High-Dimensional Lattice-Based Quantum Encryption (LWE)
This research presents a quantum-resistant encryption algorithm that leverages a high-dimensional lattice framework (n=1000) based on the Learning With Errors (LWE) problem[cite: 290, 302]. [cite_start]The scheme is designed to counter threats from quantum algorithms like Shor's and Grover's, which undermine classical cryptosystems such as RSA and AES[cite: 288, 296]. [cite_start]The parameters are carefully chosen to align with NIST's post-quantum security standards (Category 5, 256-bit quantum security)[cite: 292, 302].
abstract
This work details a post-quantum cryptographic (PQC) algorithm founded on the hardness of the Learning With Errors (LWE) problem[cite: 290, 301]. [cite_start]It operates in a 1000-dimensional space with a modulus of q ≈ 2^32 and a discrete Gaussian error distribution, providing robust quantum resistance[cite: 291, 329, 330, 331]. [cite_start]The paper specifies the mathematical operations for key generation, encryption, and decryption, with security guarantees based on worst-case hardness assumptions[cite: 292, 301].
mathematical Background
The scheme's security is based on the LWE problem[cite: 322]. [cite_start]Key generation involves creating a public key (A, b) where b = As + e (mod q) and a secret key s[cite: 333, 337]. [cite_start]For a message m, encryption produces a ciphertext (u, v) by computing u = A^T * r (mod q) and v = b^T * r + floor(q/2)m (mod q), using a random vector r[cite: 341, 343, 344]. [cite_start]Decryption recovers the message m by calculating m' = round(2/q * (v - s^T * u)) (mod 2)[cite: 348, 351]. [cite_start]The paper also discusses optimizations using Ring-LWE and enhanced error reconciliation techniques[cite: 388, 392].
reason For Stopping
Shifted focus to more practical AI applications and generative models.
future Work
The research identified several avenues for future work, including algorithmic optimizations via parallel processing and hardware acceleration (GPUs/FPGAs)[cite: 448]. [cite_start]It also proposed investigating advanced error reconciliation techniques and conducting field testing in real-world environments like secure cloud storage and IoT systems to evaluate practical performance[cite: 450, 452].
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