Computers Math

Fast algorithms on quantum computers could easily break many widely used cryptosystems, necessitating more innovative solutions for digital security. In a recent study, a team of scientists designed a stream cipher consisting of three cryptographic primitives based on independent mathematical models of chaos. The resulting cryptographic approach is robust to attacks from large-scale quantum computers and can be implemented on low-cost computers, paving the way to secure digital communications in the post-quantum era.
While for most of us cryptographic systems are things that just run “under the hood,” they are an essential element in the world of digital communications. However, the upcoming rise of quantum computers could shake the field of cryptography to its core. Fast algorithms running on these machines could break some of the most widely used cryptosystems, rendering them vulnerable. Well aware of this looming threat, cryptography researchers worldwide are working on novel encryption methods that can withstand attacks from quantum computers.
Chaos theory is actively being studied as a basis for post-quantum era cryptosystems. In mathematics, chaos is a property of certain dynamic systems that makes them extremely sensitive to initial conditions. While technically deterministic (non-random), these systems evolve in such complex ways that predicting their long-term state with incomplete information is practically impossible, since even small rounding errors in the initial conditions yield diverging results. This unique characteristic of chaotic systems can be leveraged to produce highly secure cryptographic systems, as a team of researchers from Ritsumeikan University, Japan, showed in a recent study published in IEEE Transactions on Circuits and Systems I.
Led by Professor Takaya Miyano, the team developed an unprecedented stream cipher consisting of three cryptographic primitives based on independent mathematical models of chaos. The first primitive is a pseudorandom number generator based on the augmented Lorenz (AL) map. The pseudorandom numbers produced using this approach are used to create key streams for encrypting/decrypting messages, which take the stage in the second and perhaps most remarkable primitive — an innovative method for secret-key exchange.
This novel strategy for exchanging secret keys specifying the AL map is based on the synchronization of two chaotic Lorenz oscillators, which can be independently and randomly initialized by the two communicating users, without either of them knowing the state of the other’s oscillator. To conceal the internal states of these oscillators, the communicating users (the sender and the receiver) mask the value of one of the variables of their oscillator by multiplying it with a locally generated random number. The masked value of the sender is then sent to receiver and vice-versa. After a short time, when these back-and-forth exchanges cause both oscillators to sync up almost perfectly to the same state in spite of the randomization of the variables, the users can mask and exchange secret keys and then locally unmask them with simple calculations.
Finally, the third primitive is a hash function based on the logistic map (a chaotic equation of motion), which allows the sender to send a hash value and, in turn, allows the receiver to ensure that the received secret key is correct, i.e., the chaotic oscillators were synchronized properly.
The researchers showed that a stream cipher assembled using these three primitives is extremely secure and resistant to statistical attacks and eavesdropping since it is mathematically impossible to synchronize their own oscillator to either the sender’s or the receiver’s ones. This is an unprecedented achievement, as Prof. Miyano states: “Most chaos-based cryptosystems can be broken by attacks using classical computers within a practically short time. In contrast, our methods, especially the one for secret-key exchange, appear to be robust against such attacks and, more importantly, even hard to break using quantum computers.”
In addition to its security, the proposed key exchange method is applicable to existing block ciphers, such as the widely used Advanced Encryption Standard (AES). Moreover, the researchers could implement their chaos-based stream cipher on the Raspberry Pi 4, a small-scale computer, using Python 3.8. They even used it to securely transmit a famous painting by Johannes Vermeer between Kusatsu and Sendai, two places in Japan 600 km apart. “The implementation and running costs of our cryptosystem are remarkably low compared with those of quantum cryptography,” highlights Prof. Miyano, “Our work thus provides a cryptographic approach that guarantees the privacy of daily communications between people all over the world in the post-quantum era.”
With such power of chaos-based cryptography, we may not have much to worry about the dark sides of quantum computing.
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Science Fiction novelists couldn’t have come up with a crazier plot: microrobots streaming through blood or through other fluids in our body which are driven by light, can carry drugs to cancer cells and drop off the medication on the spot. What sounds like a far-fetched fantasy, is however the short summary of a research project published in the journal Science Robotics. The microswimmers presented in the work bear the potential to one day perform tasks in living organisms or biological environments that are not easily accessible otherwise. Looking even further ahead, the swimmers could perhaps one day help treat cancer or other diseases.
