Post-Quantum Asymmetric Key Cryptosystem with Distributed Key Management
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Solution Overview
Problem
Current asymmetric key algorithms face issues such as slow data transmission, vulnerability to plaintext and brute force attacks, requirement for synchronized key updates, weakness against quantum attacks, and lack of distributed key refresh mechanisms.
Innovation Solution
A lattice algebra-based post-quantum asymmetric key generation method that generates public and private keys using a p-vector and p-array, allowing for efficient encryption and decryption, and enabling distributed key refresh without compromising security.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Reliability
If classical asymmetric key algorithms (RSA, ECC) are used, then security is provided, but encryption and decryption require relatively large amount of computation and more time is required
Solution Approach 1:
The patent changes the mathematical parameters from traditional RSA/ECC to lattice-based parameters (p-vectors, p-arrays, moduli) that enable faster computation while maintaining security. The use of different parameter sets (first and second parameter sets with different primes) allows optimization for both security and speed.
Solution Approach 2:
The patent segments the key management into multiple independent components: first public key paired with first private key, and second public key paired with second private key. This segmentation allows parallel processing and distributed key refresh without requiring synchronized updates of all keys.
2Quantity of substance
If current asymmetric key algorithms are used, then key pairs are generated, but protocols cannot send large amounts of data in a short amount of time
Solution Approach 1:
The patent introduces dynamic key selection where the system can switch between different public keys (first and second) and their corresponding private keys based on operational needs. This dynamic approach enables optimized data transmission rates without being constrained by a single key pair's performance characteristics.
3Reliability
If a user changes his/her public key for a new one, then security is improved, but all the other users need to update their private keys to be paired with the new public key
Solution Approach 1:
The patent segments the key relationship into independent first and second key pairs. When a public key needs updating, only the corresponding private key needs to be updated, not all other users' keys. This segmentation breaks the tight coupling that requires system-wide key updates.
Solution Approach 2:
The patent introduces an intermediary mechanism through the dual key pair system that mediates key updates. The first and second parameter sets act as intermediaries that allow selective key refresh without requiring all participants to synchronize their key updates.
4Reliability
If integer factorization-based algorithms (RSA, DSA) or discrete logarithm problem based algorithms (ECC) are used, then asymmetric cryptography is achieved, but they are weak against Shor's and Grover's algorithms based post-quantum attacks
Solution Approach 1:
The patent fundamentally changes the mathematical parameters from integer factorization and discrete logarithm problems to lattice-based problems (p-vectors, p-arrays, modular arithmetic with primes). Lattice-based cryptography is resistant to quantum attacks from Shor's and Grover's algorithms, providing post-quantum security while maintaining asymmetric cryptographic functionality.
Data Source
AI summary
In a post-quantum asymmetric key generation method and system, a processing unit generates, based on a prime and an arithmetic function or a classical string, a prime vector which has an infinite number of components; generates a prime array based on the prime vector; generates an associated matrix based on the prime array; obtains, based on the associated matrix and a first reference prime, a first reference inverse prime array that serves as a private key; and obtains a public key that is paired with the private key based on a second reference inverse prime array. The second reference inverse prime array is obtained based on the associated matrix, the first reference prime, a second reference prime, and a randomization array.