# Math behind Internet encryption wins top award

Abel prize awarded to number theorist John Tate.

Math behind Internet encryption wins top award Image:

By Zeeya Merali

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 \$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 a^n + b^n = c^n 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."

View
1. 1. Greg Angelo 04:09 PM 3/25/10

The use of the equation an + bn = cn as an illustration of Fermat's Last Theorem is an illustration of the abysmal editorial standards now evident in the once great Scientific American.

The correct equation familiar to any body with more than a basic understanding of the problem is a^n + b^n = c^n being the respective integers a b and c raised it to the power n and not a simple product of these three integers multiplied by n.

The form of notation chosen is due to the limitations of the text processor which can not use normal equation nomenclature which is also disgraceful for a scientific publication. I would respectfully suggest that the editors correct this glaring error ASAP.

Greg Angelo
Melbourne, Australia

2. 2. slaven41 10:12 AM 3/26/10

"I would respectfully suggest..."

This is obviously some new meaning of the word 'respectfully' that I'm not familiar with.

3. 3. Greg Angelo in reply to slaven41 03:11 AM 3/27/10

@slaven41 Use of the the term "respectfully" was deliberate as I am not a scientist but only a member of the general public with an interest in scientific matters. Accordingly in reference to the presumed greater knowledge the magazine's editors I thought it appropriate to preface my suggestion in deference to their presumed greater capacity.

It is a perhaps a measure of the relevance of these newsletters that neither has there been any other response, but also that the editors thinks so little of their own publication that they do not review the responses.

4. 4. Dedic 08:13 AM 4/2/10

Greg, I think slaven's point is, you basically said "Hey you idiots! Could you please correct your moronic mistake?"

Perhaps "abysmal editorial standards" was the tip-off, at least for me. It's hard to respectfully do anything after bashing like that. Just a thought, though...

5. 5. Dedic 08:14 AM 4/2/10

Greg, I think slaven's point is, you basically said "Hey you idiots! Could you please correct your moronic mistake?"

Perhaps "abysmal editorial standards" was the tip-off, at least for me. It's hard to respectfully suggest anything after a bashing like that. Just a thought, though...

6. 6. Greg Angelo 11:04 PM 4/2/10

To both of the respondents to my comment you have correctly interpreted my frustration even though I felt like saying what has been attributed.

I have been subscribing to Scientific American for over 40 years and in some respects quality of the magazine has deteriorated over time although overall I still find the content very interesting.

It is however important for an institution that has prided itself on excellence for over 150 years does not allow a sloppy journalism to tarnish its reputation. The quality of these electronic posts is certainly a mixed blessing.

If electronic messaging from SCIAM is to attain the same professed standards as the print medium more needs be done both in terms of the grammatical presentation and content.

I note that the erroneous content has now been corrected, but also that the editors did not pay me the courtesy of acknowledging the error and the suggested correction.

You must sign in or register as a ScientificAmerican.com member to submit a comment.
Click one of the buttons below to register using an existing Social Account.

## More from Scientific American

• Ask the Experts | 1 hour ago | 3

### What Role Does Climate Change Play in Tornadoes?

• Reuters | 2 hours ago

• Reuters | 2 hours ago

### Survivors Pulled from Oklahoma Tornado Debris

• Guest Blog | 2 hours ago

### An Unheralded Breakthrough: The Rosetta Stone of Mathematics

• Climatewire | 3 hours ago | 1

More »

## Latest from SA Blog Network

• ### 500 Million Years of Evolution in Under 4 Minutes

PsiVid | 1 hour ago
• ### An Unheralded Breakthrough: The Rosetta Stone of Mathematics

Guest Blog | 2 hours ago
• ### Scitable blog network just got bigger and better than ever!

STAFF
The Network Central | 3 hours ago
• ### USC Dornsife Scientific Diving: A New Faculty Member on the Team

Expeditions | 5 hours ago
• ### Winning the War against Cervical Cancer

Guest Blog | 6 hours ago

## Science Jobs of the Week

Math behind Internet encryption wins top award

X

### Subscribe Today

Save 66% off the cover price and get a free gift!

X

X

###### Welcome, . Do you have an existing ScientificAmerican.com account?

No, I would like to create a new account with my profile information.

X

Are you sure?

X