[Paper Review] Security, fault tolerance, and communication complexity in distributed systems

Michael O. Rabin, Donald Beaver|arXiv (Cornell University)|Jan 1, 1990

Cryptography and Data Security61 references17 citations

TL;DR

This paper presents novel, communication-efficient protocols for secure distributed computation in fault-tolerant systems, using a locally random reduction technique to achieve constant-round, low-communication complexity protocols that are provably secure under both computational and information-theoretic models, regardless of function complexity.

ABSTRACT

We present efficient and practical algorithms for a large, distributed system of processors to achieve reliable computations in a secure manner. Specifically, we address the problem of computing a general function of several private inputs distributed among the processors of a network, while ensuring the correctness of the results and the privacy of the inputs, despite accidental or malicious faults in the system. Communication is often the most significant bottleneck in distributed computing. Our algorithms maintain a low cost in local processing time, are the first to achieve optimal levels of fault-tolerance, and most importantly, have low communication complexity. In contrast to the best known previous methods, which require large numbers of rounds even for fairly simple computations, we devise protocols that use small messages and a constant number of rounds regardless of the complexity of the function to be computed. Through direct algebraic approaches, we separate the communication complexity of secure computing from the computational complexity of the function to be computed. We examine security under both the modern approach of computational complexity-based cryptography and the classical approach of unconditional, information-theoretic security. We develop a clear and concise set of definitions that support formal proofs of claims to security, addressing an important deficiency in the literature. Our protocols are provably secure. In the realm of information-theoretic security, we characterize those functions which two parties can compute jointly with absolute privacy. We also characterize those functions which a weak processor can compute using the aid of powerful processors without having to reveal the instances of the problem it would like to solve. Our methods include a promising new technique called a locally random reduction, which has given rise not only to efficient solutions for many of the problems considered in this work but to several powerful new results in complexity theory.

Motivation & Objective

• To design secure, fault-tolerant distributed protocols that maintain privacy of private inputs while ensuring correctness under both accidental and malicious faults.
• To minimize communication complexity in distributed secure computation, decoupling it from the computational complexity of the function being computed.
• To achieve provable security under both computational complexity-based cryptography and information-theoretic security models.
• To characterize the set of functions that can be securely computed by two parties with absolute privacy, and by a weak processor with the help of powerful ones without revealing input instances.
• To introduce and formalize a new technique—locally random reduction—that enables efficient solutions and new results in complexity theory.

Proposed method

• The authors employ a novel technique called locally random reduction to transform secure computation tasks into more manageable subproblems with minimal communication overhead.
• They design protocols that use small messages and a constant number of communication rounds, independent of the function's computational complexity.
• The approach separates communication complexity from the function's computational complexity through direct algebraic constructions.
• Formal definitions are developed to support rigorous, provable security claims, addressing a key gap in prior literature.
• The protocols are constructed to be resilient to both accidental and malicious faults, ensuring correctness and privacy.
• Security is analyzed under both computational complexity-based cryptography and unconditional, information-theoretic security models.

Experimental results

Research questions

• RQ1 Which functions can be securely computed by two parties with absolute privacy under information-theoretic security?
• RQ2 Can a weak processor compute a function with the help of powerful processors without revealing its input instance?
• RQ3 How can secure distributed computation be achieved with minimal communication and constant rounds, regardless of function complexity?
• RQ4 What is the communication complexity of secure computation, and can it be decoupled from the function's computational complexity?
• RQ5 What new complexity-theoretic results emerge from the use of locally random reductions in secure computation?

Key findings

• The proposed protocols achieve optimal fault tolerance and are the first to maintain low communication complexity with a constant number of rounds, irrespective of function complexity.
• Communication complexity is successfully separated from the computational complexity of the function via direct algebraic methods.
• The paper provides a formal framework of definitions that enables rigorous, provable security claims, resolving a deficiency in prior work.
• A new technique—locally random reduction—is introduced and shown to yield efficient solutions and new results in complexity theory.
• The authors characterize the set of functions that can be computed securely with absolute privacy in both two-party and client-assistance settings.
• The protocols are provably secure under both computational and information-theoretic models, ensuring robustness against malicious faults.