Messageless Secure Multi-Party Computation Using Polynomial Shares
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Solution Overview
Problem
Existing Secure Multi-Party Computation (SMPC) protocols face scalability issues due to the high communication complexity and bandwidth requirements, particularly when evaluating complex arithmetic functions, which limits their applicability in real-world scenarios.
Innovation Solution
A new SMPC protocol, referred to as MLC, enables the computation of arithmetic functions without message exchange between nodes by using polynomial shares and exponent blinding factors to conceal secrets, allowing each node to calculate shares of a degree-T polynomial that hide the secret values at a certain abscissa, and reconstructing the result without direct communication.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Reliability
If traditional SMPC protocols are used to evaluate complex arithmetic functions, then security is maintained, but communication complexity and bandwidth requirements increase significantly
Solution Approach 1:
The patent applies preliminary action by pre-processing the arithmetic function into a specific form (sum of groups of multiplications of secrets) before the actual SMPC computation. This pre-processing enables the subsequent messageless computation phase to proceed efficiently without requiring complex message exchanges during the actual computation, thus resolving the contradiction between security and communication complexity.
2Reliability
If traditional SMPC protocols are used to evaluate complex arithmetic functions, then security is maintained, but computation time increases due to message exchange overhead
Solution Approach 1:
The patent performs preliminary transformation of the arithmetic function into a suitable form that enables messageless computation. This pre-processing step allows the actual computation to be performed without the overhead of message exchanges, significantly reducing computation time while maintaining security through the preserved SMPC structure.
Solution Approach 2:
The patent extracts and removes the message exchange component from the SMPC protocol by transforming the computation into a form that can be performed locally at each node. This extraction eliminates the communication overhead that slows down traditional SMPC protocols while preserving the security guarantees through the mathematical structure of the transformed computation.
3Productivity
If message exchange is eliminated in SMPC computation, then computation time is reduced, but security against active adversaries may be compromised
Solution Approach 1:
The patent changes the parameters of the computation by transforming the arithmetic function into a specific form (sum of groups of multiplications) and using polynomial shares with specific degrees. These parameter changes enable the computation to proceed without message exchange while maintaining security, as the transformed structure preserves the necessary cryptographic properties for active adversary resistance.
Data Source
AI summary
Disclosed are methods and systems for calculating an arithmetic function expressed as addition of groups of multiplications of a set of private input secrets held by dealer nodes. Random exponent blinding factors are generated, and each computing node receives polynomial shares from each exponent blinding factor and a polynomial share and a public generator from the multiplicative group of integers modulo a prime number. The indexing integers are partitioned among the computing nodes, and each computing node computes a set of shares from the polynomial shares then sent to the dealer nodes which reconstruct the corresponding dealer blinding factor, and use it to create and send a particle to the computing nodes. The computing nodes then calculate from the received particles a result share of a polynomial which, when combined by a result node, allow the evaluation of complete polynomial which includes the result of the arithmetic function.