Multivariate Polynomial Cryptography for Quantum-Safe Low Latency
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Solution Overview
Problem
Current cryptographic methods face challenges in maintaining security against cracking attempts, especially with the advent of quantum computing, leading to increased complexity and key lengths that result in high latency and computational inefficiencies.
Innovation Solution
A cryptographic method involving the use of noise variables to compute ciphers and data elements based on public keys, allowing for secure transmission and verification of digital assets with low latency and computational simplicity, including a single-iteration Zero-Knowledge Proof protocol.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Reliability
If mathematical complexity and key length are increased to protect against quantum computing cracking attempts, then security against cracking is improved, but latency and computational effort increase significantly
Solution Approach 1:
The patent changes the mathematical parameters from traditional RSA large prime factorization to multivariate polynomial equations over finite fields. This parameter change allows achieving equivalent or higher security levels with significantly reduced computational complexity and latency, as the multivariate approach enables faster key generation, encryption, and decryption operations while maintaining resistance against quantum computing attacks.
Solution Approach 2:
The patent substitutes the traditional mechanical/mathematical approach of large number factorization with an algebraic approach using multivariate polynomial systems. This substitution replaces the computationally intensive factorization problem with solving systems of quadratic equations, which can be efficiently handled using Gröbner basis algorithms and other algebraic methods, thereby reducing latency while maintaining security.
2Reliability
If mathematical complexity and key length are increased to protect against quantum computing cracking attempts, then security against cracking is improved, but computational effort increases significantly
Solution Approach 1:
The patent changes the cryptographic parameters from traditional symmetric/asymmetric key lengths to multivariate polynomial dimensions and degrees. This parameter transformation enables achieving quantum-resistant security with reduced computational effort, as the multivariate approach allows for more efficient key operations compared to increasing key lengths in traditional systems.
Solution Approach 2:
The patent segments the cryptographic problem into multiple variables and equations rather than relying on a single large mathematical operation. By dividing the security problem into a system of multivariate equations, the computational effort is distributed and optimized through algebraic algorithms, reducing overall energy consumption while maintaining security against quantum attacks.
3Reliability
If key length is increased to maintain security in the face of quantum computing, then security is improved, but digital communication efficiency deteriorates
Solution Approach 1:
The patent fundamentally changes the cryptographic parameters from traditional key-length-based security to multivariate polynomial system complexity. This parameter revolution enables achieving quantum-resistant security with compact key sizes, thereby maintaining high digital communication efficiency without the overhead of excessively long keys that would slow down data transmission and processing.
Data Source
AI summary
Cryptographic methods and systems for key exchange, digital signature and zero-knowledge proof. In the digital signature scenario, there is provided a method of signing a digital document, comprising: obtaining a private cryptographic key associated with the signer; obtaining a digital asset from the digital document; selecting a base data element; computing a plurality of signature data elements from (i) the digital asset, (ii) the base data element and (iii) the private cryptographic key; and transmitting the digital document and the plurality of signature data elements to a recipient over a data network. Provenance of the digital document is confirmable by the recipient carrying out a predefined computation involving the digital document, the signature data elements, a plurality of noise variables and a public cryptographic key corresponding to the private cryptographic key associated with the signer. In the zero-knowledge proof scenario, the digital asset plays the role of a challenge data element.