What are some "must-read" papers for someone getting into Quantum Cryptography?

Question

I'm a graduate student that just finished a first course on quantum computation. I've also done a graduate-level course in (classical) cryptography.

I'm interested in Quantum Cryptography and would like to know what people would consider the most important papers for me to read if I want to get an intro to QC, for someone of my background. Any help would be much appreciated.

Answer 1

" I've also done a graduate-level course in (classical) cryptography. I'm interested in Quantum Cryptography and would like to know what people would consider the most important papers for me to read if I want to get an intro to QC, for someone of my background."

You would first need to learn the very basics of quantum computing, and the simplest quantum computing algorithms such as the one to solve the Deutsch problem and it's more general version called the Deutsch-Jozsa problem. For the Deustch problem and the Deutsch-Jozsa problem, the seminal papers are as follows:

• 1985 (Deutsch): Original formulation of the problem and how it can be solved on a quantum computer more efficiently than on a classical computer
• 1992 (Deutsch and Jozsa): Generalization of the problem posed in the previous paper, and how it can be solved on a quantum computer exponentially more efficiently than on a classical computer
• 1998 (Cleve, Ekert, Macchiavello, Mosca): Improved version of the quantum algorithm to solve the Deutsch and Deutch-Jozsa problems. This is the version often described in textbooks.

One of the simplest and earliest papers in the field of "quantum cryptography" is the BB84 paper, for which I've provided a link to the PDF below, because an HTML version doesn't seem to exist:

• 1984 (Bennett and Brassard): Original publication of the BB84 protocol.

However, I think you will find it much easier if you were to just read about the above topics (basics of quantum computing, Deutsch/Deutsch-Jozsa problems and how they're solved more efficiently on quantum computers than classical computers, and the BB84 protocol) in an introduction textbook on quantum computing, such as the one by Nielsen and Chuang.

Otherwise you're going to be reading papers that were written with notation and typesetting that isn't the same as how it's been presented in the last two decades, and you'll have to put far more effort into your journey towards learning quantum cryptography since those papers were primary research articles (not didactic introductory textbooks).

Answer 2

What constitutes "the most important papers" is highly subjective, so I will mention some of the papers that I think are influencial and that I have enjoyed reading.

I would start with this historical piece:

• Brassard, Gilles. "Brief history of quantum cryptography: A personal perspective." IEEE Information Theory Workshop on Theory and Practice in Information-Theoretic Security, 2005.. IEEE, 2005

Then, depending on your interests, there are several potential directions.

On quantum two-party crypto, some early papers had flawed (or incomplete) security proofs, but they are still a fun read. For example:

• Brassard, Gilles, et al. "A quantum bit commitment scheme provably unbreakable by both parties." Proceedings of 1993 IEEE 34th Annual Foundations of Computer Science. IEEE, 1993.
• Bennett, Charles H., et al. "Practical quantum oblivious transfer." Annual international cryptology conference. Springer, Berlin, Heidelberg, 1991.

Impossibility results:

• Dominic Mayers. Unconditionally secure quantum bit commitment is impossible.
• Lo, Hoi-Kwong, and Hoi Fung Chau. "Why quantum bit commitment and ideal quantum coin tossing are impossible." Physica D: Nonlinear Phenomena 120.1-2 (1998): 177-187.

The bounded storage model is a nice assumption that can be used to overcome the impossibility.

• Ivan Damgård, Serge Fehr, Louis Salvail, and Christian Schaffner. Cryptography in the bounded-quantum-storage model.

On quantum key distribution protocols and proofs:

• The QKD protocols themselves are better learned through textbooks, e.g. Nielsen and Chuang's.
• Renato Renner's thesis introduced much of the theoretical foundation used to analyze QKD and other quantum cryptographic protocols.

On quantum money:

• Aaronson, Scott, and Paul Christiano. "Quantum money from hidden subspaces." Proceedings of the forty-fourth annual ACM symposium on Theory of computing. 2012.
• Zhandry, Mark. "Quantum lightning never strikes the same state twice. or: quantum money from cryptographic assumptions." Journal of Cryptology 34.1 (2021): 1-56.

I you want to see more recent work in quantum cryptography, some conferences to follow include:

• The IACR track of conferences (Crypto, Eurocrypt, TCC, etc.)
• QCrypt (specific to quantum crypto, theory + practice)
• To a lesser extent QIP and TQC, which are general quantum conferences.

Answer 3

For an interesting starting paper, that nearly was never a paper see Stephen Wisener's paper on Conjugate Coding. This paper started off things like the BB 84. The paper is paywalled though, and a typewritten copy (with typos too,), as it was written sometime in the 60s or 70s is an interesting read, to start, or to get a historical perspective.