If a quantum computer with a sufficient number of qubits were to be constructed, Shor’s algorithm could be used to break public-key cryptography schemes such as the widely used RSA scheme. RSA is based on the assumption that factoring large numbers is computationally infeasible. So far as is known, this assumption is valid for classical (non-quantum) computers; no classical algorithm is known that can factor in polynomial time. However, Shor’s algorithm shows that factoring is efficient on a quantum computer, so a sufficiently large quantum computer can break RSA. It was also a powerful motivator for the design and construction of quantum computers and for the study of new quantum computer algorithms. It has also facilitated research on new cryptosystems that are secure from quantum computers, collectively called post-quantum cryptography.
Tag Archives: mathematics
Venn diagrams for 11 sets
So called 2-Venn (two circles) and 3-Venn diagrams are very familiar. But higher dimension Venn diagrams that are (relatively) easy to grasp (‘ll explain what I mean by that below) are actually difficult to produce – and until last month nobody had managed to get beyond 7.
Meet Hyperborean, the Poker-Playing AI
The CPRG’s poker programs, named “Hyperborean” in the ACPC, are constructed quite differently compared to programs for “perfect information games” such as chess.
A Faster Fourier Transform
The principle of the Fourier transform, which dates back to the 19th century, is that any signal, such as a sound recording, can be represented as the sum of a collection of sine and cosine waves with different frequencies and amplitudes. This collection of waves can then be manipulated with relative ease—for example, allowing a recording to be compressed or noise to be suppressed. In the mid-1960s, a computer-friendly algorithm called the fast Fourier transform (FFT) was developed. Anyone who’s marveled at the tiny size of an MP3 file compared with the same recording in an uncompressed form has seen the power of the FFT at work.
via A Faster Fourier Transform – Technology Review.
A faster transform means that less computer power is required to process a given amount of information—a boon to energy-conscious mobile multimedia devices such as smart phones.
Note the higlighted statement. Power consumption is trumping speed in modern computing devices. Also Note: The author of the linked to article isn’t me.
handymath.com
Our mission is to provide mathematical tools and solutions for technicians to aid them in their work. This website is dedicated to all laboratory technicians, manufacturing technicians, carpenters, mechanics, welders, electricians, plumbers, handymen, do it yourselfers, etc. It is our aim to apply practical mathematics.
via Mission.
The elusive capacity of networks
What makes that question particularly hard to answer is that no one knows how to calculate the data capacity of a network as a whole — or even whether it can be calculated. Nonetheless, in the first half of a two-part paper, which was published recently in IEEE Transactions on Information Theory, MIT’s Muriel Médard, California Institute of Technology’s Michelle Effros and the late Ralf Koetter of the University of Technology in Munich show that in a wired network, network coding and error-correcting coding can be handled separately, without reduction in the network’s capacity. In the forthcoming second half of the paper, the same researchers demonstrate some bounds on the capacities of wireless networks, which could help guide future research in both industry and academia.
The Traveling Salesman Problem
Given a collection of cities and the cost of travel between each pair of them, the traveling salesman problem, or TSP for short, is to find the cheapest way of visiting all of the cities and returning to your starting point. In the standard version we study, the travel costs are symmetric in the sense that traveling from city X to city Y costs just as much as traveling from Y to X.
via The Problem.
Mathematician claims breakthrough in Sudoku puzzle
The emerging consensus among mathematicians at a conference in Boston, Massachusetts, on 7 January was that McGuire’s proof is probably valid and an important advance in the growing field of Sudoku maths.
via Mathematician claims breakthrough in Sudoku puzzle : Nature News & Comment.
Data modeling
Data modeling is a method used to define and analyze data requirements needed to support the business processes of an organization. The data requirements are recorded as a conceptual data model with associated data definitions. Actual implementation of the conceptual model is called a logical data model.