Lattice Public Key Cryptosystem with Asymmetric Polynomial Rings
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Solution Overview
Problem
Lattice-based cryptosystems face vulnerabilities to side channel attacks and resource inefficiencies due to long encryption keys and constrained parameter selection, posing security risks, especially with the advent of quantum computers.
Innovation Solution
A lattice-based public key cryptosystem using polynomials defined over quotient rings by specific polynomials φ(X), such as Xp−X−1 or Xn−Xn2+1, to generate public and secret keys, ensuring high security and flexibility in parameter selection.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Reliability
If lattice-based cryptosystem uses traditional polynomial structures, then key generation is straightforward, but the system becomes vulnerable to side channel attacks and algebraic attacks
Solution Approach 1:
The patent applies asymmetry by using polynomials with asymmetric structures - specifically polynomials where the degree n has a special form (n = 2^a * 3^b) and coefficients follow specific patterns. This asymmetric structure makes the polynomial harder to analyze algebraically while maintaining efficient computation, thereby resisting both algebraic attacks and side channel attacks.
Solution Approach 2:
The patent changes critical parameters of the polynomial structure - specifically the degree n is chosen as n = 2^a * 3^b (a product of powers of 2 and 3), and coefficients are selected from specific ranges. These parameter changes create a polynomial structure that is computationally efficient yet resistant to traditional algebraic attacks, resolving the contradiction between security and simplicity.
2Reliability
If lattice-based cryptosystem uses long encryption keys for security, then security against quantum computers is improved, but resource consumption increases
Solution Approach 1:
The patent changes the parameter selection for polynomial degrees and coefficients to optimize the balance between security and resource usage. By selecting n = 2^a * 3^b and specific coefficient ranges, the system achieves quantum-resistant security with more efficient key lengths compared to traditional lattice-based systems, reducing the quantity of computational resources required.
3Productivity
If lattice-based cryptosystem uses polynomials with high structure for ease of computation, then processing speed is improved, but vulnerability to algebraic attacks increases
Solution Approach 1:
The patent applies local quality by making different parts of the polynomial have different properties - the degree n follows a specific form (2^a * 3^b) for computational efficiency, while the coefficients are selected from specific ranges to resist algebraic attacks. This localized differentiation of polynomial properties allows the system to achieve both fast computation and high security.
Solution Approach 2:
The polynomial structure uses asymmetry where the degree and coefficients have different selection criteria - the degree n = 2^a * 3^b provides computational structure, while the coefficient selection provides security against algebraic attacks. This asymmetric design allows efficient computation without compromising security.
Data Source
AI summary
Embodiments of the present disclosure may include a key generation device of a lattice-based public key cryptosystem. In some embodiments, the key generation device may include a communication unit, a storage unit, and a processor that may be configured to control the key generation device to perform operations. In some embodiments, the operations may include generating a public key by using a public key polynomial, where the public key polynomial may belong to a first polynomial ring. In some embodiments, the operations may additionally include generating a secret key that may correspond to the public key. In some embodiments, the secret key may be generated by using a secret key polynomial that may belong to a second polynomial ring. In some embodiments, the operations may additionally include storing the public key and the secret key.