Indeterminate Equation Encryption for Quantum Security
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Solution Overview
Problem
Current public-key cryptography systems, such as RSA and elliptic curve cryptography, are vulnerable to decryption by quantum computers, and existing solutions either require large key sizes or are inefficient for low-power devices.
Innovation Solution
A public-key cryptography system based on indeterminate equations, where a bivariable symmetric indeterminate equation is used as a public key, and random polynomials are generated to create ciphertext, ensuring security against quantum computers while reducing key and ciphertext sizes.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Reliability
If quantum computers are used to break cryptography, then current public-key systems like RSA and elliptic curve cryptography can be decrypted, but this creates a security vulnerability
Solution Approach 1:
The patent changes the mathematical parameters from traditional RSA/ECDSA to indeterminate equation-based cryptography. The public key is defined as an indeterminate equation X(x, y) = 0, and the private key as a solution pair (u, v). This parameter transformation creates a cryptographic system that is resistant to quantum computer attacks while maintaining security properties.
Solution Approach 2:
The patent replaces the mechanical number-theoretic systems (prime factorization, discrete logarithm) with an algebraic geometry-based system. Instead of relying on computational hardness of number theory problems, the system uses the hardness of solving indeterminate equations over finite fields, which is believed to be resistant to quantum algorithms.
2Reliability
If traditional quantum-resistant cryptography is implemented, then security against quantum computers is improved, but key sizes and ciphertext sizes become large
Solution Approach 1:
The patent applies local quality by using symmetric polynomials with specific structural properties. The symmetric polynomial s(x, y) has coefficients that are symmetric functions, which allows for more efficient representation and computation. This local structural optimization reduces the overall key size and ciphertext size while maintaining quantum security.
Solution Approach 2:
The patent transitions from traditional one-dimensional number-theoretic parameters to two-dimensional polynomial structures. By working with polynomials in two variables x and y, and using symmetric polynomial relationships, the system achieves quantum resistance with reduced key sizes compared to traditional approaches that would require larger single-parameter keys.
3Reliability
If larger key sizes are used to ensure quantum security, then cryptographic strength is improved, but computational efficiency for low-power devices deteriorates
Solution Approach 1:
The patent applies partial action by using symmetric polynomials that capture only the essential cryptographic information needed for security. Instead of requiring full-degree polynomials or complex multi-variable systems, the symmetric polynomial structure provides sufficient cryptographic strength with reduced computational complexity, making it suitable for low-power devices.
Solution Approach 2:
The patent creates a composite cryptographic system that combines indeterminate equations with symmetric polynomials and noise polynomials. This composite structure leverages the properties of each component: the indeterminate equation provides the cryptographic challenge, the symmetric polynomial enables efficient representation, and the noise polynomial ensures security. The composite approach achieves quantum security with optimized computational requirements.
Data Source
AI summary
According to one embodiment, an encryption device includes a memory and one or more processors. The one or more processors are configured to: acquire, as a public key, an n-variable symmetric indeterminate equation having an element not more than a constant degree of Fp[t] and determined depending on a total degree of each term, and being symmetric for at least two variables; randomly generate an n-variable polynomial having an element not more than a constant degree of Fp[t], randomly generate an n-variable symmetric polynomial having an element not more than a constant degree of Fp[t] and determined depending on a total degree of each term, and being symmetric for at least two variables, and randomly generate a noise polynomial having an element not more than a constant degree of Fp[t]; and generate a ciphertext from the three polynomials and the n-variable symmetric indeterminate equation for the n-variable plaintext polynomial.