On a Grover-Based Quantum Signature Scheme and a Teleportation-Based Design.

Abstract

Quantum computation, with tools including Grover's algorithm, quantum walks, and quantum teleportation, plays an important role in quantum signature designs. Although such designs offer signature functionality, they sometimes come at the cost of security. This paper first reviews a Grover-based scheme and shows how man-in-the-middle attacks enable complete key recovery, Alice's disavowal, and Bob's forgery. We then propose an arbitrated quantum signature scheme based on quantum teleportation and a strengthened quantum one-time pad. The scheme is designed for quantum messages with known classical descriptions, not for arbitrary unknown quantum states. The security of the proposed scheme is analyzed through a formal adversarial model for unforgeability and non-repudiation, and its resilience against replay, intercept-and-resend, man-in-the-middle, entanglement, and collective or coherent attacks is examined. Numerical simulations and an asymptotic resource analysis further illustrate the practicality of the scheme.