Choosing the Right Secure Computation Protocol

Author: Denis Avetisyan

A new systematic evaluation reveals that the ‘best’ multi-party computation protocol depends heavily on the specifics of your application and network.

This paper provides a comprehensive performance analysis of various MPC protocols under diverse threat models and network conditions, demonstrating that protocol selection should be driven by workload characteristics.

Despite the strong theoretical guarantees of Multi-Party Computation (MPC), its practical adoption remains hindered by performance overhead and a lack of clear guidance for protocol selection. This paper, ‘SoK: Demystifying the multiverse of MPC protocols’, systematically evaluates the performance landscape of diverse MPC protocols across varying primitives and threat models. Our analysis reveals no universally ‘best’ protocol, demonstrating that optimal choice is fundamentally dictated by specific workload characteristics and network constraints. Consequently, how can developers and researchers best bridge the gap between MPC’s potential and its real-world applicability, and what novel techniques will be crucial to unlock its full capabilities?

The Allure of Concealed Computation

The contemporary landscape of data analysis is fueled by an insatiable demand for insights derived from increasingly sensitive information. Fields like healthcare, finance, and personalized advertising rely heavily on datasets containing deeply personal details – medical records, transaction histories, and behavioral patterns. This trend presents a paradox: maximizing the utility of data often requires detailed computation, yet the very act of processing this data introduces substantial privacy risks. Modern analytical techniques, including machine learning and predictive modeling, benefit from large, richly detailed datasets, driving a need to compute on private information while simultaneously protecting it from unauthorized access or exposure. The challenge lies in extracting valuable knowledge without compromising individual privacy, a growing concern for both individuals and organizations.

Contemporary data analytics often relies on consolidating information from numerous sources, but this aggregation frequently necessitates exposing raw data to centralized processing. This practice introduces substantial security vulnerabilities and privacy risks, as breaches or malicious access can compromise highly sensitive personal or proprietary information. Traditional approaches, like simple data sharing or cloud-based analysis without robust protections, create single points of failure and leave individuals and organizations susceptible to data misuse, identity theft, and financial losses. The inherent exposure in these conventional methods highlights the urgent need for innovative techniques that prioritize data confidentiality during computation, prompting exploration into alternatives like secure multi-party computation and federated learning.

Multi-Party Computation (MPC) represents a paradigm shift in data analysis, enabling collaborative calculations on sensitive information while preserving complete privacy. Unlike traditional methods where data is aggregated and exposed during processing, MPC distributes the computation across multiple parties, each holding only a portion of the overall dataset. Through clever cryptographic protocols, these parties can jointly compute a function – such as a statistical average or a machine learning model – on their combined data without ever revealing their individual contributions. This is achieved by ensuring that no single party gains access to the raw data of others; instead, only encrypted shares and intermediate results are exchanged. The result of the computation is then revealed, but the underlying private data remains secure, offering a robust solution for scenarios demanding data privacy, like collaborative medical research, financial modeling, and secure auctions. Essentially, MPC unlocks the power of collective data analysis without sacrificing individual privacy, paving the way for previously impossible data collaborations.

The Foundations of Secret Agreements

Secure Multi-Party Computation (MPC) protocols are built upon a limited set of core computational primitives. These include the inner product operation, defined as $ \sum_{i=1}^{n} a_i b_i $, which is fundamental for many cryptographic tasks. Matrix multiplication, involving the product of two matrices, is also frequently utilized, particularly in applications involving large datasets. Finally, comparison operations, determining the relative order of two values, are essential for conditional logic and decision-making within the MPC protocol. The efficient and secure implementation of these primitives is critical to the overall performance and security of any MPC system.

