SPDZ Secure Multiparty Inner Product Protocol Optimization
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Solution Overview
Problem
The SPDZ protocol for secure multiparty computation is computationally intensive due to the large number of multiplication operations required in the online phase for inner product computations, leading to significant computational and communication overhead.
Innovation Solution
The proposed method reduces the number of multiplications and Beaver triples needed in the online phase by sharing additional precomputed data among parties, specifically using an optimized protocol (Protocol IP+) that performs N/2 multiplication operations, thereby improving the efficiency of both online and offline phases for multiparty inner product computations.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Reliability
If the straightforward implementation of secure inner product with SPDZ is used, then security against malicious corrupted parties is achieved, but the computational overhead and communication overhead increase significantly due to N pairwise multiplications
Solution Approach 1:
The patent applies preliminary action by performing precomputation of multiplication triples (a, b, c where c = a·b) during an offline phase before the actual inner product computation. These precomputed triples are stored and reused during the online phase, eliminating the need to perform N pairwise multiplications in real-time and significantly reducing computational overhead while maintaining security guarantees
Solution Approach 2:
The patent segments the inner product computation into two distinct phases: an offline phase for generating and distributing multiplication triples, and an online phase for performing the actual inner product computation using precomputed values. This segmentation allows computationally intensive operations to be performed in advance when resources are available, improving online computational efficiency
2Manufacturing precision
If N pairwise multiplications are performed in the online phase, then the inner product is computed correctly, but the communication overhead increases due to the large number of multiplication operations
Solution Approach 1:
The patent performs preliminary computation of multiplication triples (a, b, c) where c = a·b, and distributes these triples to parties before the online phase. During the online phase, parties use these precomputed triples to compute inner products through addition and comparison operations rather than direct multiplication, significantly reducing communication overhead while maintaining computational accuracy
Solution Approach 2:
The patent creates copies of precomputed multiplication triples and distributes them to multiple parties in advance. Each party receives relevant triples that enable them to perform local computations without needing to communicate multiplication results with other parties during the online phase, thereby reducing communication overhead
Data Source
AI summary
A method for implementing a secure multiparty inner product computation between two parties using an SPDZ protocol involves having a first party and a second party compute, for i=1, . . . , k, a vector (I)=(II) based on a vector (x={x1, . . . , xN}), and a vector (w={W1, WN}), respectively, where (I)=(X2i-1X2i) (III)=W2i-1W2i, N is the total number of elements in the vectors k=N/2. The vectors (I), and (III) are securely shared between the parties. The parties then jointly compute SPDZ protocol Add([w2i], [x2i-1]) and Add([w2i], [x2i-1]) to determine shares [w2i-1+x2i] and [w2i+x2i-1] respectively, and then compute, for i=1, . . . , k, inner product shares [di] by performing SPDZ protocol Mult([w2i-1+x2i], [w2i+x2i-1]). SPDZ protocol ([Add d1], . . . , [dk], -(IV), . . . , -(V), -(VI), -, (VII)) is then performed to determine the inner product.