Homomorphic Encryption Scalar Key Generation
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Solution Overview
Problem
Current homomorphic encryption methods face challenges in accurately calculating concealment distances, such as Hamming distance, in an encrypted state, leading to inaccurate decryption results and requiring significant memory and processing power for matrix calculations.
Innovation Solution
The implementation of an ideal lattice-based homomorphic encryption method that uses a key generation vector to generate a secret key matrix and public key matrix, allowing for efficient encryption and decryption processes while reducing the need for large memory and processing resources by using scalar values for public and secret keys.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Adaptability or versatility
If matrix-based homomorphic encryption methods are used to enable fully homomorphic operations, then versatility of cryptographic operations is improved, but device complexity and memory requirements worsen
Solution Approach 1:
The patent transforms the cryptographic system from using matrix-based keys to scalar-based keys. Specifically, it changes the parameter representation from n×n matrices to single scalar values, fundamentally altering the mathematical structure while preserving homomorphic encryption capabilities. This parameter change resolves the contradiction by eliminating matrix complexity while maintaining operational versatility through scalar arithmetic operations.
Solution Approach 2:
The patent extracts the essential cryptographic functionality from complex matrix operations and isolates it into simplified scalar key pairs. By separating the core encryption/decryption logic from the cumbersome matrix structures, the invention retains the ability to perform homomorphic operations while removing the computational overhead and memory requirements associated with matrix calculations.
2Reliability
If traditional homomorphic encryption methods are used to calculate concealment distances, then encryption capability is improved, but measurement precision of decrypted results worsens
Solution Approach 1:
The patent introduces a new parameter relationship between public and secret keys using scalar values with specific mathematical properties. The secret key is defined as the modular multiplicative inverse of the public key, creating a precise mathematical relationship that ensures accurate decryption. This parameter change eliminates the precision loss that occurs in traditional matrix-based methods during decryption operations.
3Reliability
If matrix-based key systems are used in homomorphic encryption, then cryptographic security is improved, but processing speed worsens
Solution Approach 1:
The patent replaces the mechanical matrix multiplication and inversion operations with simpler scalar arithmetic operations. Instead of performing complex matrix computations during encryption and decryption, the system uses scalar multiplication and modular inverse calculations, which are computationally much less intensive. This substitution maintains cryptographic security through the mathematical hardness of the scalar discrete logarithm problem while dramatically improving processing speed.
Data Source
AI summary
A device that uses homomorphic encryption is disclosed. The device includes a public key data generator configured to generate public key data, and a secret key data generator configured to generate secret key data that includes, as a secret key, an integer that is an element of a matrix obtained as a product of the first public key matrix element and an inverse matrix of the secret key matrix and that is not a multiple of the plain text space size.