In their paper “Light-driven carbon nitride microswimmers with propulsion in biological and ionic media and responsive on-demand drug delivery,” a team of scientists from the Max Planck Institute for Intelligent Systems (MPI-IS) and its neighboring institute, the Max Planck Institute for Solid State Research (MPI-FKF), demonstrate organic microparticles that can steer through biological fluids and dissolved blood in an unprecedented way. Even in very salty liquids, the microswimmers can be propelled forward at high speed by visible light, either individually or as a swarm. Additionally, they are partially biocompatible and can take up and release cargo on demand. At MPI-IS, scientists from the Physical Intelligence Department led by Metin Sitti were involved and at MPI-FKF, scientists from the Nanochemistry Department led by Bettina Lotsch.
Designing and fabricating such highly advanced microswimmers seemed impossible up until now. Locomotion by light energy is hindered by the salts found in water or the body. This requires a sophisticated design that is difficult to scale up. Additionally, controlling the robots from the outside is challenging and often costly. Controlled cargo uptake and on-the-spot delivery is another supreme discipline in the field of nanorobotics.
The scientists used a porous two-dimensional carbon nitride (CNx) that can be synthesized from organic materials, for instance, urea. Like the solar cells of a photovoltaic panel, carbon nitride can absorb light which then provides the energy to propel the robot forward when light illuminates the particle surface.
High ion tolerance
“The use of light as the energy source of propulsion is very convenient when doing experiments in a petri dish or for applications directly under the skin,” says Filip Podjaski, a group leader in the Nanochemistry Department at MPI-FKF. “There is just one problem: even tiny concentrations of salts prohibit light-controlled motion. Salts are found in all biological liquids: in blood, cellular fluids, digestive fluids etc. However, we have shown that our CNx microswimmers function in all biological liquids — even when the concentration of salt ions is very high. This is only possible due to a favorable interplay of different factors: efficient light energy conversion as the driving force, as well as the porous structure of the nanoparticles, which allows ions to flow through them, reducing the resistance created by salt, so to speak. In addition, in this material, light favors the mobility of ions — making the particle even faster.”
Having shown the swimmers are salt-tolerant, the team then tackled the challenge to use them as drug carriers. “This is also possible due to the material’s porosity,” Varun Sridhar explains. He is a postdoctoral researcher at MPI-IS and the first author of the publication. He and his team loaded the small pores of the swimmers with the anti-cancer drug Doxorubicin. “The particles adsorbed the drug like a sponge, up to unprecedentedly high amounts of 185% of the carrier mass while staying stably bound to the carbon nitride — even longer than a month. We then showed that controlled release of the drug is possible in a fluid with an acidic pH level. In addition, we were able to illuminate the microswimmers and thus release the drug, regardless of a change in pH. And even when loaded to full capacity, the swimmer did not slow down significantly, which is great.” More

A new power transfer technology makes it possible to conveniently charge devices without using any wires or plugs. Warehouse robots, kitchen appliances, and even phones or laptops can receive power anywhere over the charging area, and because the power transfer continues even while the device is in motion, this technology could one day power electric vehicles while they’re on the go.
The basics of wireless power transfer have been in place for some time, but existing systems are not able to charge devices placed anywhere within a large area. Using a single large transmitter to cover the entire area leads to unwanted electromagnetic exposure and means that the power flow to individual devices cannot be controlled. If many small transmitters are used, the receiving devices must be in a known position, and the transmitter and receiver have to be precisely aligned. This means the system either has to use fixed charging locations or incorporate position sensors, communication protocols, and processing to track the location of each receiver.
Researchers at Aalto University have tackled these problems, developing a power transfer technology that works regardless of the position and orientation of the transmitter and receiver. The key idea is to arrange the transmitters in a grid with the current in neighbouring transmitters running in opposite directions — for example, a clockwise loop in one transmitter and counter-clockwise loops in its neighbours.
