arbitrarily small
$$\epsilon >0$$
ϵ>0 fraction below 1/3), this is improved to O(1) bits instead of O(n).

2011

CRYPTO

#### Program Committees

- TCC 2020
- Eurocrypt 2018
- Asiacrypt 2015

#### Coauthors

- Alexandre Bois (1)
- Hao Chen (2)
- Ronald Cramer (4)
- Ivan Damgård (5)
- Bernardo Machado David (1)
- Bernardo David (3)
- Nico Döttling (2)
- Rafael Dowsley (1)
- Oriol Farràs (1)
- Dario Fiore (1)
- Irene Giacomelli (2)
- Jaron Skovsted Gundersen (1)
- Robbert de Haan (1)
- Dongwoo Kim (1)
- Felipe Lacerda (1)
- Jesper Buus Nielsen (2)
- Samuel Ranellucci (2)
- Roberto Trifiletti (1)
- Chaoping Xing (3)
- Chen Yuan (1)