Generating Randomness: A Laser-Based Scramble for Random Numbers

Random Number Generator - Elaine Cheng

Art courtesy of Elaine Cheng.

When you play the violin, you can trace back its sound to the vibration of its strings. These energy vibrations—the sound waves—transfer from the strings to the violin’s bridge, and then to its body, eventually vibrating the air before reaching our ears as sound. The hollow wooden body serves as a resonator for acoustic waves. Its shape is tailored to resonate with many acoustic frequencies, producing the rich, resonant quality of sound that we appreciate as music.

This is how Hui Cao, John C. Malone Professor of Applied Physics and of Physics at Yale, explained the design of a new laser developed in her lab. Her team is leveraging this innovative technology to generate random numbers at revolutionary speeds.

In an article published in Science on February 26, Cao and her collaborators wrote about their new laser design with a random bit generation (RBG) rate of two hundred fifty terabits per second—faster than existing versions by more than a hundredfold. Functioning by a completely different mechanism, their laser uses many different channels to generate random numbers in parallel, while increasing the RBG rate of each individual channel.

Like the sound waves produced by a violin string that are amplified in the wooden body, the laser produces light waves that are amplified in an optical resonator, which Cao designed in a bow-tie shape. This shape allows the laser to resonate with many optical modes of different frequencies, analogous to the multiple tones of a violin string. “The breakthrough is a different mechanism,” Cao said. Whereas conventional lasers only have one or a few modes, the many modes of this new laser can interfere with each other to create complex spatio-temporal patterns—which is where the randomness originates.

Leveraging Lasers for Cybersecurity

Doing basic research in understanding complex laser behaviors opens up the possibility for a multitude of applications, some of which come in unexpected forms. “The original goal was not generating random numbers, but just changing the shape of the cavity and studying the laser dynamics,” said Kyungduk Kim, a graduate student in Cao’s group. Cao explained that by working with more complex laser designs, her lab is tapping into potential new functions of lasers. “Lasers are probably one of the most important inventions in science and technology in the last century,” Cao said. 

Among all the potential applications of lasers, random number generation represents a particularly important one. In a world increasingly dependent on digital communication and exchange, random number generation is integral to ensuring online security. One ubiquitous example is in the creation of encryption keys—used to scramble private information such as passwords, banking information, or messages to prevent them from being intercepted when sent through online channels, like emails. The random quality of the selected key is integral to preventing potential attackers from breaking into messages and stealing information. Predictable keys, or even keys based on sophisticated algorithms whose pattern can be uncovered, could leave sensitive private data vulnerable.

Additionally, random numbers have a variety of applications in scientific research. The modelling of stochastic processes that involve random probabilities, such as the spreading of viruses or fluctuations in the stock market, relies on streams of random numbers that can simulate the unpredictability of these systems. Statistical analysis also relies on random number generation to choose random samples from a population in order to prevent biases that may make the analysis less reliable.

Laser-to-Randomness Fundamentals

Not even the most powerful supercomputer can generate true random numbers on its own. This is because computers run on algorithms, and any finite algorithm will eventually loop back and repeat itself, yielding a specific pattern of outputs. To generate true randomness, one has to rely on external physical sources of entropy, or naturally occurring disorder in the universe. Through monitoring systems that have dynamics that cannot be predicted, they can be used as a source of randomness. One way that scientists have done this is by using lasers.

Light waves in the lasers that the researchers work with, called broad-area semiconductor lasers, often naturally experience irregular fluctuations from the interaction of light with the lasing medium. Previously, researchers leveraged this property of light as a source of randomness, translating fluctuations of light intensity into zeros and ones. The randomness comes from the chaotic pattern of the stream of bits generated. However, there is a limit on how quickly those lasers can generate random number streams. This depends entirely on how fast the fluctuations occur. To increase the RBG rate of a laser beyond that limit, one would need to either increase the number of bit streams generated in parallel or use a new mechanism as a source of randomness that has faster dynamics. The Yale team’s new laser does both.