This creates a chessboard-like grid of ‘positive’ and ‘negative’ transmitting coils with a magnetic flux between them. A receiver above the grid of transmitters captures the magnetic flux between positive and negative transmitters, which generates an electric current to charge the device.
‘The beauty of our method is that it’s very simple yet quite sophisticated,’ says Prasad Jayathurathnage, the postdoctoral researcher who led the project. ‘We don’t need a high-end processor or lots of computations to make the transmitters intelligent. At the end of the day, it’s all an electromagnetic system, and our approach was to figure out how we could detect the receiver’s presence and position electromagnetically.’
Because the presence of a receiver triggers the power transfer, the system can work without any positional tracking and communication between the receivers and transmitters. This also means that power is only transferred to the receiver, rather than the entire area being energised, and it makes it possible for several devices to be charged simultaneously.
Tiling transmitters together produces a charging area of the desired size and shape. A subset of the transmitters is then activated at lower power. ‘That’s basically a search — the transmitters are listening for a receiver,’ explains Shamsul Al Mahmud, a doctoral student in the project. If power transfer to a receiver begins, the neighbouring transmitters switch from being off into an alert mode, primed to transfer power if the receiver appears over them.
‘With this configuration, we had almost constant efficiency and constant power received regardless of the receiver’s position and orientation,’ says Ishtiaque Panhwar, a researcher involved in the project, and the power transfer continued smoothly even as the receiving device moved around.
The technology has been tested with commercial warehouse robots in cooperation with Finnish firm Solteq Robotics, and Jayathurathnage also leads the project Parkzia, a project funded by Business Finland. The project aims to commercialize this new technology for industry and transport. ‘Taking this technology out of the lab and seeing it work in the warehouse was an exciting moment for me personally,’ says Jayathurathnage. ‘I was finally bringing the product of ten years of research out of the lab.’
More familiar applications can also improve our daily life. ‘Take kitchen appliances, for example,’ says Jayathurathnage. ‘At the moment, you need to put a rice cooker or a blender at a particular spot for it to get energy. But with our technology we can make the whole kitchen counter a source of power for appliances or even phones, but the electromagnetic field is only generated under the devices.’
Although the technology is essentially ready for real-world applications, it still needs commercial packaging and certification. In the meantime, Jayathurathnage’s team will continue to refine and improve this technology. One of their goals is to boost the power levels from about 1 kW to around 20 kW so that the technology could be used to charge electric vehicles. ‘There are pilot projects on electrifying roads across the world,’ says Jayathurathnage. ‘Electric vehicles are a really great application of this technology.’
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Imagine a ball thrown in the air: it curves up, then down, tracing an arc to a point on the ground some distance away. The path of the ball can be described with a simple mathematical equation, and if you know the equation, you can figure out where the ball is going to land. Biological systems tend to be harder to forecast, but Whitehead Institute Member Jonathan Weissman, postdoc in his lab Xiaojie Qiu, and collaborators at the University of Pittsburgh School of Medicine are working on making the path taken by cells as predictable as the arc of a ball. Rather than looking at how cells move through space, they are considering how cells change with time.
Weissman, Qiu, and collaborators Jianhua Xing, professor of computational and systems biology at the University of Pittsburgh School of Medicine, and Xing lab graduate student Yan Zhang have built a machine learning framework that can define the mathematical equations describing a cell’s trajectory from one state to another, such as its development from a stem cell into one of several different types of mature cell. The framework, called dynamo,can also be used to figure out the underlying mechanisms — the specific cocktail of gene activity — driving changes in the cell. Researchers could potentially use these insights to manipulate cells into taking one path instead of another, a common goal in biomedical research and regenerative medicine.
The researchers describe dynamo in a paper published in the journal Cell on February 1. They explain the framework’s many analytical capabilities and use it to help understand mechanisms of human blood cell production, such as why one type of blood cell forms first (appears more rapidly than others).
“Our goal is to move towards a more quantitative version of single cell biology,” Qiu says. “We want to be able to map how a cell changes in relation to the interplay of regulatory genes as accurately as an astronomer can chart a planet’s movement in relation to gravity, and then we want to understand and be able to control those changes.”
