Top view of the framed knots generated in this work.
In a world first, researchers from the University of Ottawa in collaboration with Israeli scientists have been able to create optical framed knots in the laboratory that could potentially be applied in modern technologies.
Their work opens the door to new methods of distributing secret cryptographic keys – used to encrypt and decrypt data, ensure secure communication and protect private information. The group recently published their findings in Nature Communications.
“This is fundamentally important, in particular from a topology-focused perspective, since framed knots provide a platform for topological quantum computations,” explained senior author, Professor Ebrahim Karimi, Canada Research Chair in Structured Light at the University of Ottawa.
“In addition, we used these non-trivial optical structures as information carriers and developed a security protocol for classical communication where information is encoded within these framed knots.”
The researchers suggest a simple do-it-yourself lesson to help us better understand framed knots, those three-dimensional objects that can also be described as a surface.
“Take a narrow strip of a paper and try to make a knot,” said first author Hugo Larocque, uOttawa alumnus and current PhD student at MIT.
“The resulting object is referred to as a framed knot and has very interesting and important mathematical features.”
The group tried to achieve the same result but within an optical beam, which presents a higher level of difficulty. After a few tries (and knots that looked more like knotted strings), the group came up with what they were looking for: a knotted ribbon structure that is quintessential to framed knots.
“In order to add this ribbon, our group relied on beam-shaping techniques manipulating the vectorial nature of light,” explained Hugo Larocque. “By modifying the oscillation direction of the light field along an “unframed” optical knot, we were able to assign a frame to the latter by “gluing” together the lines traced out by these oscillating fields.”
According to the researchers, structured light beams are being widely exploited for encoding and distributing information.
“So far, these applications have been limited to physical quantities which can be recognized by observing the beam at 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 the ribbon orientation in conjunction with prime number factorization can be used to extract a so-called “braid representation” of the knot.”
“The structural features of these objects can be used to specify quantum information processing programs,” added Hugo Larocque. “In a situation where this program would want to be kept secret while disseminating it between various parties, one would need a means of encrypting this “braid” and later deciphering it. Our work addresses this issue by proposing to use our optical framed knot as an encryption object for these programs which can later be recovered by the braid extraction method that we also introduced.”
“For the first time, these complicated 3D structures have been exploited to develop new methods for the distribution of secret cryptographic keys. Moreover, there is a wide and strong interest in exploiting topological concepts in quantum computation, communication and dissipation-free electronics. Knots are described by specific topological properties too, which were not considered so far for cryptographic protocols.”
The idea behind the project emerged in 2018, during a discussion with Israeli researchers at a scientific meeting in Crete, Greece.
The project then crossed the Mediterranean Sea and the Atlantic Ocean before ending up in Dr. Karimi’s lab located in the Advanced Research Complex at the University of Ottawa. That’s where the experimental procedure was developed and conducted. The resulting data were then analyzed, and the braid structure extracted through a specially devised program.
“Current technologies give us the possibility to manipulate, with high accuracy, the different features characterizing a light beam, such as intensity, phase, wavelength and polarization,” said Hugo Larocque. “This allows to encode and decode information with all-optical methods. Quantum and classical cryptographic protocols have been devised exploiting these different degrees of freedom.”
“Our work opens the way to the use of more complex topological structures hidden in the propagation of a laser beam for distributing secret cryptographic keys.”
“Moreover, the experimental and theoretical techniques we developed may help find new experimental approaches to topological quantum computation, which promises to surpass noise-related issues in current quantum computing technologies,” added Dr. Ebrahim Karimi.
The Latest Updates from Bing News & Google News
Go deeper with Bing News on:
Distributing secret cryptographic keys
- Hashing explained: Why it's your best bet to protect stored passwordson January 13, 2021 at 3:01 am
Hashing is a one-way cryptographic function while encryption is designed to work both ways. Encryption algorithms take input and a secret key and generate a random looking output called a ciphertext.
- If not WhatsApp, then what? Consider these alternativeson January 11, 2021 at 7:53 am
Many of these apps feature AES methods which, according to a National Institute of Standards and Technology report, is the use of “cryptographic keys of ... platform’s Secret Chats use an ...
- Cryptographic LCDs Use The Magic Of XORon January 10, 2021 at 4:00 pm
We love a good discussion of cryptography and security around here; [John McMaster]’s talk on crypto ignition keys was a particular hit at Supercon last year. Video after the break.
- Hackers can clone Google Titan 2FA keys using a side channel in NXP chipson January 8, 2021 at 5:13 am
Nevertheless, this work shows that the Google Titan Security Key (or other impacted products) would not avoid [an] unnoticed security breach by attackers willing to put enough effort into it,” ...
- Quantum cryptography network spans 4600 km in Chinaon January 7, 2021 at 10:20 am
Quantum light: a 2000::km fibre optic network enables quantum key cryptography between four cities in China. (Courtesy: iStock/MorePixels) A network for quantum key distribution (QKD) spanning ...
Go deeper with Google Headlines on:
Distributing secret cryptographic keys
Go deeper with Bing News on:
Optical framed knots
- 5 best ski goggles to get in 2021, according to expertson January 12, 2021 at 3:23 am
“Goggles are a way to protect your eyes and enhance your optical clarity ... condition while enjoying a secure magnetic lens-to-frame seal against the elements. Oakley is a “powerhouse ...
- Epic optical illusion makes it seem like an Aussie man is jumping off a cliffon January 11, 2021 at 6:11 am
Deceptive footage of a man appearing to jump off a 'cliff' has gone viral on TikTok. Viewers were left holding their breath as they watched Liam Attard cling to the railing of a seemingly high ...
- How To Reverse Engineer Mechanical Designs For 3D Modelingon January 10, 2021 at 4:00 pm
We were reverse engineering parts with features that were too small to be seen by the human eye, so we had some fancy equipment like high-magnification optical ... items in the frame to get ...
- Sam Armytage ties the knot in a simple cocktail dress from Carla Zampattion December 30, 2020 at 9:48 pm
Sam Armytage married her millionaire fiancé Richard Lavender in an intimate ceremony in the Southern Highlands on New Year's Eve. The blushing bride, 44, opted for simple elegance in a custom ...
- What if life was a video game? Reddit has the answerson December 23, 2020 at 7:01 am
"Even added bonus garlic knots to my inventory ... kept sharing fun content about 'glitches' or graphics problems like optical illusions." (Given the anonymous nature of Reddit, the sources ...