Homomorphic Encryption Bitwise Decomposition
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Solution Overview
Problem
Fully homomorphic encryption systems require significant storage space and processing power, and known implementations, such as RLWE-based schemes, need to maintain a modulus chain that increases the size of prime numbers and perform resource-intensive operations, leading to inefficiencies and data access pattern leakage.
Innovation Solution
A process and system for homomorphic encryption that performs bitwise decomposition and matrix multiplication on ciphertexts, allowing for efficient multiplication and addition operations using a polynomial-based fully homomorphic cryptographic scheme, with the option to distribute computations among processing cores and utilize a graphics processing unit (GPU), reducing the need for resource-intensive operations and secret key expansion.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Reliability
If RLWE-based FHE schemes are used, then homomorphic encryption functionality is achieved, but storage space and processing power requirements increase significantly
Solution Approach 1:
The patent changes the fundamental parameters of the encryption scheme by using polynomial-based FHE with bitwise decomposition instead of traditional RLWE-based approaches. This parameter change reduces the storage requirements for secret keys and ciphertexts while maintaining homomorphic encryption functionality.
Solution Approach 2:
The patent applies segmentation by decomposing ciphertexts into bitwise components. This allows the encryption scheme to operate on individual bits rather than requiring storage of large modulus chain structures, thereby reducing overall storage requirements while preserving the ability to perform homomorphic operations.
2Reliability
If RLWE-based FHE schemes are used, then homomorphic encryption functionality is achieved, but processing power requirements increase due to modulus chain maintenance and key switching operations
Solution Approach 1:
The patent extracts and eliminates the modulus chain structure from the encryption scheme. By removing this resource-intensive component and replacing it with polynomial-based operations and bitwise decomposition, the scheme achieves homomorphic functionality without requiring powerful processing for modulus switching and key switching operations.
Solution Approach 2:
The patent substitutes the mechanical modulus chain operations with polynomial arithmetic and bitwise operations. This replacement reduces the computational complexity and processing power requirements while maintaining the essential homomorphic encryption capabilities.
3Reliability
If conventional FHE systems are used, then encryption security is maintained, but device complexity and resource requirements make the system cumbersome
Solution Approach 1:
The patent changes the operational parameters from large modulus arithmetic to polynomial-based bitwise operations. This parameter change simplifies the device complexity by enabling more efficient implementation of encryption and decryption operations while maintaining security through the mathematical properties of polynomial rings and bitwise decomposition.
Data Source
AI summary
Remote terminals are configured to generate ciphertexts from plaintext polynomials. Each ciphertext corresponds to a plaintext polynomial bound to a message space of a polynomial-based fully homomorphic cryptographic scheme. At least one server is configured to receive ciphertexts via a network from the plurality of remote terminals. The server performs a multiplication operation and an addition operation on the ciphertexts to obtain resultant ciphertexts. The multiplication operation includes performing a bitwise decomposition function on a ciphertext to obtain a bitwise decomposed ciphertext. The bitwise decomposition function maps a multi-bit data type to a sequence of bits. The multiplication operation further includes performing matrix multiplication on the bitwise decomposed ciphertext and a data element belonging to a set of data elements. Message filters, data search engines, and other applications are discussed.