How to map a cell’s future journey
Dynamo uses data from many individual cells to come up with its equations. The main information that it requires is how the expression of different genes in a cell changes from moment to moment. The researchers estimate this by looking at changes in the amount of RNA over time, because RNA is a measurable product of gene expression. In the same way that knowing the starting position and velocity of a ball is necessary to understand the arc it will follow, researchers use the starting levels of RNAs and how those RNA levels are changing to predict the path of the cell. However, calculating changes in the amount of RNA from single cell sequencing data is challenging, because sequencing only measures RNA once. Researchers must then use clues like RNA-being-made at the time of sequencing and equations for RNA turnover to estimate how RNA levels were changing. Qiu and colleagues had to improve on previous methods in several ways in order to get clean enough measurements for dynamo to work. In particular, they used a recently developed experimental method that tags new RNA to distinguish it from old RNA, and combined this with sophisticated mathematical modeling, to overcome limitations of older estimation approaches. More

The concept of smart cities is founded on sophisticated cellular networks that would not only connect humans in the future but also humans to other smart devices. However, this would also require huge energy consumption. In the wake of climate change, this can make matters worse for our environment by increasing the greenhouse gas emissions. Thus, we not only need smart cities but also greener smart cities.
One way to address this issue is by switching off base stations (BSs), radio transmitters/receivers that serve as the hub of the local wireless network, when they have little to no traffic load. Laboratory testing has shown that active BSs consume as much as 60% of the maximum energy consumption even under no traffic load and switching them off can bring it down to 40%. However, there is a trade-off: putting BSs to sleep makes their traffic logs unavailable, which also reduces the accuracy of traffic prediction. Is there a way to avoid this compromise between accuracy and sustainability?
The answer, according to a new study, seems to be “yes.” The study, led by Professor Ryoichi Shinkuma from Shibaura Institute of Technology (SIT), Japan, and his colleagues, Associate Professor Kaoru Ota from Muroran Institute of Technology, Japan and Associate Professor Takehiro Sato from Kyoto University, Japan, proposed a novel scheme that not only reduced energy consumption but demonstrated a higher traffic prediction accuracy compared to the benchmark schemes! This paper was published in Volume 35, Issue 6 of the journal IEEE Network Magazine on November/December 2021.
How did the researchers achieve this remarkable feat? Prof. Shinkuma explains, “We applied software defined network (SDN) and edge computing to a cellular network such that each BS is equipped with an SDN switch, and an SDN controller can turn off any BS according to the traffic prediction results. An edge server collects the traffic logs through the SDN switches and predicts traffic volume using machine learning (ML).”
The ML method used by the researchers decided which BSs could be put into “sleep mode” based on the importance of their traffic logs in improving the prediction accuracy. Thus, BSs with low contribution to the accuracy for previous time slots were put to sleep at the next slot to save energy.
To validate their scheme, the researchers used real-world mobile traffic data collected over two months and compared its performance against that of two benchmark schemes. To their delight, the new scheme outperformed the benchmark schemes in its robustness against reducing the number of active BSs and different BS sets.
Could this study be a harbinger of greener cellular networks and smart cities? Prof. Shinkuma is optimistic. “By intelligently controlling the operation of BSs, renewable energy sources could be used to power future networks and, depending on the availability of renewable energy resource, the sleep schedules of the BSs can be determined,” he speculates.
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Physicists from the University of Amsterdam have proposed a new architecture for a scalable quantum computer. Making use of the collective motion of the constituent particles, they were able to construct new building blocks for quantum computing that pose fewer technical difficulties than current state-of-the art methods. The results were recently published in Physical Review Letters.
The researchers work at QuSoft and the Institute of Physics in the groups of Rene Gerritsma and Arghavan Safavi-Naini. The effort, which was led by the PhD candidate Matteo Mazzanti, combines two important ingredients. One is a so-called trapped-ion platform, one of the most promising candidates for quantum computing that makes use of ions — atoms that have either a surplus or a shortage of electrons and as a result are electrically charged. The other is the use of a clever method to control the ions supplied by optical tweezers and oscillating electric fields.
