Elliptic-Curve Key Exchange Using Isomorphic Mapping Against Quantum Attacks
Find Innovative SolutionsGenerate Solutions
Solution Overview
Problem
Current asymmetric cryptography methods, such as Elliptic-Curve-Diffie-Hellman key exchange, are vulnerable to quantum computer attacks and lack standardized, secure post-quantum cryptography solutions.
Innovation Solution
A method for arranging a shared cryptographic key using isomorphic and inverse mappings between elliptic curves, where points on a first elliptic curve are exchanged via a public channel after point compression, and the key is determined through a non-trivial inverse mapping, ensuring security against quantum computer attacks.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Reliability
If standard ECDH key exchange is used, then implementation is simple and well-established, but security is vulnerable to quantum computer attacks
Solution Approach 1:
The patent introduces an intermediary isomorphic mapping function Φ that transforms points between two elliptic curves E and E'. This mapping acts as a mediator that allows the key exchange to occur on curve E' (which is secure against quantum attacks) while maintaining the mathematical structure needed for Diffie-Hellman key exchange. The mapping function bridges the gap between standard ECDH implementation and post-quantum security requirements without requiring completely new protocols.
Solution Approach 2:
The patent changes the parameters of the elliptic curve system by introducing a second elliptic curve E' that is isomorphic to the original curve E through mapping Φ. By performing key exchange operations on the transformed curve E' and then mapping results back to E, the system achieves post-quantum security while maintaining compatibility with existing ECDH infrastructure. This parameter transformation allows the same mathematical operations to provide enhanced security.
2Productivity
If point compression is applied to reduce transmission data, then communication efficiency improves, but key reconstruction difficulty must be maintained
Solution Approach 1:
The patent applies asymmetric treatment to point compression by compressing points on curve E' differently than points on curve E. The isomorphic mapping Φ transforms uncompressed points from E to compressed points on E' for transmission. This asymmetric compression approach allows efficient communication while the non-trivial nature of the isomorphic mapping ensures that compressed points cannot be easily reversed to reconstruct the original key material, maintaining security against reconstruction attacks.
Data Source
AI summary
Various embodiments of the teachings herein include a method for arranging a shared cryptographic key with a communication partner. The method may include: selecting a first point of a first elliptic curve; sending the first point to the communication partner using a public channel; receiving a second point of the first elliptic curve from the communication partner; and determining the shared key using a non-trivial, inverse shared mapping of the second point with respect to a shared isomorphic mapping of a second elliptic curve onto the first elliptic curve.