Inner-Product Functional Encryption for Quantum-Resistant Data Security
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Solution Overview
Problem
Existing encryption schemes, particularly those based on Learning With Error (LWE) and lattice problems, are unsuitable for applications like IoT, TLS, and cloud computing due to large parameter sizes, low speed, and vulnerability to quantum computer attacks.
Innovation Solution
A functional encryption system utilizing a key generation device, encryption device, and decryption device based on LWE and lattice problems to generate and decrypt encrypted data, incorporating random noise to create an approximation of inner products, enhancing security against quantum attacks.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Reliability
If LWE-based public key encryption is used, then security against quantum computer attacks is improved, but encryption speed and parameter size efficiency deteriorate
Solution Approach 1:
The patent changes the mathematical parameters and structure of the encryption scheme by introducing functional encryption based on inner product computations. Instead of using traditional LWE parameters that result in large key sizes and slow computation, the patent employs vector-based representations and inner product operations that reduce computational complexity while maintaining quantum resistance through the hardness of the underlying lattice problem.
Solution Approach 2:
The patent substitutes traditional mechanical encryption operations with mathematical operations on vectors and matrices. By replacing conventional public key encryption mechanisms with functional encryption based on inner products, the system achieves both quantum resistance and improved computational efficiency, as inner product computations can be optimized using vector operations and linear algebra techniques.
2Reliability
If LWE-based public key encryption is used, then security against quantum computer attacks is improved, but parameter size increases
Solution Approach 1:
The patent fundamentally changes the parameter representation by using compact vector forms instead of traditional LWE parameters. The functional encryption scheme represents keys and messages as vectors in lower-dimensional spaces, and uses inner product operations that require fewer bits to represent. This parameter transformation maintains the security guarantees of lattice-based cryptography while dramatically reducing the size of public keys, private keys, and ciphertexts.
Solution Approach 2:
The patent uses vector copies and linear combinations to represent encryption information more efficiently. Instead of storing large LWE parameters, the system stores compact vector representations that can be replicated and combined through inner product operations. This copying mechanism allows the same security functionality to be achieved with much smaller parameter sizes by utilizing the redundancy and structure inherent in vector spaces.
3Reliability
If random noise is introduced to create approximation of inner products, then security is improved, but measurement precision deteriorates
Solution Approach 1:
The patent converts the harmful effect of noise (which normally degrades precision) into a beneficial security feature. By deliberately introducing random noise into the inner product computation, the system ensures that even if an attacker intercepts the encrypted data, they cannot recover the exact inner product value. The noise acts as a masking mechanism that preserves security while the approximation remains sufficient for the intended functional encryption applications, such as private information retrieval and secure machine learning.
Data Source
AI summary
A functional encryption system includes a key generation device configured to generate a public key and a secret key, based on a master key and a parameter vector, an encryption device configured to generate encrypted data by encrypting an input vector, based on the public key, and a decryption device configured to generate decrypted data corresponding to an approximation value of an inner product of the parameter vector and the input vector by decrypting the encrypted data based on the secret key. Security of data used in machine learning, biometric authentication, etc. may be reinforced and attacks using quantum computers may be blocked by incurring random noise in the decrypted data based on the functional encryption using the LWE problem and the lattice problem.