Computational primitives in Multi-Party Computation (MPC) are not abstract operations but concrete calculations performed within defined arithmetic domains. These domains include binary, where operations are limited to $0$ and $1$; arithmetic, encompassing integers and modular arithmetic; and fields, such as prime fields ($GF(p)$) or extension fields, which provide the mathematical structure for performing addition, subtraction, multiplication, and crucially, division. The choice of domain directly restricts the available operations; for instance, computations in binary can only represent boolean logic, while field arithmetic is essential for secure division and inversion required in many cryptographic protocols. Furthermore, the size of the domain-the number of elements within it-impacts the computational cost and the security level achieved, as larger domains generally offer greater resistance to certain attacks.

The selection of an arithmetic domain – whether prime fields like those based on large prime numbers, or ring domains such as integers modulo a composite number – directly influences the performance and security characteristics of Multi-Party Computation (MPC) protocols. Prime fields offer strong cryptographic guarantees and efficient computation for many protocols, but can require larger data representation to avoid collisions. Ring domains, particularly those based on polynomial rings, can provide computational advantages through techniques like Fast Fourier Transforms (FFTs), reducing communication complexity. However, ring-based MPC is susceptible to modulus switching attacks if not carefully implemented, potentially compromising security. The trade-off involves balancing the computational cost of operating within a larger field with the need to maintain robust security against potential adversaries, and is highly dependent on the specific MPC protocol and application requirements. For instance, protocols relying on secret sharing benefit from the properties of fields, while those employing garbled circuits may be optimized for ring structures.

The Art of Distributed Secrets

Additive and Shamir’s secret sharing are cryptographic techniques that divide a secret into multiple parts, distributed among participating parties. Additive secret sharing, a simpler method, represents the secret as the sum of random shares, ensuring no individual share reveals the original value. Shamir’s Secret Sharing, based on polynomial interpolation, constructs a polynomial of degree $k-1$ where the secret is the constant term, and each party receives a point on the polynomial; reconstructing the secret requires at least $k$ shares. Both methods achieve information dispersal, meaning no subset of shares smaller than the required threshold can reveal the secret, effectively masking individual inputs and enhancing data security by preventing any single party from possessing the complete secret.

Replicated secret sharing improves the fault tolerance of secret sharing schemes by representing each share of a secret as a collection of n sub-shares distributed among the participating parties. This contrasts with standard secret sharing where a single share is held by each party. Consequently, the scheme can tolerate up to $t$ compromised or unavailable parties without revealing the original secret, where $t$ is determined by the redundancy level and the overall scheme parameters. The number of sub-shares and the distribution method are critical; a common approach involves creating $m$ sub-shares from each original share, distributing each sub-share to a different participant, and requiring a threshold of $t$ sub-shares from different participants to reconstruct any original share. This redundancy is particularly valuable in adversarial environments where parties may be malicious or subject to failures, ensuring the continued availability and confidentiality of the secret.

Local share conversion is an optimization technique used in secure multi-party computation (MPC) to reduce communication complexity when performing operations on shared integers. Rather than requiring all parties to exchange their entire shares for each operation, local share conversion allows parties to exchange only a small number of shares with a subset of other parties. Specifically, a party holding a share $x$ of an integer can convert it into a share $y$ of another integer by interacting with a limited number of other parties, without revealing the original value $x$. This is achieved through protocols that exchange additive shares, effectively decomposing the original integer into multiple shares and reconstructing it in a different form. The efficiency gains are significant, particularly when dealing with large numbers of parties or frequent computations, as it minimizes the amount of data transmitted across the network.

Beaver triples, denoted as $(a, b, c)$, are pre-shared random values used to enable secure multiplication in Multi-Party Computation (MPC) protocols. These triples satisfy the relationship $c = a \times b$, but are known only collectively by the participating parties; individual values of $a$, $b$, and $c$ remain secret. During secure computation, parties can compute $x \times y$ without revealing either input by leveraging a pre-shared triple; one party contributes $x$ masking $a$, while another contributes $y$ masking $b$, and the resulting masked product reveals only $c = a \times b$. This allows the computation of $x \times y$ as $c$ without revealing the original inputs, circumventing the need for direct exchange of sensitive data and protecting privacy.

