So in my previous article on quantum computing, we talked about where we are today, and where we are headed in regards to breakthroughs in the technology as well as touching on some basics of “what is quantum computing“. In this article, I explore what quantum cryptography and cryptography is like in a post-quantum world.

So, a refresher: quantum computing is set to transform cryptography due to the revolutionary, non-deterministic way of operating.

How will they affect existing cryptography algorithms and which options do we know today for doing cryptography in a post-quantum world?

For one, quantum technology will significantly impact current state-of-the-art cryptographic algorithms. Asymmetric algorithms that rely on a public key derived from a private key that relies on hard mathematical problems will not stand to quantum computers that offer enough qubits (the unit in which quantum machines operate) to work on their respective key sizes.

However, as it stands, quantum computers will offer compelling new cryptographic options of themselves, even going so far as to prevent eavesdropping possibly wholly. How does this work? Quantum cryptography relies on transmitting qubits in the form of photons, one at a time, on the transportation layer to the receiving unit. The information is coded into these photons as a trait of it, possibly polarisation or phase.

Photons are not as easily monitored as today’s electrical bit-signals are. Instead, these qubits exist in so-called superposition states, representing each possible state (one and zero) at the same, time, essentially. It is only when the qubits are observed that this state becomes fixed. However, a transmission with a fixed state of qubits is not the same as a transmission in a state of superposition. Thus, if an eavesdropper intercepts a transmission and observes it, they will not be able to retransmit it in the same state as they found it in, invariably giving their actions away to the intended receiver — no more undetected wiretapping.

While this is nice, how will we secure against quantum computers breaking today’s encryption algorithms? Several approaches exist so far, being developed by researchers all over the world and collected by the NIST post-quantum project.

Lattice-based quantum cryptography, first described in a paper by researcher Oded Regev, is based on the problem of finding the shortest vector in a structure called a lattice, represented by a set of linear polynomial equations, essentially forming an n-dimensional space. Initially, the problem of lattice-based systems had been their huge key sizes, but they have since then been reduced to manageable levels, and lattice-based cryptography will likely be production-ready soon.

Isogenies could informally be described as elliptic curves on steroids. The field of elliptic-curve cryptography has always been known to be a more arcane form of the area, and isogenies do not disappoint in taking all of this a little bit further out. An isogeny is primarily a function to transmute one elliptic curve into another one in a way that keeps the group structure of the first curve (a property known as group homomorphism). There is a specific subset of an elliptic curve with a fixed number of these isogenies. In this scheme, the curves themselves are the public keys, and the chain of isogenies becomes the secret key. This class of algorithms has miniature key sizes, but on the downside, it is very slow to calculate on today’s hardware.

The latest big group of algorithms on the bunch is generically referred to as „codes“, with the McEliece cryptosystem being the most prominent specimen considered quantum-safe despite being almost 40 years old. All algorithms in this category rely on using an error-correcting code as a private key to transmuting a pre-selected binary matrix containing the secret message.

Post-quantum cryptography is a fast-paced area of research that is becoming more and more relevant as quantum computers are approaching levels that threaten conventional cryptographic algorithms like RSA. It must be noted, however, that while the field is very active and algorithms are in ongoing development, none of the presented algorithms has yet reached a consensual recommendation by institutions such as the NIST as a standard to implement in systems that aim to be quantum-proofed. Many of the schemes suffer from performance issues or require massive amounts of memory to be executed. Most likely, quantum-securing today’s applications will require an intermediate-term sacrifice in either space or processing time. It remains to be seen which of the algorithms will emerge as being the first one to be recommended for commercial applications.

In my next article in this series on quantum computing, I will touch on how cloud computing ties in, and more specifically what companies such as Microsoft, Alibaba Cloud and others have accomplished so far and plan to in this exciting field that seems right now is only limited by processing time, which may very well be solved by the hyperscale cloud datacenters.

Let me know what you think either in the comment field below or over on Twitter @UlvBjornsson

 

Previous articles on Quantum Computing:
Quantum computing and cybersecurity: A quantum of solace or a massive threat?