Homomorphic Encryption Scheme with Bootstrapping for Noise Management
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Solution Overview
Problem
Current homomorphic encryption schemes face challenges with large ciphertext expansion, limited number of homomorphic operations due to noise growth, and security concerns, particularly in cloud computing and blockchain applications, where efficient and secure analytics on encrypted data are needed without decryption.
Innovation Solution
A Fully Homomorphic Encryption (FHE) scheme with cipher expansion of 6 or less under private-key encryption and 7+log2(n) or less under public-key encryption, using a bootstrapping processor that generates valid LWE ciphers with bounded noise size, enabling unlimited homomorphic operations on encrypted data while maintaining security based on LWE and RLWE problems, even against quantum computers.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Adaptability or versatility
If homomorphic operations are performed on ciphertexts, then analytics on encrypted data can be achieved, but noise grows quickly and limits the number of operations
Solution Approach 1:
The patent applies bootstrapping as a preliminary action to refresh ciphertexts before they are used in homomorphic operations. This process reduces noise accumulation by performing decryption and re-encryption on the ciphertexts, allowing them to be used for unlimited homomorphic operations without noise growth limitations. The bootstrapped ciphertexts serve as fresh inputs that reset the noise budget.
Solution Approach 2:
The patent introduces bootstrapping as an intermediary process between ciphertext storage and homomorphic computation. This intermediary step transforms noisy ciphertexts into refreshed ciphertexts with reduced noise, enabling sustained homomorphic operations. The bootstrapping mechanism acts as a mediator that reconciles the conflict between performing analytics and managing noise growth.
2Reliability
If traditional encryption schemes are used, then privacy protection is achieved, but analytics cannot be performed without decryption
Solution Approach 1:
The patent implements a homomorphic encryption scheme that provides dual functionality: it maintains the privacy protection of traditional encryption while simultaneously enabling analytics on encrypted data. The encryption scheme is designed to support both confidentiality and computability, allowing ciphertexts to be used directly in homomorphic operations without decryption.
Solution Approach 2:
The patent changes the cryptographic parameters and mathematical structure of the encryption scheme to enable homomorphic properties. By using specific lattice-based cryptographic constructions and parameter selections, the scheme achieves both strong privacy protection and the ability to perform analytics on encrypted data through homomorphic operations.
3Quantity of substance
If cipher expansion is reduced for compact storage, then storage costs decrease, but the complexity of maintaining security and functionality increases
Solution Approach 1:
The patent optimizes cryptographic parameters to achieve compact ciphertext expansion while maintaining security. By carefully selecting lattice dimensions, modulus values, and error distribution parameters, the scheme reduces ciphertext size compared to previous homomorphic encryption schemes while preserving security based on hard mathematical problems.
Solution Approach 2:
The patent applies different optimization strategies to different parts of the encryption scheme. Specific components such as key generation, encryption, and bootstrapping are optimized with tailored parameter selections and algorithmic improvements, allowing compact ciphertexts while managing overall system complexity through localized optimizations.
Data Source
AI summary
This is a system and method for homomorphic encryption comprising: a key generation module configured to generate a secret key, a public key and a bootstrapping key; a private-key encryption module configured to generate a first ciphertext using the secret key; a public-key encryption module configured to generate a second cyphertext using the public key; a private-key decoding module configured to decode a first ciphertext, a second ciphertext and an encrypted analytic result; a homomorphic computational module configured to perform an analytical operation, according to an analytical operation request on the first ciphertext and the second ciphertext without decrypting the first ciphertext and the second ciphertext using the bootstrapping key; and, wherein the encrypted analytical result is provided by the homomorphic computational module and are encrypted with the secret key.