Boolean Circuit Evaluation in Homomorphic Encryption
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Solution Overview
Problem
Evaluating Boolean circuits in computational environments that support only a limited set of operations, such as additions and multiplications, is complex and time-consuming due to the need for simulating Boolean operations, particularly in Homomorphic Encryption schemes where operations on encrypted data are more complex and lengthy.
Innovation Solution
The method involves analyzing Boolean circuits to identify patterns of XOR operations over groups of four input variables, using defined logical gates like XORT and pseudo logical gates ANDP and XORP to replace multiplication operations with complex conjugate operations, and calculating AND operations on adjacent XORed pairs, optimizing the evaluation process within environments that support only additions and multiplications.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Adaptability or versatility
If Boolean operations are simulated by arithmetic operations in limited computational environments, then the circuit can be evaluated in Homomorphic Encryption schemes, but the computational complexity and computation time increase significantly
Solution Approach 1:
The patent transforms Boolean operations into arithmetic operations by changing the parameter domain from binary {0,1} to real numbers. Specifically, it maps Boolean AND to multiplication and Boolean XOR to a combination of addition and multiplication by -1, enabling evaluation in Homomorphic Encryption schemes that operate over real numbers rather than binary fields.
Solution Approach 2:
The patent replaces the mechanical Boolean logic gate system with an arithmetic computation system. Instead of using discrete Boolean operations (AND, OR, XOR gates), it substitutes these with arithmetic operations (multiplication, addition) that can be performed on encrypted data in Homomorphic Encryption schemes, thereby enabling cloud-based secure computation.
2Adaptability or versatility
If Boolean operations are simulated by arithmetic operations, then the circuit can be evaluated in limited computational environments, but the computation time increases
Solution Approach 1:
The patent changes the parameter representation from binary Boolean values to real numbers, allowing the use of efficient arithmetic operations. By representing Boolean inputs as real numbers (0 or 1) and using multiplication for AND operations and addition with sign flipping for XOR operations, the patent enables evaluation in Homomorphic Encryption schemes while minimizing the overhead of simulation.
3Adaptability or versatility
If multiplication operations are used to simulate Boolean AND operations, then the circuit evaluation is compatible with Homomorphic Encryption, but the number of required multiplications increases computational overhead
Solution Approach 1:
The patent optimizes the parameter transformation by mapping Boolean AND directly to multiplication of real numbers. This allows the use of Homomorphic Encryption's native multiplication operation to compute AND gates, while representing XOR gates through addition and sign manipulation, thereby reducing the total number of multiplications required compared to generic simulation approaches.
Data Source
AI summary
A computer-implemented method comprising: receiving a Boolean circuit embodied in a digital file and input variables associated with the Boolean circuit; analyzing a structure of the Boolean circuit to identify a pattern of Boolean operations comprising one or more chains of XOR operations over groups of four of the input variables; automatically evaluating each of the one or more chains of XOR operations over the groups of four input variables, using a defined logical gate XORT which replaces at least some required multiplication operations with complex conjugate operations; and automatically calculating any identified AND operations performed on adjacent XORed pairs in the Boolean circuit, using defined pseudo logical gates ANDP and XORP.