Secure Multiparty Comparison Protocol for Encrypted Data
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Solution Overview
Problem
Existing methods for comparing encrypted or shared numbers across multiple parties are inefficient and complex, particularly when the numbers are split across multiple parties, making it difficult to determine which number is larger without revealing sensitive information.
Innovation Solution
The COMPARE-Z protocol uses a recursive approach with XOR, AND, and shift operations to compare 64-bit shares efficiently, leveraging fast processor instructions and Beaver triples for secure multiparty computation, allowing parties to determine which number is larger without revealing the actual numbers, and optimizing memory usage through compression and pipelining.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Reliability
If existing methods are used to compare encrypted or shared numbers across multiple parties, then security and privacy are maintained, but computational efficiency and speed deteriorate
Solution Approach 1:
The patent segments the comparison operation into distinct phases: preprocessing phase where parties generate and share random values and intermediate results, and comparison phase where final comparison is performed. This segmentation allows complex secure comparisons to be broken down into manageable steps that can be optimized independently, improving overall computational efficiency while maintaining security through distributed computation.
Solution Approach 2:
The patent performs preliminary actions by pre-computing and sharing random values, intermediate comparison results, and auxiliary data before the actual comparison is needed. Parties prepare Beaver triples, pre-compute modular exponentiations, and establish shared secrets in advance, which significantly accelerates the actual comparison operation while maintaining cryptographic security.
2Reliability
If numbers are split across multiple parties to maintain privacy, then security is improved, but device complexity and operational difficulty worsen
Solution Approach 1:
The patent implements a universal comparison protocol that handles multiple comparison scenarios (encrypted numbers, shared secret numbers, partially revealed numbers) through a single unified framework. The same core comparison mechanism works across different privacy requirements and number representations, reducing the need for multiple specialized protocols and simplifying system implementation.
Solution Approach 2:
The patent introduces intermediary computational elements such as Beaver triples, auxiliary random values, and intermediate comparison results that facilitate secure multi-party computation. These intermediaries enable parties to perform comparisons without directly sharing sensitive data, acting as mediators that preserve privacy while enabling computation.
3Reliability
If complex cryptographic protocols are used to compare shared numbers, then security is maintained, but memory usage and computational overhead increase
Solution Approach 1:
The patent discards intermediate computational values and random padding data after they serve their purpose in the comparison protocol. Parties can safely discard Beaver triples, temporary shared secrets, and intermediate comparison results once the comparison is complete, recovering only the essential comparison outcome. This reduces memory usage by eliminating the need to retain large amounts of transient cryptographic data.
Data Source
AI summary
Systems and methods are provided for comparing a first number Abit with a second number Bbit. A method includes receiving, from a first computing device associated with the first number Abit, a share a1bit and a share b1bit; receiving, from a second computing device associated with the second number Bbit, a share a2bit and a share b2bit, wherein the first number Abit=a1bit+a2bit mod 264 and wherein the second number Bbit=b1bit+b2bit mod 264. The first number Abit=a1bit XOR a2bit and the second number Bbit=b1bit XOR b2bit. The XOR operation includes an XOR function that applies addition modulo 2 to corresponding pairs of bits of two strings. The method includes comparing, via a comparison function that compares numbers as modulo 264, the first number Abit and the second number Bbit to generate a shared output bit indicating which number is larger.