As the name suggests, trapped-ion quantum computers use a crystal of trapped ions. These ions can move individually, but more importantly, also as a whole. As it turns out, the possible collective motions of the ions facilitate the interactions between individual pairs of ions. In the proposal, this idea is made concrete by applying a uniform electric field to the whole crystal, in order to mediate interactions between two specific ions in that crystal. The two ions are selected by applying tweezer potentials on them — see the image above. The homogeneity of the electric field assures that it will only allow the two ions to move together with all other ions in the crystal. As a result, the interaction strength between the two selected ions is fixed, regardless of how far apart the two ions are.
A quantum computer consists of ‘gates’, small computational building blocks that perform quantum analogues of operations like ‘and’ and ‘or’ that we know from ordinary computers. In trapped-ion quantum computers, these gates act on the ions, and their operation depends on the interactions between these particles. In the above setup, the fact that those interactions do not depend on the distance means that also the duration of operation of a gate is independent of that distance. As a result, this scheme for quantum computing is inherently scalable, and compared to other state-of-the-art quantum computing schemes poses fewer technical challenges for achieving comparably well-operating quantum computers.
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A team of mathematicians and physicists has discovered how ice formations are shaped by external forces, such as water temperature. Its newly published research may offer another means for gauging factors that cause ice to melt.
“The shapes and patterning of ice are sensitive indicators of the environmental conditions at which it melted, allowing us to ‘read’ the shape to infer factors such as the ambient water temperature,” explains Leif Ristroph, an associate professor at New York University’s Courant Institute of Mathematical Sciences and one of the authors of the paper, which appears in the journal Physical Review Letters.
“Our work helps to understand how melting induces unusual flow patterns that in turn affect melting, which is one of the many complexities affecting the ice on our planet,” adds author Alexandra Zidovska, an associate professor in NYU’s Department of Physics.
The paper’s other authors were Scott Weady, an NYU graduate student, and Josh Tong, an undergraduate in NYU’s College of Arts and Science at the time of the study.
In NYU’s Applied Mathematics Laboratory and Center for Soft Matter Research, the researchers studied, through a series of experiments, the melting of ice in water and, in particular, how the water temperature affects the eventual shapes and patterning of ice. To do so, they created ultra-pure ice, which is free of bubbles and other impurities. The team recorded the melting of ice submerged into water tanks in a “cold room,” which is similar to a walk-in refrigerator whose temperature is controlled and varied.
“We focused on the cold temperatures — 0 to 10 degrees Celsius — at which ice in natural waters typically melts, and we found a surprising variety of shapes that formed,” says Ristroph, who directs the Applied Mathematics Laboratory. More

Researchers at the Yale School of Public Health were able to accurately predict outbreaks of COVID-19 in Connecticut municipalities using anonymous location information from mobile devices, according to a new study published in Science Advances.
The novel analysis applied in the study could help health officials stem community outbreaks of COVID-19 and allocate testing resources more efficiently, the researchers said.
The study was conducted by data scientists and epidemiologists from the Yale School of Public Health, the Connecticut Department of Public Health, the U.S. Centers for Disease Control and Prevention and Whitespace Ltd., a spatial data analytics firm.
The key to the findings was the precision with which researchers were able to identify incidents of high frequency close personal contact (defined as a radius of 6 feet) in Connecticut down to the municipal level. The CDC advises people to keep at least six feet of distance with others to avoid possible transmission of COVID-19.
“Close contact between people is the primary route for transmission of SARS-CoV-2, the virus that causes COVID-19,” said the study’s lead author Forrest Crawford, an associate professor of biostatistics at the Yale School of Public Health and an associate professor of ecology and evolutionary biology, management, statistics and data science at Yale.
“We measured close interpersonal contact within a 6-foot radius everywhere in Connecticut using mobile device geolocation data over the course of an entire year,” Crawford said. “This effort gave Connecticut epidemiologists and policymakers insight to people’s social distancing behavior statewide.”
Other studies have used so-called “mobility metrics” as proxy measures for social distancing behavior and potential COVID-19 transmission. But that analysis can be flawed. More