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.
Efficient Information-Theoretic Secure Multiparty Computation over Z/pkZ 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.
Multiparty computation (MPC) over rings such as Z232 or Z264 has received a great deal of attention recently due to its ease of implementation and attractive performance. Several actively secure protocols over these rings have been implemented, for both the dishonest majority setting and the setting of three parties with one corruption. However, in the honest majority setting, no concretely efficient protocol for arithmetic computation over rings has yet been proposed that allows for an arbitrary number of parties.
Abstract. Secure multi-party computation (MPC) allows a set P of n players to evaluate a function f in presence of an adversary who corrupts a subset of the players. In this paper we consider active, general adversaries, characterized by a so-called adversary structure Z which enumerates all possible subsets of corrupted players. In particular for small sets of players general adversaries better capture real-world requirements than classical threshold adversaries. Protocols for general adversaries are “efficient ” in the sense that they require |Z | O(1) bits of communication. However, as |Z | is usually very large (even exponential in n), the exact exponent is very relevant. In the setting with perfect security, the most efficient protocol known to date communicates O(|Z | 3) bits; we present a protocol for this setting which communicates O(|Z | 2) bits. In the setting with statistical security, O(|Z | 3) bits of communication is needed in general (whereas for a very restricted subclass of adversary structures, a protocol with communication O(|Z | 2) bits is known); we present a protocol for this setting (without limitations) which communicates O(|Z | 1) bits.
Secure multiparty computation (MPC) is perhaps the most popular paradigm in the area of cryptographic protocols. It allows several mutually untrustworthy parties to jointly compute a function of their private inputs, without revealing to each other information about those inputs. In the case of unconditional (information-theoretic) security, protocols are known which tolerate a dishonest minority of players, who may coordinate their attack and deviate arbitrarily from the protocol specification. It is typically assumed in these results that parties are connected pairwise by authenticated, private channels, and that in addition they have access to a “broadcast ” channel. Broadcast allows one party to send a consistent message to all other parties, guaranteeing consistency even if the broadcaster is corrupted. Because broadcast cannot be simulated on the point-to-point network when more than a third of the parties are corrupt, it is impossible to construct general MPC protocols in this setting without using a broadcast channel (or some equivalent addition to the model). A great deal of research has focused on increasing the efficiency of MPC, primarily in terms of round complexity and communication complexity. In this work we propose a refinement of the round complexity which we term broadcast complexity. We view the broadcast channel as an expensive resource
Abstract. Most protocols for distributed, fault-tolerant computation, or multi-party computation (MPC), provide security guarantees in an all-or-nothing fashion: If the number of corrupted parties is below a certain threshold, these protocols provide all specified security guarantees. Beyond this threshold, they provide no security guarantees at all. Furthermore, most previous protocols achieve either information-theoretic (IT) security, in which case this threshold is low, or they achieve only computational security, in which case this threshold is high. In contrast, a hybrid-secure proto-col provides different security guarantees depending on the set of corrupted parties and the com-putational power of the adversary, without being aware of the actual adversarial setting. Thus, hybrid-secure MPC protocols allow for graceful degradation of security. We present a hybrid-secure MPC protocol that provides an optimal trade-off between IT robustness and computational privacy: For any robustness parameter ρ < n 2, we obtain one MPC protocol that is simultaneously IT secure with robustness for up to t ≤ ρ actively corrupted parties, IT secure with fairness (no robustness) for up to t < n 2, and computationally secure with agreement on abort
Secure multiparty generation of an RSA biprime is a challenging task, which increasingly receives attention, due to the numerous privacy-preserving applications that require it. In this work, we construct a new protocol for the RSA biprime generation task, secure against a malicious adversary, who can corrupt any subset of protocol participants. Our protocol is designed with generic multiparty computation (MPC), making it both platform-independent and allowing for weaker security models to be assumed (e.g., honest majority), should the application scenario require it. By carefully "postponing" the check of possible inconsistencies in the shares provided by malicious adversaries, we achieve noteworthy efficiency improvements. Concretely, we are able to produce additive sharings of the prime candidates, from multiplicative sharings via a semi-honest multiplication, without degrading the overall (active) security of our protocol. This is the core of our sieving technique, increasing the probability of our protocol sampling a biprime. Similarly, we perform the first biprimality test, requiring several repetitions, without checking input share consistency, and perform the more costly consistency check only in case of success of the Jacobi symbol based biprimality test. Moreover, we propose a protocol to convert an additive sharing over a ring, into an additive sharing over the integers. Besides being a necessary sub-protocol for the RSA biprime generation, this conversion protocol is of independent interest. The cost analysis of our protocol demonstrated that our approach improves the current state-of-the-art (Chen et al.-Crypto 2020), in terms of communication efficiency. Concretely, for the two-party case with malicious security, and primes of 2048bits, our protocol improves communication by a factor of ~37.
Secure Multiparty Computation (MPC) is an expression encompassing cryptographic techniques that allow mutually distrustful parties to jointly perform computations over private data, ensuring correctness and preserving privacy despite malicious behavior. Guaranteed output is the strongest security goal for MPC: protocols with this property always deliver results. This is in contrast with weaker notions that allow malicious aborts. The seminal works of Ben-Or, Goldwasser, and Wigderson (STOC’88) and Rabin and Ben-Or (STOC’89) showed interactive protocols to compute any function with guaranteed output and perfect security if fewer than one third of parties are corrupted, or with statistical security (with a small error probability) if fewer than half are corrupted. These results hold when the set of participants is fixed throughout the execution. Ostrovsky and Yung’s proactive model (PODC’91) relaxes this assumption by allowing the set of corrupted parties to evolve over time, better capturing the dynamics of long-lived computations, where machines may be periodically compromised and recovered. The recent YOSO (You Only Speak Once) and fluid MPC models (CRYPTO’21) push this ambitious modelling even further by allowing for fully dynamic participation, with parties joining and leaving the computation at will. In this setting, known protocols with guaranteed output fall short of optimal resilience or rely on non-standard communication and adversarial assumptions. Matching the classical BGW and Rabin–Ben-Or bounds in these settings remained an open problem. We resolve these questions within the Layered MPC abstraction of David et al. (CRYPTO’23), in which the interaction pattern of a protocol is restricted to be a layered graph, meaning parties are partitioned into a sequence of disjoint sets (layers) and can send private and broadcast messages to parties in immediately subsequent layers. We match the BGW and Rabin and Ben-Or bounds in this model, fully characterizing the feasibility landscape of Layered MPC with guaranteed output. As a stepping stone towards our statistically secure protocol, we construct a more efficient and conceptually simpler computationally secure protocol relying on linear non-interactive commitments. Our results yield optimally-resilient and maximally-proactive MPC protocols with guaranteed output for both perfect and statistical security.