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**A research team led by Assistant Professor Kang Hao Cheong at Singapore University of Technology and Design (SUTD) attempted to use concepts from Parrondo’s quantum paradox in search of a working protocol for semi-classical encryption.**

The study found that the chaotic switching of the quantum coin Parrondo’s games have underlying ideas and working dynamics similar to encryption. The study entitled “Chaotic switch for quantum coin Parrondo’s games with application to encryption” was published in the journal *Physical examination search letter.*

Parrondo’s paradox is a phenomenon that leads to a winning outcome by alternating between two losing games. The authors introduce the two-sided quantum coin toss game that has been showcased in previous work that the random and particular periodic toss of two quantum coins can transform the expected position of quantum walkers from a losing position to a fair winning position, respectively.

In this game, the quantum walker is given a set of instructions on the method of moving based on the results of the quantum toss.

After drawing inspiration from the underlying principles of this quantum game, lead author of the study, Joel Lai of SUTD, detailed, “*Suppose I show you the result of the quantum walker after 100 coin tosses, knowing the initial position, can you tell me the sequence of throws that lead to this result?*â€œThis task can be either very easy or very difficult.

In the case of a random switch, it is almost impossible to determine the sequence of throws that leads to the end result. However, for periodic throws, we could get the throw sequence quite easily, because a periodic sequence has structure and is deterministic..Joel Lai, lead author of the study, Singapore University of Technology and Design

High uncertainty can be encountered in random sequencing. In contrast, periodic sequences are deterministic. This resulted in the possibility of combining chaotic sequences as a means of performing switching. The researchers found that using chaotic switching via a pre-generated chaotic sequence greatly improved the job.

In the case of an observer who is unaware of some part of the information needed to produce the chaotic sequence, deciphering the throw sequence is similar to identifying a random sequence. But for an agent who has data on how to generate the chaotic sequence, it is similar to a periodic sequence.

The researchers note that the data on the generation of the chaotic sequence is analogous to the encryption keys. By simply knowing the keys and the result (i.e. the encrypted message), these results can be reversed to get the original state of the quantum walker (i.e. the original message ).

The introduction of chaotic switching, when combined with the Parrondo paradox, extends the application of the Parrondo paradox from a simple mathematical tool used in quantum information for classification or identification of state initial and end result to whoever has real world engineering applicationsKang Hao Cheong, Study Lead Author and Assistant Professor, Singapore University of Technology and Design

## Journal reference:

Lai, JW & Cheong, KH (2021) Chaotic switching for Parrondo quantum coin games with application to encryption. *Physical examination of research*. doi.org/10.1103/PhysRevResearch.3.L022019.

Source: https://www.sutd.edu.sg/

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