Maths behind Internet encryption wins top award

[Cees Binkhorst]

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Waardeloze research die pas na 10-tallen jaren iets oplevert ;)

Groet / Cees

Published online 24 March 2010 | Nature | doi:10.1038/news.2010.150

News
Maths behind Internet encryption wins top award
http://www.nature.com/news/2010/100324/full/news.2010.150.html

Abel prize awarded to number theorist John Tate.

Zeeya Merali
John Tate.John Tate.C. Fondville /The Abel Prize/The Norwegian Academy
of Science and Letters

The Abel prize — considered the 'Nobel' prize of mathematics — has been
awarded to John Tate, recently retired from the University of Texas at
Austin, for his work on algebraic number theory, the mathematical
discipline that deals with connections between whole numbers and lies at
the heart of Internet security.

Established in 2002, the Abel Prize is presented annually by the King of
Norway and carries a cash award of US$1 million.

"Number theory knits together the subtle and strange properties of whole
numbers in a beautiful way," says mathematician Ian Stewart at the
University of Warwick in Coventry, UK. "Tate has really made himself the
master of number theory."

Tate's work in number theory helped to crack one of the most famous
challenges in mathematics: proving Fermat's Last Theorem. The theorem
states that you cannot find three positive integers a, b and c that
satisfy the equation an + bn = cn for any integer value of n greater
than two. The theorem was solved in 1995 by Andrew Wiles of Princeton
University in New Jersey, thanks in part to Tate's research into the
rules obeyed by 'elliptic curves' — curves generated by a particular
family of equations in number theory.

"Fermat's Last Theorem is simple to state, but took 350 years to prove,
using the machinery of number theory developed by Tate," says Stewart.

Long thought to be one of the purest forms of pure mathematics — as it
had little real-world relevance — number theory has now become vitally
important for securely encoding data to be transmitted across the
Internet. "If you go back to the 1950s, most mathematicians would have
agreed that number theory wasn't particularly useful — some thought that
a vice and some a virtue — but then along came the computer," says Stewart.
King of the code

One important method for ensuring secure transmission across the
Internet uses encryption keys based on 200-digit numbers that are the
multiple of two prime numbers. Thanks to Tate's developments in number
theory, algorithms can easily generate such numbers for encoding
purposes, says Stewart. However, there are no algorithms to perform the
reverse operation — working out the constituent primes of the 200-digit
number — making it impossible to for hackers to crack the codes. "Try to
find the prime factors of a 200-digit number with pencil and paper — or
even with a computer program — and it would take longer than the age of
the Universe," says Stewart.

Tate's work is also at the heart of error-correcting codes that allow
corrupted digital information to be reconstructed. "When you're driving
along, listening to music and hit a bump, the reason your CD doesn't
skip is thanks to these error-correcting codes," says Stewart. "It's
also the reason that the messages that you send on your mobile phones
aren't garbled by all the other radio signals flying through the air."

Tate is a popular choice for the Abel award, says mathematician Helge
Holden at the Norwegian University of Science and Technology in
Trondheim. "Tate's achievements in number theory go right back to his
doctoral thesis, which became famous, and span more than 60 years during
which his name has been given to many different theorems in the field,"
Holden says. "This is a well-deserved award for lifetime achievement."

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