The Optimization of Hidden Computations

Offline computation in secure multi-party computation (MPC) involves pre-processing and distributing data that does not require secrecy prior to the online phase. This pre-calculation addresses a key performance bottleneck: communication costs. By determining and sharing non-secret intermediate values beforehand, the amount of data exchanged during the online computation – where sensitive data is involved – is significantly reduced. This approach is particularly effective for workloads with a high ratio of non-secret to secret values, as it minimizes the online communication burden and improves overall computation speed. The effectiveness of offline computation is dependent on a trusted setup phase to generate the pre-calculated values, but it offers substantial performance gains in bandwidth-constrained environments.

Yao’s garbled circuits represent an early and influential approach to secure two-party computation, enabling two parties to jointly compute a function on their private inputs without revealing those inputs to each other. The core mechanism involves transforming a boolean circuit representing the function into an encrypted form – the garbled circuit – where each gate is encrypted using symmetric keys known only to the respective inputting party. A specialized garbled circuit evaluation protocol then allows both parties to collaboratively evaluate the function without disclosing their individual data. While computationally intensive, particularly for complex circuits, Yao’s garbled circuits established a fundamental building block for subsequent advancements in MPC and continue to serve as a benchmark for comparing the efficiency of newer protocols.

MP-SPDZ is a comprehensive framework designed to facilitate the implementation and evaluation of a broad range of secure Multi-Party Computation (MPC) protocols. It supports various functionalities, including arithmetic, boolean, and cryptographic operations, and provides tools for protocol composition and optimization. The framework features a hybrid approach, allowing users to combine different MPC techniques-such as Yao’s garbled circuits, secret sharing, and homomorphic encryption-to tailor protocols to specific application requirements. MP-SPDZ offers a flexible architecture with support for both active and passive security models, along with a modular design that enables researchers to easily integrate new protocols and evaluate their performance across diverse network configurations and workloads. It includes tools for performance profiling, communication analysis, and automated benchmarking, making it a valuable resource for both MPC researchers and practitioners.

Bandwidth limitations represent a significant obstacle to scaling Multi-Party Computation (MPC) deployments. Empirical analysis demonstrates a strong correlation between MPC protocol performance and both workload characteristics and available network bandwidth. Specifically, the Yao garbled circuits protocol exhibits substantially higher data transmission requirements compared to alternative protocols; this increased communication overhead can become a bottleneck, particularly in scenarios with limited bandwidth or high latency networks. Workload structure, encompassing factors like data size, computational complexity, and the number of parties involved, further exacerbates these bandwidth constraints, necessitating careful protocol selection and optimization strategies to achieve practical scalability.

The Limits of Security and the Future of Distributed Trust

Secure Multi-Party Computation (MPC) isn’t a one-size-fits-all solution; its implementation hinges critically on the assumed threat model. Protocols designed under the semi-honest model, where adversaries follow the protocol but attempt to learn more than they should from the data, are comparatively efficient but offer limited protection. In contrast, protocols built to withstand malicious adversaries – those who can arbitrarily deviate from the protocol – demand significantly more complex constructions, often incorporating techniques like zero-knowledge proofs and verifiable secret sharing to guarantee correctness even with compromised participants. This trade-off between security and efficiency necessitates careful consideration of the application’s risk profile; a system handling sensitive financial data, for instance, would prioritize a robust malicious adversary model, while a less critical application might accept the performance benefits of a semi-honest approach. The selection directly impacts the computational overhead, communication costs, and overall feasibility of deploying MPC in a given scenario, influencing everything from the choice of cryptographic primitives to the protocol’s architectural design.

