Protocols for counterfactual and twin-field quantum digital signatures

Quantum digital signature (QDS) is the quantum version of its classical counterpart and can offer security against attacks of repudiation, signature forging, and external eavesdropping on the basis of quantum -mechanical no-go principles. Here we propose a QDS scheme based on quantum counterfactuality, which leverages the concept of interaction -free measurement. Employing the idea behind twin -field cryptography, we show how this two-way protocol can be turned into an equivalent noncounterfactual, one-way protocol that is both more practical and also theoretically helpful in assessing the experimental feasibility of the first protocol. The proposed QDS protocol can be experimentally implemented with current quantum technology.