Actually, the field of information protection – known as “cryptography”, or “hidden writing” – isn’t new. The problem with this is that anyone can intercept read the message you have sent.Īn internet-based economy therefore requires a new kind of security technology in order to protect information people send online. The danger with modern internet transactions is that you must send private data through a public network in order to reach its destination, such as your bank. In the age of the internet, when we use the internet to conduct business transactions, check our bank account, use credit cards to buy things online, and take cash out of an ATM, security technologies such as armed guards, armored trucks, and X-ray machines simply don’t work. You’re right! They’re easy to conceptualize, but their sometimes mind-boggling properties actually have crucial applications in the modern world, which we’ll see in this article.
What could be more simple than the natural numbers 1, 2, 3,…? While they’re deceptively easy to conceive and understand, their study has gained its reputation as the “queen of mathematics”, and many of the greatest mathematicians have devoted study to their properties, which are not as simple as you might expect. Number theory studies the properties of the natural numbers: 1, 2, 3,… You might also think of them as the “counting numbers”. This has happened with a number of results in the field of mathematics known as number theory. So oftentimes, theoretical results in mathematics turn out to have completely unexpected applications. This happened, for example, when non-Euclidean geometries described by the mathematicians Karl Gauss (pictured below) and Bernard Riemann turned out to provide a model for the relativity between space and time, as shown by Albert Einstein. One of the amazing things about theoretical mathematics – mathematics done for its own sake, rather than out of an attempt to understand the “real world” – is that sometimes, purely theoretical discoveries can turn out to have practical applications. Introduction: how ‘pure’ mathematics can have unexpected applications
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Otherwise, feel free to read through the beginnings of these sections, and skim through the more technical parts and head to the final section for a brief outline of the mathematics involved. Some of the mathematics in the section on prime numbers and Fermat’s Little Theorem, and the encryption scheme known as RSA, are on the level of a typical intermediate level university mathematics course if you have a few hours and want to understand exactly how this encryption scheme works, you can work through the mathematics of this. Let’s see how some discoveries in mathematics unexpectedly made the age of secure online transactions possible. Online security presents new challenges for security. The Art of the Hidden Message: The role of number theory and prime numbers in online security
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