The foundational security assumptions within Multi-Party Computation (MPC) dramatically impact the complexity and efficiency of resulting protocols. When designing an MPC system, developers must first consider whether to assume an honest majority – where most participants follow the protocol – or to prepare for a dishonest majority where adversaries might attempt to compromise the computation. Protocols built under the honest majority assumption, while simpler and faster, are vulnerable if a significant portion of the parties are malicious. Conversely, protocols designed to withstand a dishonest majority employ more sophisticated cryptographic techniques – such as zero-knowledge proofs and verifiable secret sharing – adding considerable overhead in terms of computation and communication. This trade-off means that a protocol perfectly suited for a trusted consortium might prove impractical in an open, permissionless environment, and vice versa. Consequently, selecting the appropriate security assumption isn’t merely a theoretical choice; it’s a critical engineering decision that dictates the feasibility and performance of any real-world MPC deployment.

Secure multiparty computation (MPC) often requires a distinction between online and offline phases to efficiently process dynamic inputs. While offline computation – pre-processing performed on static, known data – significantly boosts performance by reducing the computational burden during the online phase, it cannot handle inputs only known at runtime. Therefore, a crucial design consideration involves finding the optimal balance between these two phases; maximizing the amount of computation done offline minimizes online communication and computation costs, but a purely offline approach is impractical when dealing with variable or unpredictable data. The effectiveness of this balance is highly dependent on the specific MPC protocol and the nature of the inputs; scenarios with frequent changes necessitate a greater emphasis on online computation, while static datasets allow for substantial pre-processing, resulting in faster and more scalable secure computations.

Real-world deployment of secure multi-party computation (MPC) hinges on overcoming bandwidth constraints, particularly when handling high volumes of data. Investigations reveal a significant performance disparity between different MPC protocols and the specific computations they perform; for instance, the YAO protocol demonstrates minimal latency in comparative tests, while protocols tailored for arithmetic operations prove superior in tasks like inner product and matrix multiplication. Scalability also presents a challenge, as some protocols, such as SY-SHAMIR, struggle to maintain efficiency as the number of participating parties increases. Conversely, in environments with limited bandwidth, protocols like PS-REP-RING offer a practical advantage due to their reduced data transmission overhead, highlighting the crucial need to select an MPC approach aligned with both computational demands and network capabilities.

The study meticulously charts a landscape where ‘best’ is an illusion, a comforting narrative against the inherent trade-offs in secure computation. It echoes a sentiment that scalability is merely the word used to justify complexity, as each protocol’s performance is inextricably linked to the specific threat model and network conditions. Ada Lovelace observed that “the Analytical Engine has no pretensions whatever to originate anything.” Similarly, these MPC protocols don’t create security; they translate it, shifting the cost between computation, bandwidth, and resilience. The pursuit of a universally optimal solution is, therefore, a myth – a necessary one, perhaps, to keep the endeavor sane, but a myth nonetheless.

What Shadows Remain?

This systematization of multi-party computation protocols reveals, predictably, that optimization is merely a postponement of inevitable compromise. The search for a ‘best’ protocol is a phantom chase; each configuration excels within a narrow band of assumptions, a fleeting victory before the tide of real-world constraints washes over it. The paper highlights the crucial interplay between primitive, threat model, and – most acutely – network bandwidth. It is not a question of building a perfect solution, but of cultivating an ecosystem where protocols can adapt, degrade gracefully, and reveal their failings early.

The current emphasis on performance metrics, while valuable, risks masking a deeper issue: the brittleness of these systems. Each protocol embodies a specific vision of trust, of acceptable failure modes. The coming years will not be defined by incremental speed improvements, but by the exposure of those hidden assumptions. Expect to see attacks that exploit the shape of communication, not merely its content – focusing on subtle deviations from idealized network models.

The true challenge lies not in selecting the right tool for the job, but in designing systems that can absorb the shock of protocol failure. A future architecture will treat MPC protocols not as building blocks, but as transient components, constantly monitored, assessed, and replaced – a distributed, self-healing network of secure computation, acknowledging that every line of code is, at its core, a prophecy of eventual entropy.

Original article: https://arxiv.org/pdf/2512.11699.pdf

Contact the author: https://www.linkedin.com/in/avetisyan/