Abstract
With the practical implementation of continuous-variable quantum cryptographic protocols, security problems resulting from measurement-device loopholes are being given increasing attention. At present, research on measurement-device independency analysis is limited in quantum key distribution protocols, while there exist different security problems for different protocols. Considering the importance of quantum digital signature in quantum cryptography, in this paper, we attempt to analyze the measurement-device independency of continuous-variable quantum digital signature, especially continuous-variable quantum homomorphic signature. Firstly, we calculate the upper bound of the error rate of a protocol. If it is negligible on condition that all measurement devices are untrusted, the protocol is deemed to be measurement-device-independent. Then, we simplify the calculation by using the characteristics of continuous variables and prove the measurement-device independency of the protocol according to the calculation result. In addition, the proposed analysis method can be extended to other quantum cryptographic protocols besides continuous-variable quantum homomorphic signature.
Highlights
Quantum cryptography is believed to be unconditionally secure because its security is ensured by physical laws rather than computational complexity
We point out that a Continuous-variable quantum digital signature (CVQDS) protocol is measurement-device-independent if its error rate is negligible on condition that all measurement devices are untrusted
According to the objective of CVQDS, we proposed that a CVQDS protocol is measurement-device-independent if its error rate is negligible on condition that all measurement devices are untrusted
Summary
Quantum cryptography is believed to be unconditionally secure because its security is ensured by physical laws rather than computational complexity. Since continuous-variable quantum cryptographic protocols are very probable to be implemented in practice, such analysis which assumes all devices are perfect is insufficient to judge whether a protocol is truly secure or not. In 2006, Acin et al [1] proposed the first device-independent quantum key distribution (DI-QKD) protocol and proved its security against individual attacks. Compared to DI quantum cryptographic protocols, measurement-device-independent (MDI) quantum cryptographic protocols can achieve higher efficiency with practical implementation while not losing much security, so it is widely studied. To improve practicability and efficiency of QKD, several continuous-variable measurement-device-independent quantum key distribution (CV-MDI-QKD). Since there exist different security problems for different protocols, device independency analysis of other continuous-variable quantum cryptographic protocols except QKD protocols should be explored. (1) We analyze the measurement-device independency of a continuous-variable quantum digital signature scheme. Since the random variable follows the Gaussian distribution, the probability can be immediately obtained without calculation
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