Time series classification using quantum reservoir computing

Cryptography is a technique that ensures the confidentiality of information exchanged between two parties. Nowadays, most Internet exchanges are encrypted. Computers encode our messages following certain protocols before sending the information over the networks, then decode them for the recipient. This way, messages cannot be read by intermediaries.

Obviously, security flaws exist and many major players in the industry are making considerable efforts to identify these to better protect themselves from possible malicious actions. It is precisely with this objective in mind that the French company Thales partnered last year with Institut quantique’s (IQ) AlgoLab to explore how certain quantum algorithms could potentially represent a threat to the security of exchanged data. The research project also benefited from a collaboration with Professor Soumaya Cherkaoui and post-doctoral fellow Zoubeir Mlika from Polytechnique Montreal.

Cryptography 101

A byte is a unit of information of eight bits that can represent 256 characters such as letters of the alphabet, numbers or punctuation. A computer processes information by manipulating bytes. The encryption of a message is done using a key: a sequence of bytes kept secret. To simplify the explanation, we’ll consider the case where the message and the key are composed of a single byte. An encryption protocol prescribes certain operations that must be performed between both the message and the key bytes, resulting in the production of a new byte. Without the key that was used to encrypt the message, it is impossible to extract information. The encryption protocol also provides the blueprint for reconstructing the original message.

Side Channel Attack

A side channel attack (SCA) is a hacking technique that seeks to take advantage of certain measurable information while a computer is performing a task. This measurable information can be, for example, electrical power consumption, electromagnetic or acoustic emissions. When the computer encrypts a message following a given protocol, this measurable information can be used to extract sensitive information related to the executed cryptographic protocol.

“We tried to see if there is something in the encryption process that is emitted by the computer that could be captured that would carry a signature associated with the bytes used to encrypt a message,” explains Simon Corbeil-Létourneau, PhD and an Artificial Intelligence (AI) researcher at Thales Digital Solutions.

The data used in the project is called a time series, which is a sequence of real values recorded at fixed intervals. It’s easy to assume that the differences between two time series corresponding to different keys are very subtle.

“In cases like this, AI techniques are used to automatically learn the factors that distinguish the signals. The dataset we used for our project is power consumption,” explains Jean Frédéric Laprade, a quantum softare developer with IQ’s AlgoLab. We can imagine a malicious device installed in an electrical outlet that would measure the power used by the processor to encrypt a byte of information. We try to learn how the signal corresponding to the encryption with a key, like 11111111, differs from the signal associated with another key, for example 00000000. This learning is done in a supervised manner, that is, using a set of power consumption traces for which we know the key that is used.”

Classifying a power consumption signal based on the key used in an encryption protocol is complex. The project explored the potential of quantum computing for this specific task.

Quantum reservoir computing

Reservoir computing is an approach that relies on the high dimensionality and non-linearity of a dynamic system to transform a signal into a form that is more amenable to learning. “To do reservoir computing, we inject a temporal signal into the dynamic system and measure the response of the reservoir over time. Then, we perform a simple linear regression to predict the evolution of a signal or to associate it with a class,” continues Jean Frédéric. Various dynamic systems have been studied to accomplish this task, including certain types of neural networks, physical systems such as the surface of a water basin, and quantum systems.”

Thus, the project explored different approaches to implement and characterize quantum reservoir computing (QRC) in the context of classifying signals associated with the power consumption of a computer performing a cryptographic task.

“In our project, the dynamic system consisted of interacting qubits. The temporal signal is injected, one element at a time: the state of a qubit is fixed according to the current data and then the system is allowed to evolve for a certain period. The same sequence is then repeated for the next data, and so on. In this way, the information spreads throughout all the states,” explains Sarah Blanchette, a quantum computing developer with AlgoLab (2021-22), who also contributed to the project. The idea was to see if measuring this signal could allow us to classify our time series to associate it with a specific encryption byte.”

Reaching the current limits

The team successfully implemented three quantum reservoir models proposed in scientific literature and evaluated their performance against the SCA task. They also compared them to classical machine learning models of equivalent size. While the work carried out confirmed the potential of this approach, it did not accurately identify the encryption keys used.

With the inherent noise of current quantum computers, applying this approach on a larger scale for a long time series is not yet feasible. “A typical time series can be composed of hundreds or even thousands of values. If we wanted to process this series with a quantum computer, the resulting circuit would be much too deep given the coherence times of current quantum computers,” Jean Frédéric concedes.

The value of an exploratory project

One of the AlgoLab’s mandates is to accompany companies that wish to prepare for the impact of quantum computers in their field. This project allowed Thales to explore the potential of quantum computing for specific applications. It has also contributed to the development of internal expertise within the company.

“A key motivation behind this project was to take the first steps in quantum computing in order to develop an internal knowledge base,” explains Simon. Although we focused on a specific problem that is difficult to scale up to a larger data set, it gave us a better understanding of the current limitations of quantum computing and the challenges and opportunities that lie ahead.”

A scientific article¹ has been submitted to IET Quantum Communication. It is awaiting publication. A new collaboration in quantum machine learning also began earlier this year with the Thales project team, Polytechnique Montréal and the Quantum AlgoLab as well as with the company Zetane and Professor Shengrui Wang of UdeS.

[1] User Trajectory Prediction in Mobile Wireless Networks Using Quantum Reservoir Computing (2023), Zoubeir Mlika, Soumaya Cherkaoui, Jean Frédéric Laprade, Simon Corbeil-Letourneau