Continuous-variable quantum digital signatures over insecure channels

Abstract

Digital signatures ensure the integrity of a classical message and the authenticity of its sender. Despite their far-reaching use in modern communication, currently used signature schemes rely on computational assumptions and will be rendered insecure by a quantum computer. We present a quantum digital signatures (QDS) scheme whose security is instead based on the impossibility of perfectly and deterministically distinguishing between quantum states. Our continuous-variable (CV) scheme relies on phase measurement of a distributed alphabet of coherent states, and allows for secure message authentication against a quantum adversary performing collective beamsplitter and entangling-cloner attacks. Crucially, for the first time in the CV setting we allow for an eavesdropper on the quantum channels and yet retain shorter signature lengths than previous protocols with no eavesdropper. This opens up the possibility to implement CV QDS alongside existing CV quantum key distribution (QKD) platforms with minimal modification.

Digital Signatures with Quantum Candies

“…An open question is, therefore, the study of “lossy” qandy channels and establishing what kind of digital signatures are achievable over a lossy channel (see, for example, [ 26 ]) using qandy communication. In addition, the field of continuous-variable quantum information attempts to employ physical continuous variables towards the task of quantum cryptography and quantum digital signatures in particular [ 27 , 28 ]. Therefore, another potential research direction is the study of whether (and how) the qandy model can extended to enable digital signatures with “continuous-variable qandies”.…”

Agile and versatile quantum communication: signatures and secrets

“…The χ denotes Bob's Holevo information about Charlie's distributed state. Then the final signature length L required to sign a 1 bit message with ε f ail probability of failure is implicitly given by [19,20]…”

“…A QDS protocol in which Alice sends quantum coherent states was previously considered in Ref. [19]. There, it is Bob and Charlie who form eliminated signatures, and check for mismatches between their eliminated signatures and Alice's declaration of which states she sent.…”

“…To go beyond [19] we apply the postselection technique to QDS-f , which decreases the number of quantum states L required to sign a message, particularly in the presence of channel noise. Since (in contrast to QDS-b) it is now Bob and Charlie who heterodyne, rather than Alice, both terms p e and p err now change with the choice of postselection region.…”

“…(B3) under the model described in Appendix B, which includes both channel excess noise ξ, ascribed to Eve, and a detector efficiency of 50% which Eve cannot exploit. We allow Eve to perform the entangling cloner attack [19] which is expected to be optimal in the limit α → 0, and close to optimal for the small α's used here, and probability p e may be estimated as in Appendix A once the worstcase α and ξ have been estimated from data. The ideal signature lengths for QDS-b are displayed in Fig.…”