Coherent Signal Transfer and Quantum Digital Signatures

Digital signatures are ubiquitous in modern communications. Designed to fulfil the same ends as a handwritten signature, a digital signature attached to a classical message ensures the message's validity, integrity and transferability. The signature prevents a malevolent party from creating a fake message, from tampering with an existing message, and prevents a sender from denying she sent her message. Currently used classical digital signature schemes, such as RSA, DSA and ECDSA, all rely on the computational complexity of certain mathematical tasks. For example, the security of RSA signatures relies on the difficulty of finding the prime factors of large numbers. Because a quantum computer will render these current schemes insecure [1], it is important to look for unconditionally secure signature schemes [2].

Unconditionally secure digital signature schemes relying on quantum mechanics exist. Instead of basing security on the difficulty of mathematical problems, these Quantum Digital Signature (QDS) schemes base their security on the inability to perfectly distinguish between non-orthogonal quantum states. The original QDS scheme [3] required the quantum signature states to be stored until needed. This requirement for quantum memory is practically difficult, and in classical digital signature schemes it is common for the signatures to be distributed up to months before they are used. Recent developments (protocol described in [4] and implemented in [5]) remove the requirement for quantum memory, thus making implementation of QDS schemes plausible in the near future.

A recent scheme [6] was proposed and experimentally demonstrated, in which continuous-variable (CV) coherent states of light are distributed, and then measured with homodyne detection. This CV protocol requires only short signature lengths (~10^4 quantum states) and is compatible with existing telecoms technology and infrastructure. The PhD project aims to expand this CV QDS scheme to a more realistic scenario where an eavesdropper is permitted to listen to and interfere with the distribution of the coherent states. Several different "alphabets" of coherent states will be considered, and the protocol modified to ensure unconditional security against arbitrary attacks. The modified protocols will be experimentally implemented and analysed to ensure that the security requirements are met in real systems.



References:
[1] P. W. Shor, "Polynomial-Time Algorithms for Prime Factorization and Discrete Logarithms on a Quantum Computer," SIAM J. Sci. Stat. Comput., vol. 26, no. 5, pp. 1484-1509, 1997.
[2] R. Amiri and E. Andersson, "Unconditionally Secure Quantum Signatures," Entropy, vol. 17, pp. 5635-5659, 2015.
[3] D. Gottesman and I. Chuang, "Quantum Digital Signatures," arXiv:quant-ph/0105032, 2001.
[4] V. Dunjko, P. Wallden, and E. Andersson, "Quantum Digital Signatures without quantum memory," Phys. Rev. Lett., vol. 112, no. 4, p. 40502, 2014.
[5] R. J. Collins, R. J. Donaldson, V. Dunjko, P. Wallden, P. J. Clarke, E. Andersson, J. Jeffers, and G. S. Buller, "Realization of Quantum Digital Signatures without the Requirement of Quantum Memory," Phys. Rev. Lett., vol. 113, no. 4, p. 40502, 2014.
[6] C. Croal, C. Peuntinger, B. Heim, I. Khan, C. Marquardt, G. Leuchs, P. Wallden, E. Andersson, and N. Korolkova, "Free-space quantum signatures using heterodyne detection," Phys. Rev. Lett., vol. 117, no. 10, p. 100503, 2016.

Training:Attend weekly school colloquia
Attend 10 days per year of generic and research skills training, eg. GradSkills courses, summer schools, study visits, conferences, etc.
Attend 40 hours technical SUPA courses.
Attend 20 hours Core Skills SUPA courses.

Courses on scientific writing, presentation and communication are highly encouraged.

Keywords: Information, Optics, Security