The RSA system has been presented many times, following the excellent expository article of Martin Gardner in the August 1977 issue of Scientific American. There is no need for yet another explanation of the system; the essentials are contained in the Wikipedia article RSA (cryptosystem), and in many other articles.
The purpose of this note is to give an example of the method using numbers so small that the computations can easily be carried through by mental arithmetic or with a simple calculator.
Continue reading ‘A Toy Example of RSA Encryption’
The National Security Agency is the largest employer of mathematicians in America. Mathematics is a core discipline at NSA and mathematicians work on signals intelligence and information security (US citizenship is a requirement for employment). Why is NSA so interested in mathematics? [See TM096, or search for “thatsmaths” at irishtimes.com].
Flag of the National Security Agency
Continue reading ‘Can Mathematics Keep Us Secure?’
Most of us use computer terminals, tablets and smart phones, absorbing information quickly and easily. How do the many thousands of Irish people who are blind or visually impaired manage to interact with computers? For them, entering data by keyboard or voice is easy, but special software is needed to convert the text on screen into a form for output to a loudspeaker or headphones, or to drive a refreshable Braille display [TM095, or search for “thatsmaths” at irishtimes.com].
Braille display (www.humanware.com)
Continue reading ‘Computers Speaking in Irish’
The world is awash with data. Large data sets have been available for many decades but in recent years their volumes have grown explosively. With mobile devices and internet connections data capture is simple and with powerful computers the analysis of “big data” is feasible [see TM092, or search for “thatsmaths” at irishtimes.com].
Google image search for “Big Data”
But there are challenges: many data sets are too large and too complex to be analysed or understood using traditional data processing methods. Our current armoury of analysis techniques is inadequate and new mathematical methods are needed.
Continue reading ‘Big Data: the Information Explosion’
Modern weather forecasts are made by calculating solutions of the mathematical equations that express the fundamental physical principles governing the atmosphere [TM083, or search for “thatsmaths” at irishtimes.com]
The solutions are generated by complex simulation models with millions of lines of code, implemented on powerful computer equipment. The meteorologist uses the computer predictions to produce localised forecasts and guidance for specialised applications.
Continue reading ‘Richardson’s Fantastic Forecast Factory’
Networks are everywhere in the modern world. They may be physical constructs, like the transport system or power grid, or more abstract entities like family trees or the World Wide Web. A network is a collection of nodes linked together, like cities connected by roads or people genetically related to each other. Such a system of nodes and links is what mathematicians call a graph [TM078; or search for “thatsmaths” at irishtimes.com ].
Continue reading ‘It’s a Small – Networked – World’
The readable surface of a Compact Disc has a spiral track over 5 km in length.
The quality of music recordings on compact discs or CDs is excellent. In the age of vinyl records, irritating clicks resulting from surface scratches were almost impossible to avoid. Modern recording media are largely free from this shortcoming. But this is curious: there are many reasons why CD music can be contaminated: dirt on the disc surface, flaws in the plastic substrate, errors in burning on the recording, scratches and fingerprints, and so on [TM077; or search for “thatsmaths” at irishtimes.com ]
Continue reading ‘New Tricks: No Clicks’