Multivariate Polynomial Encryption for Quantum-Resistant Low-Power Security
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Solution Overview
Problem
Current public-key cryptography methods, such as RSA and elliptic curve cryptography, are vulnerable to quantum computer attacks and require large key sizes and high computational power, making them unsuitable for low-power devices and efficient in a quantum computer era.
Innovation Solution
A public-key cryptography system that uses a nonlinear polynomial with noise to hide the private key, employing indeterminate equations and polynomial operations to generate and encrypt data, ensuring security even with a practical quantum computer, and optimizing for low-power environments.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Reliability
If RSA or elliptic curve cryptography is used, then encryption security is provided, but the system becomes vulnerable to quantum computer attacks
Solution Approach 1:
The patent changes the mathematical foundation of cryptography from RSA/elliptic curve to multivariate polynomial equations over finite fields. This parameter change in the underlying mathematical problem makes the system resistant to quantum computer attacks while maintaining encryption security.
Solution Approach 2:
The patent replaces the traditional cryptographic mechanisms (RSA, elliptic curve) with a new mechanism based on multivariate polynomial equations. This substitution introduces a fundamentally different approach that is not susceptible to quantum algorithms like Shor's algorithm.
2Reliability
If RSA or elliptic curve cryptography is used, then encryption capability is provided, but key size and computational power requirements increase
Solution Approach 1:
The patent segments the encryption problem into multivariate polynomial equations with multiple variables and coefficients. This segmentation allows for more compact key representation and reduces the overall computational complexity compared to traditional methods.
Solution Approach 2:
By changing to multivariate polynomial equations over finite fields, the patent achieves encryption capability with smaller key sizes and reduced computational requirements, making it suitable for resource-constrained devices.
Data Source
AI summary
An encryption device includes one or more hardware processors functioning as the following units. A unit acquires, as a public key, n-variable indeterminate equations X having coefficients with a predetermined degree of a univariate polynomial ring Fp[t] on a finite field Fp. A unit embeds a plaintext m into coefficients of n-variable plaintext polynomial factors m having coefficients with a predetermined degree of the Fp[t]. A unit generates an n-variable plaintext polynomial M by multiplying the n-variable plaintext polynomial factors mi whose number is one or more. A unit randomly generates n-variable polynomials sk (k=1, 2), n-variable polynomials rk, and noise polynomial ek, each having coefficients with a predetermined degree of the Fp[t]. A unit generates a ciphertext ck by executing an operation including at least one of adding, subtracting, and multiplying the sk, the rk, the ek, and the X to, from, or by the M.