QUANTUM SECRET SHARING ALGORITHMS IN NOISY ENVIRONMENT WITH CHEAT-IDENTIFICATION

Abstract

Secure communication has emerged as one of the most promising areas in the contemporary age. This is a critically important area for all enterprises and organizations, and its progress is growing substantially. Quantum secret sharing (QSS) is a crucial component of quantum cryptography that provides a secure technique for transferring confidential data. It utilizes quantum mechanics to ensure that data can only be accessed collectively by authorized individuals, thereby preventing any single participant from affecting the information. This thesis investigates and proposes several QSS algorithms addressing security, noise resilience, and practical implementation challenges in communication. A QSS algorithm based on Grover’s search algorithm is presented. The scheme utilizes Grover’s three-particle quantum state for secret information sharing and eavesdropping detection. The protocol is evaluated in two different noisy channels: amplitude-dampingandphase-dampingnoise. Thesimulationanalysisofthescheme is done on the cloud platform IBM-QE thereby showing the practical feasibility. The protocol’s application in visual cryptography using GNEQR representation of images is explored. The second algorithm proposes a cheating identifiable d-dimensional (t,m) threshold scheme. The dealer distributes both classical and quantum secret information utilizing the generalized Bell states and unitary operations. This protocol allows the dealer to detect and mitigate dishonest behavior through unitary transformations and Bell state analysis, providing a more adaptable and effective solution compared to existing schemes. The protocol is reliable in identifying dishonest participants and negating any eavesdropping. The influence of various noisy environments is examined using quantum fidelity.