Improvements in Quantity and Quality

Previously implemented lasers had flat edges. With this conventional shape, laser intensity fluctuations were correlated with both time and space, limiting the lasers’ effectiveness: correlations over time decrease the quality of the randomness sampled from a single location, and correlations over space decrease the number of different locations one could measure to get random numbers.

By curving the edges of the laser cavity, Cao and her collaborators were able to substantially increase the number of lasing modes (think: violin string tones). “When you have this curved edge, the light can come out at many different spatial locations,” Cao said. “When you measure the intensity at each spatial location, these intensities will fluctuate in time.” By recording output from multiple positions simultaneously, they could use the laser to generate multiple random number streams in parallel.

In addition to inducing multiple RBG streams at once, the new laser also enhances the random bit generation rate of every individual stream by using a new mechanism. Whereas conventional chaotic lasers rely on the irregular fluctuations on a time scale set by their response time to extract randomness, the research team’s laser uses a different source of randomness: the interference of the multiple lasing modes. 

Since the light waves in each mode have different frequencies, by summing them up at different points in space and time—that is, their spatio-temporal interference—the researchers could use the variation in interference intensity as a source of randomness. Because the interference pattern fluctuates much faster than the emission from chaotic lasers, it can generate random numbers at a much faster rate.

Breaking into a New Field

Cao mentioned that this project was her lab’s first venture into the field of random number generation, and they did not have any previous experience or connections to other researchers in the field. Having realized that her work could be applied to a new mechanism for random number generation, she assembled an interdisciplinary team to study techniques including translating measured intensities into digital bits and quality testing random numbers. “We learned a lot through this adventure, and I think that is how scientific research gives us a lot of surprises. And sometimes, we also get some reward,” Cao said.

To get published in a scientific journal, every article must undergo a thorough review process in which peer researchers in the field must provide feedback on the work. “The reviewers of our papers … were very critical and made sure we did everything right,” Cao said. “On the other hand, they really helped us by suggesting the additional tasks we need to do to convince people our method works.” Cao cited the support received from the random number generation community, which was helpful to her team as they broke into the field.

Kim also attested to the important role of collaboration in the project. “It was very lucky that I met good collaborators,” Kim said. Researchers from Nanyang Technological University in Singapore built the lasers that the Yale team designed, which are cutting-edge chip-scale lasers fabricated on a semiconductor wafer. Kim also emphasized that his work directly built upon the work of previous researchers in the lab, highlighting the cumulative process of building knowledge in the scientific field.

Scaling Down to Scale Up

Looking forward, the next challenge facing this new laser is integrating the system into a smaller medium, such as a chip. In this study, to measure the spatiotemporal interference of the light waves (the source of randomness), a special camera was used. This streak camera measured the light emission at an extremely rapid rate, recording an image of the emission every picosecond, resulting in one image produced per every trillionth of a second. A resolution this high comes with a steep cost, so the camera is primarily used by researchers. Additionally, its bulkiness presents a hurdle to wide-scale adoption. Taking the new laser forward would require engineering laser chips with integrated photodetectors. 

Nevertheless, the work done by the Yale researchers takes the field of random number generation a step forward—or in this case, two whole orders of magnitude forward. For Cao, the potential of basic research to be leveraged into concrete applications inspires the team to continue studying the complex physics of laser dynamics.

About the Author:

Alexa Jeanne Loste is a first-year prospective Molecular Biophysics & Biochemistry major in Ezra Stiles College. In addition to writing for YSM, she is a project head for GREEN at Yale, a member of the Environmental Education Collaborative, the STEM Panel Chair for the Conference Committee of the Women’s Leadership Initiative, and a copy desk staffer at the Yale Daily News.


The author would like to thank Kyungduk Kim and Dr. Hui Cao for their time and enthusiasm in sharing their research.

Extra Reading:

Kim, Kyungduk, Stefan Bittner, Yongquan Zeng, Stefano Guazzotti, Ortwin Hess, Qi Jie Wang, and Hui Cao. 2021. “Massively Parallel Ultrafast Random Bit Generation with a Chip-Scale Laser.” Science 371 (6532): 948–952.