Quantum secret-sharing: single photon-based (<i>t,n</i>) threshold scheme with identity authentication

Abstract The <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mo stretchy="false">(</mml:mo> <mml:mi>t</mml:mi> <mml:mo>,</mml:mo> <mml:mi>n</mml:mi> <mml:mo stretchy="false">)</mml:mo> </mml:math> -threshold schemes offer significant advantages over <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mrow> <mml:mfenced close=")" open="("> <mml:mrow> <mml:mi>n</mml:mi> <mml:mo>,</mml:mo> <mml:mi>n</mml:mi> </mml:mrow> </mml:mfenced> </mml:mrow> </mml:math> -threshold schemes due to their flexibility, fault tolerance, and practicality. In this paper, a <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mo stretchy="false">(</mml:mo> <mml:mi>t</mml:mi> <mml:mo>,</mml:mo> <mml:mi>n</mml:mi> <mml:mo stretchy="false">)</mml:mo> </mml:math> -threshold quantum secret-sharing (QSS) and quantum state sharing schemes based on single photons are proposed by incorporating unitary phase shift operations. The proposed scheme employs symmetric bivariate polynomials and utilizes polynomial interpolation for secret sharing. This approach facilitates the secure distribution of classical data and quantum states while maintaining confidentiality and integrity during transmission. Mutual identity authentication between the dealer and participants is ensured, and the accuracy of secret reconstruction is achieved using Lagrange interpolation. The analysis demonstrates that the proposed scheme is resilient against common interception methods, including eavesdropping attacks and participant-driven threats such as entanglement swapping. Additionally, the scheme is characterized by ease of implementation within physical frameworks and adaptability to various applications offering a practical and efficient alternative to existing methods.