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Researchers create glass-framed knots to encode information

'Classified knots': uOttawa researchers create optical framed knots to encode information

Top look at the framed knots formed in this work. Credit: University of Ottawa

In a world first, researchers from the University of Ottawa in collaboration with Israeli scientists have created optical frame knots in the laboratory that can be applied to modern technologies. Their work will open the door to new methods of distributing secret cryptographic keys ̵

1; used to encrypt and decrypt data, ensure secure communication and protect private information. The team recently published their findings on Communications in Nature.

“This is fundamentally important, especially from a topology-oriented perspective, because framed knots provide a platform for topological totals of calculation,” explains senior author, Professor Ebrahim Karimi , Canada Research Chair in Structured Light at the University of Ottawa.

“In addition, we have used these non-small optical structures as carriers of information and developed a security protocol for classical communication where information is encoded within these framed knots. . “

The concept

Researchers suggest a simple do-it-yourself lesson to help us better understand framed knots, three-dimensional objects that can also be described as a surface.

“Take a narrow piece of paper and try to make a knot,” said first author Hugo Larocque, uOttawa alumnus and current Ph.D. students at MIT.

“The resulting object is defined as a framed knot and has very interesting and important mathematical features.”

The team tried to achieve the same result but within an optical beam, showing a higher level of difficulty. After some testing (and knots that look like knotted strings), the group came up with what they were looking for: a knot ribbon structure that is quintessential in framed knots.

'Classified knots': uOttawa researchers create optical framed knots to encode information

Encryption strategy of a framed braid within a framed knot. The knot along a pair of numbers can be used to recover the encrypted braid by a method that relies on the basic assumption. Credit: University of Ottawa

“To add to this ribbon, our team relies on beam-shaped techniques that manipulate the nature of the light vector,” Hugo Larocque explains. By changing the direction of the oscillation of the light field along with an “unstructured” optical knot, we were able to assign a frame eventually by “gluing” together the lines traced by the oscillating fields this. “

According to the researchers, structured light beams are widely exploited for encoding and disseminating information.

“Right now, these applications are limited in physical quantities that can be identified by observing the beam in a given position,” said uOttawa Postdoctoral Fellow and co-author of this study, Dr . Alessio D’Errico.

“Our work shows that the number of twists in ribbon orientation in conjunction with prime number factorization can be used to obtain a so-called” braid representation “of the knot.”

“The structural features of these objects can be used to define information processing programs as a whole,” Hugo Larocque added. “In a situation where this program wants to remain secret while it is being disseminated between different parties, one will need a way to encrypt this” braid “and later decipher it. Our work addresses this issue by proposing to use our optical framed knot as something encrypted for these programs that can be recovered later in the process of getting the braid we also introduced . “

“For the first time, these complex 3-D structures have been exploited to develop new methods for distributing secret cryptographic keys. Moreover, there is a broad and strong interest in the exploitation of topological concept in computation of totality, communication and electronics without expansion. Knots are also described by specific topological features, which are not considered at this time for cryptographic protocols. “

'Classified knots': uOttawa researchers create optical framed knots to encode information

Adjustment of the rebuilt structure of a framed trefoil knot formed inside an optical beam. Credit: University of Ottawa

The origin

The idea behind the project emerged in 2018, during a discussion with Israeli researchers at a scientific conference in Crete, Greece.

Scientists from Ben-Gurion University of Negev and Bar-Ilan University, in Israel, have developed a prime number encoding protocol.

The project crossed the Mediterranean and Atlantic Ocean before graduating from Dr. Karimi located in the Advanced Research Complex at the University of Ottawa. There the experimental method was developed and carried out. The resulting data were then analyzed, and the braid structure obtained through a specially thought out program.


“Current technologies give us the possibility to manipulate, with high accuracy, the various features that characterize a light beam, such as intensity, phase, wavelength and polarization,” says Hugo Larocque. “It allows encoding and decoding information using all-optical methods. Quantitative and classical cryptographic protocols have been described as exploiting different levels of this freedom.”

“Our work will pave the way for the use of more complex topological structures hidden in the proliferation of a laser beam for the distribution of cryptographic key secrets.”

Moreover, the experimental and theoretical strategies we have developed can help find new experimental strategies in calculating the topological sum, which promises to overcome noise-related issues with current technologies in computing the whole, “added Dr. Ebrahim Karimi |

The paper “Optical wrapped knots as bearers of information” was recently published in Communications in Nature.

Researchers are developing a novel process for developing materials as a whole

Additional information:
Hugo Larocque et al, Optical framed knots as information carriers, Communications in Nature (2020). DOI: 10.1038 / s41467-020-18792-z

Provided by the University of Ottawa

Citation: ‘Classified knots’: Researchers create glass-framed knots to encode information (2020, October 17) retrieved on October 17, 2020 from https://phys.org/news/ 2020-10-optical-encode.html

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