Title: Quantum Entanglement-Driven Modular Arithmetic

Jincheng Zhang

Published Aug 31, 2026• 0 citations

Abstract

Quantum entanglement, a cornerstone of quantum mechanics, presents a unique opportunity to revolutionize cryptographic systems. Traditional hashing methods are vulnerable to various attacks, while the inherent correlations within entangled states offer a novel approach for key generation and verification. This paper introduces a new method of modular arithmetic utilizing quantum entanglement, shifting away from conventional hashing and leveraging non-local correlations to enhance security and resilience. We explore the fundamental principles behind this approach, detailing the algorithm's design, mathematical foundations, and potential security implications. This work focuses on establishing a robust and verifiable key generation system based on entanglement, potentially surpassing the limitations of existing cryptographic techniques.

DOI: 10.5281/zenodo.22199451

Related papers

Quantum-Enhanced Modular Arithmetic for Cryptographic Key Distribution

Jincheng Zhang

Quantum-enhanced modular arithmetic represents a significant advancement in cryptographic key distribution, leveraging the principles of quantum entanglement to establish a fundamentally more secure system than conventional methods. This paper explores the potential of this approach, detailing a novel quantum-enhanced modular arithmetic protocol designed to exhibit near-perfect key security against known attacks. We outline the core mechanism, emphasizing the crucial role of entangled qubits in creating a robust key generation process. This investigation addresses the challenges inherent in transitioning from classical to quantum cryptography, highlighting the potential benefits of this enhanced security paradigm.

Aug 31, 20260 citations

Title: Quantum Entanglement-Driven Algorithm for Prime Number Generation

Jincheng Zhang

Quantum entanglement, a phenomenon where two or more particles become linked and share the same fate, offers a unique pathway for computation and communication. This research explores the potential of leveraging this quantum property to enhance the generation and verification of prime numbers, a computationally challenging task. We propose a novel algorithm, dubbed the "Quantum Entanglement-Driven Prime Generation" (QEDPG), that utilizes entangled particle pairs to explore prime number sequences with significantly increased precision and speed compared to traditional methods. This work details the core mechanism, the rationale behind the design choices, and the preliminary results demonstrating the algorithm's efficacy. The focus is on establishing a fundamentally new approach that exploits quantum entanglement to unlock more efficient prime number distribution.

Sep 6, 20260 citations

Quantum-Enhanced Modular Arithmetic for Cryptography

Jincheng Zhang

Quantum-enhanced modular arithmetic presents a revolutionary approach to cryptography, capitalizing on the unique properties of quantum mechanics to create fundamentally more secure keys. This paper investigates the implementation of a novel quantum-based 'entangled parity' operation, demonstrating its potential to substantially improve the security of cryptographic keys through enhanced resistance to known attacks. We explore the core mechanism of this system, outlining its potential to significantly reduce computational overhead while bolstering resistance to brute-force attacks and other established vulnerabilities. The research focuses on demonstrating a practical implementation and showcasing the advantages of this quantum-enhanced approach compared to traditional methods.

Sep 2, 20260 citations

Title: Non-Euclidean Geometry for Quantum Entanglement Measurement

Jincheng Zhang

Quantum entanglement, a cornerstone of quantum mechanics, presents a profound challenge for experimental verification and manipulation. Traditional measurement techniques often fail to capture the true essence of this correlated state, leading to inaccuracies and limitations. This paper explores the utilization of non-Euclidean geometry as a foundational framework for understanding and quantifying entanglement, proposing a novel metric designed to address the inherent challenges associated with measurement. The core claim is to extend the concept of non-Euclidean geometry to provide a rigorous framework for understanding and quantifying the entanglement of quantum systems, specifically focusing on the problem of measurement. This investigation will detail the introduction of a new metric, its mathematical properties, and its potential for revolutionizing entanglement measurement. The research will also delve into the implications of this approach for quantum computing and communication, highlighting the potential for a more fundamental and precise understanding of these complex phenomena.

Sep 3, 20260 citations

Title: Quantum-Enhanced Topological Search for Cryptographic Keys

Jincheng Zhang

The increasing reliance on cryptographic keys makes them a prime target for attack. Traditional methods often struggle with the complexity of searching vast, highly interconnected topological data spaces. This research proposes a novel quantum algorithm designed to significantly enhance the efficiency of cryptographic key search, leveraging quantum entanglement and superposition to explore the space more effectively. The core mechanism centers around exploiting quantum properties to reduce the search time and improve the security of encryption protocols. We present a framework for quantum topological search, detailing the design of a quantum search algorithm that utilizes entangled qubits to efficiently traverse the search space, minimizing computational bottlenecks. The proposed algorithm promises substantial improvements in key search speed and potentially enhances the robustness of cryptographic systems. This work explores the potential of quantum computing to revolutionize cryptographic key management, addressing a critical challenge in the field of information security.

Aug 29, 20260 citations

Title: Quantum Complexity Theory - Entanglement-Driven Verification

Jincheng Zhang

Quantum Complexity Theory (QCT) offers a novel framework for verifying the correctness of complex mathematical proofs, moving beyond traditional verification methods reliant on computational complexity. This paper introduces a new protocol leveraging quantum entanglement to simultaneously assess multiple steps within a proof, dramatically increasing the probability of detecting subtle inconsistencies. The core mechanism involves creating entangled qubits to explore the proof space in a fundamentally different way, revealing logical errors with significantly enhanced precision. We demonstrate the effectiveness of this approach through a detailed analysis of a simplified example, highlighting its potential to revolutionize the verification process. The research explores the inherent challenges and opportunities presented by quantum mechanics in this domain, emphasizing the potential for a paradigm shift in mathematical assurance.

Sep 4, 20260 citations