Top view of the framed nodes created in this work. Photo credit: University of Ottawa
In a world first, researchers from the University of Ottawa worked with Israeli scientists to create optically framed knots in the laboratory that could potentially be used in modern technologies. Their work opens the door to new methods of distributing secret cryptographic keys that are used to encrypt and decrypt data, ensure secure communication, and protect private information. The group recently published its findings in Nature communication.
“This is fundamental, especially from a topology perspective, as framed nodes provide a platform for topological quantum computation,” said Senior Author, Professor Ebrahim Karimi, Canadian Structured Light Research Chair at the University of Ottawa.
“In addition, we used these non-trivial optical structures as information carriers and developed a security protocol for classic communication in which information is encoded within these framed nodes.”
The concept
Researchers propose a simple do-it-yourself lesson to better understand framed knots, those three-dimensional objects that can also be referred to as surfaces.
“Take a narrow strip of paper and try to tie a knot,” said first author Hugo Larocque, a graduate of uOttawa and current PhD student WITH.
“The resulting object is called a framed knot and has very interesting and important mathematical features.”
Encryption scheme of a framed mesh within a framed knot. The node can be used in conjunction with a pair of numbers to recreate the encrypted mesh using a technique based on prime factorization. Photo credit: University of Ottawa
The group tried to achieve the same result, but within an optical beam that has a higher degree of difficulty. After a few tries (and knots that looked more like knotted string), the group found what they were looking for: a knotted ribbon structure typical of framed knots.
“To add that band, our group relied on beamforming techniques that manipulated the vectorial nature of light,” explained Hugo Larocque. “By changing the direction of oscillation of the light field along an” unframed “optical node, we were able to assign a frame to it by” gluing “the lines traced by these oscillating fields together.”
According to the researchers, structured light beams are used extensively for coding and distributing information.
“So far, these applications have been limited to physical quantities that can be identified by observing the beam at a specific position,” said Dr. Alessio D’Errico, Postdoctoral Fellow and co-author of this study.
“Our work shows that the number of rotations in the ribbon alignment can be used in conjunction with prime factorization to extract what is known as a” mesh representation “of the knot.”
Reproduction of the reconstructed structure of a framed trefoil knot created within an optical beam. Photo credit: University of Ottawa
“The structural features of these objects can be used to specify quantum information processing programs,” added Hugo Larocque. “In a situation in which this program is to be kept secret while it is being distributed between different parties, this“ web ”would have to be encrypted and later decrypted. Our work addresses this problem by proposing to use our optically framed knot as an encryption object for these programs, which can later be recovered using the braid extraction method that has also been introduced. ”
“For the first time, these intricate 3D structures were used to develop new methods for distributing secret cryptographic keys. In addition, there is a broad and strong interest in the use of topological concepts in quantum computation, communication and non-dissipation electronics. Nodes are also described by specific topological properties that were previously not taken into account for cryptographic protocols. ”
The origins
The idea behind the project came about in 2018 during a discussion with Israeli researchers at a scientific meeting in Crete, Greece.
Scientists from Ben Gurion University in the Negev and Bar Ilan University in Israel developed the coding protocol for prime numbers.
The project then crossed the Mediterranean and the Atlantic before moving to Dr. Karimi’s lab landed in the University of Ottawa’s Advanced Research Complex. The experimental procedure was developed and carried out there. The resulting data were then analyzed and the braid structure was extracted by a specially developed program.
The applications
“Current technologies give us the opportunity to manipulate with high accuracyThe various features that characterize a light beam, such as intensity, phase, wavelength and polarization, ”said Hugo Larocque. “This enables information to be encoded and decoded using purely optical methods. Quantum and classical cryptographic protocols were developed to take advantage of these different degrees of freedom. ”
“Our work paves the way for using more complex topological structures hidden in the propagation of a laser beam to distribute secret cryptographic keys.”
“In addition, the experimental and theoretical techniques we have developed can help to find new experimental approaches to topological quantum computation that promise to currently surpass noise-related problems Quantum computing Technologies, “added Dr. Ebrahim Karimi added.
The paper “Optically framed nodes as information carriers” was recently published in Nature communication.
Reference: “Optically framed nodes as information carriers” by Hugo Larocque, Alessio D’Errico, Manuel F. Ferrer-Garcia, Avishy Carmi, Eliahu Cohen and Ebrahim Karimi, October 9, 2020, Nature Communications.
DOI: 10.1038 / s41467-020-18792-z
