Graph Isomorphism Zero-Knowledge Proof Authentication
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Solution Overview
Problem
Existing user authentication methods, such as username/password systems, are insecure when transmitted over networks and require complex key management, making them difficult for casual users to implement securely within web browsers.
Innovation Solution
A zero-knowledge proof (ZKP) authentication protocol based on graph isomorphism, which generates a private key from a user's password within the browser, allowing secure authentication without transmitting private information across the network, using Ajax and JavaScript for implementation.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Reliability
If username and password are transmitted over the network for authentication, then user authentication can be performed, but security is compromised as credentials are prone to interception
Solution Approach 1:
The patent extracts the private key from the authentication transmission entirely. Instead of sending passwords or private keys over the network, the system uses zero-knowledge proofs where only cryptographic commitments and challenges are transmitted. The private key remains exclusively on the client device and never leaves the device, eliminating the security vulnerability of credential interception.
Solution Approach 2:
The patent introduces cryptographic protocols (zero-knowledge proofs based on graph isomorphism) as intermediaries between the user and server. These protocols enable authentication without direct transmission of sensitive credentials. The mathematical structures act as mediators that verify identity without revealing private information, transforming the authentication process from direct credential sharing to indirect cryptographic verification.
2Reliability
If asymmetric cryptography with digital certificates is used for secure authentication, then authentication security is improved, but device complexity increases due to key management requirements
Solution Approach 1:
The patent removes the complex key management infrastructure from the authentication process. Instead of requiring users to manage private keys, digital certificates, and cryptographic libraries, the system extracts only the essential authentication function. Private keys are generated and stored locally without requiring external key management systems, and authentication is achieved through cryptographic protocols that don't require traditional certificate infrastructure.
Solution Approach 2:
The system enables self-service authentication where the user's browser autonomously generates and manages cryptographic credentials without external intervention. The private key is generated locally in the browser, stored securely without external key management, and used automatically in zero-knowledge proof protocols. This eliminates the need for users to manually manage complex cryptographic infrastructure.
3Reliability
If traditional ZKP protocols based on discrete logarithm or elliptic curve cryptography are implemented, then authentication security is improved, but ease of operation deteriorates due to infeasibility within web browsers
Solution Approach 1:
The patent changes the mathematical parameters and structures used in zero-knowledge proofs from traditional discrete logarithm or elliptic curve problems to graph isomorphism problems. This parameter change enables the protocol to be implemented efficiently in web browsers using standard JavaScript, while maintaining cryptographic security. The graph-based approach uses different mathematical foundations that are more compatible with browser-based computation.
Solution Approach 2:
The patent substitutes complex cryptographic mechanics with a more browser-friendly alternative. Instead of relying on heavyweight cryptographic libraries for discrete logarithm or elliptic curve operations, the system uses graph isomorphism protocols that can be implemented with basic JavaScript array manipulations and graph algorithms, making the system feasible for browser-based implementation without requiring specialized cryptographic infrastructure.
4Reliability
If private keys are stored locally on the user's machine, then authentication security is improved, but ease of operation worsens due to requirements for secure local storage
Solution Approach 1:
The system implements self-service key management where the browser automatically generates, stores, and manages private keys without requiring user intervention or external secure storage infrastructure. The private key is generated locally in the browser's memory and stored using the browser's native secure storage mechanisms, eliminating the need for users to manually configure secure storage solutions.
Solution Approach 2:
The patent leverages the universal capabilities of modern web browsers to handle private key storage. Instead of requiring specialized secure storage hardware or software, the system uses the browser's built-in cryptographic capabilities and secure storage mechanisms that are already universally available. This multi-functional approach uses the browser for key generation, storage, and cryptographic operations, eliminating the need for separate secure storage infrastructure.
Data Source
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AI summary
A method of generating a private key for use in an authentication protocol comprises, at a client: receiving a user specific identifier; converting the identifier through a one-way function to a string of a pre-determined length; and mapping said string to a permutation ppriv of a pre-determined order, said permutation being operable with a first graph G1 to generate a second graph G2 = ppriv (G1).