Binomial Noise Sampling for Differentially Private MPC
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Solution Overview
Problem
Existing secure multiparty computation (MPC) protocols face challenges in maintaining differential privacy, as function results can leak information about private inputs due to the nature of the computed functions, necessitating improved methods to introduce random noise effectively.
Innovation Solution
An offline-online model is employed where offline parties generate a random binary number and function table segments, which are used by online parties to simulate a binomial distribution for random noise generation, utilizing XOR operations and Hamming weights to introduce noise efficiently into MPC results.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Reliability
If random noise is introduced into MPC results to achieve differential privacy, then privacy protection is improved, but computational complexity increases
Solution Approach 1:
The patent applies preliminary action by precomputing function table segments offline before the actual MPC execution. The offline computation of binomial distribution functions and their segmentation is performed in advance, storing results in tables that can be quickly referenced during online MPC operations. This shifts the heavy computational burden to a preliminary stage, reducing real-time computational complexity while maintaining privacy protection through proper noise generation.
Solution Approach 2:
The patent divides the large function table into multiple smaller function table segments based on the bit representation of input values. Instead of computing one large table, the function is segmented into chunks that can be independently computed and stored. During online operation, multiple small lookups are performed and combined, reducing memory access complexity and computational overhead while still generating the correct binomial distribution noise for differential privacy.
2Productivity
If function tables are precomputed for random noise generation, then noise generation speed is improved, but memory requirements increase
Solution Approach 1:
The patent segments the large function table into multiple smaller tables based on bit ranges of the input value. Each segment covers a specific range of bit patterns, allowing the system to store smaller memory units that can be individually managed. During noise generation, only the relevant segment needs to be accessed based on the input value's bit representation, reducing peak memory requirements while maintaining fast lookup speed through targeted segment access.
Solution Approach 2:
The patent applies local quality by making different parts of the memory structure serve different purposes based on the input value's characteristics. The function table segments are organized such that each segment handles specific bit patterns, allowing efficient memory utilization where only the necessary portion is loaded or accessed at any given time. This localized access pattern reduces overall memory requirements compared to loading the entire function table into memory simultaneously.
3Productivity
If offline precomputation is performed for binomial distribution sampling, then online computation efficiency is improved, but communication overhead increases
Solution Approach 1:
The patent segments the precomputed function table into smaller units that can be efficiently transmitted. Instead of communicating large monolithic tables, the system divides the function data into manageable segments that can be sent in smaller packets. The segmentation allows selective transmission of only the necessary segments based on the specific MPC instance requirements, reducing overall communication overhead while still providing the needed precomputed values for efficient online sampling.
Data Source
AI summary
Methods, systems, and apparatus, including computer programs encoded on computer storage media, for generating a random noise value for use in providing differential privacy in multiparty computation. One of the method includes receiving, by a first party participating in a multiparty secure computation (“MPC”) instance, a share of a first n-bit random binary number and a plurality of function table segments; generating a share of a second n-bit random binary number; calculating a first value based on a comparison between the share of the first and second n-bit random binary numbers; reconstructs an overall value of a comparison between the first and second n-bit random binary numbers; and determining a share of the random noise value based on the overall value and the plurality of function table segments.