Multivariable Public-Key Encryption with Compact Quantum-Safe Ciphertext
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Solution Overview
Problem
Existing public-key cryptography systems, such as RSA and elliptic curve cryptography, are vulnerable to decryption by quantum computers, and existing alternatives like lattice-based cryptography are inefficient for low-power environments and require large key sizes.
Innovation Solution
A new public-key cryptography system using algebraic surfaces and multivariable polynomials, where a symmetric indeterminate equation is used to generate a ciphertext with a noise polynomial, ensuring security against quantum computers and reducing ciphertext length.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Reliability
If lattice-based cryptography is used to ensure quantum security, then security against quantum computers is improved, but key size and computational complexity increase making it inefficient for low-power environments
Solution Approach 1:
The patent changes the mathematical parameters from traditional lattice-based structures to multivariable polynomial equations over finite fields. By using equations with multiple variables and symmetric structures, the system achieves quantum security with significantly reduced key sizes and computational requirements, making it suitable for low-power environments while maintaining security against quantum attacks.
2Ease of operation
If traditional public-key cryptography (RSA, elliptic curve) is used, then ease of operation is maintained, but security is compromised when quantum computers appear
Solution Approach 1:
The patent substitutes the mathematical foundation from number-theoretic problems (factoring, discrete logarithms) to polynomial equation solving over finite fields. This replacement maintains operational simplicity through standardized cryptographic protocols while providing quantum security, as solving multivariable polynomial equations with symmetric constraints is computationally hard even for quantum computers.
3Reliability
If quantum-resistant cryptography is implemented, then security is improved, but ciphertext length increases
Solution Approach 1:
The patent employs asymmetric structures in the polynomial equations where the public key consists of equations with specific symmetric properties, while the private key exploits asymmetric knowledge of the factorization structure. This asymmetry enables compact ciphertext representation similar to traditional cryptography while maintaining quantum resistance through the hardness of solving the multivariable polynomial system.
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 being symmetric for at least two variables; embed the plaintext into coefficients of an n-variable plaintext polynomial having an element not more than a constant degree of Fp[t]; 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 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 equation for the n-variable plaintext polynomial.