Secure Multiparty Inner Product Computation with Reduced Beaver Triples
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Solution Overview
Problem
The SPDZ protocol for secure multiparty computation is computationally and communicatively intensive due to the large number of multiplication operations required for inner product computations, particularly in the online phase, which increases overhead between parties.
Innovation Solution
The method involves performing multiparty additions and multiplications with reduced Beaver triple generation, using a processor and network interface to generate and distribute shares efficiently, and employing encryption and resharing operations to compute the inner product with fewer multiparty multiplications, specifically halving the number of multiplications required for vectors of equal length.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Reliability
If the SPDZ protocol uses traditional multiparty multiplication operations for inner product computation, then security and privacy preservation are maintained, but computational and communication overhead increase significantly
Solution Approach 1:
The patent segments the inner product computation into two distinct phases: an offline phase for generating Beaver triples (random values and their products) and an online phase for the actual computation. This segmentation allows expensive multiplication operations to be pre-computed and stored, reducing the computational burden during the actual secure computation phase while maintaining security through the use of shared secrets and Beaver triples.
2Productivity
If the SPDZ protocol performs inner product computation with N elements, then complete computation is achieved, but the number of multiparty multiplications required is N, increasing communication overhead
Solution Approach 1:
The patent applies preliminary action by pre-generating Beaver triples (random values a, b and their product c=ab) during an offline phase before the actual inner product computation. These pre-computed triples are then used in the online phase to perform multiplications more efficiently, reducing the number of interactive multiparty multiplication operations from N to approximately N/2 while still achieving complete computation of the inner product.
3Reliability
If Beaver triples are generated for each multiplication operation, then security is maintained, but the offline phase becomes computationally intensive
Solution Approach 1:
The patent uses copying by generating multiple Beaver triples in advance during the offline phase and storing them for reuse. Instead of generating fresh Beaver triples for each multiplication operation during the online phase, the system copies and reuses the pre-generated triples, significantly reducing the computational intensity of the offline phase while maintaining security through the cryptographic properties of the pre-computed values.
Data Source
AI summary
A method for secure multiparty computation of an inner product includes performing multiparty additions to generate a first sum share and a second sum share between two shares of alternating elements from corresponding pairs of elements in a first vector and a second vector, performing multiparty multiplications with at least one other node to generate inner product pair shares corresponding to products of the first sum shares and the second sum shares corresponding to pairs of elements in the first and second vectors, and performing another multiparty addition of each inner product pair share with a first negated shares of pair products corresponding to pairs of elements in the first vector and a second negated shares of pair products corresponding to pairs of elements in the second vector to generate a share of an inner product of the first and second vectors.