Scientists Envision Applications for Pi In Encrypted Internet Transactions





  • Printer Friendly Printer Friendly
  • Comments Comments (0)

Nearly 3,000 years after ancient craftsmen attempted to unlock the secrets of pi-3.14, the number that often tortures geometry students-to build the great Temple of Solomon, Lawrence Berkeley National Laboratory scientists are taking another look at the mysterious number, which could be used to secure Internet transactions.

It is commonly known that pi is irrational, meaning the sequence of digits never repeats itself. But the lab scientists are now trying to prove that pi, commonly abbreviated as 3.14159, is "random."

If this mathematical theory is proven, the applications are enormous. If pi is proven to be random, the number could be securely used to encrypt sensitive information traveling through the World Wide Web, since cryptography is often based on random numbers.

Random numbers are favored for encrypted data. If a lazy encryption specialist used numbers that cycle themselves, like 6.363636363, there would be far more chances to select a "6" or a "3," and it would be much easier to crack the code.

But if pi is found to be a random number, it could be used as a basis for a good encryption.

Lab scientist David Bailey, who is researching the project, is a member of a team trying to prove that pi is random. Being a random number would mean that out of all the digits in pi, which has an infinite number of digits, there is an equal chance of picking any digit.

Or, in mathematical terms, "Every block of digits appears with the appropriate frequency," said Bailey, a chief scientist at the lab's scientific computing center.

For example, a potential code-breaker would have the same chance of picking a "5" or a "9" out of pi, making it extremely difficult to break an encryption.

If and when the randomness of numbers like pi is proved, it would be a historic moment for the field of mathematics.

"This is a long-standing open question," Bailey said.

Supercomputers have calculated pi to billions of places, lending support to the hypothesis that pi is random. But scientists have yet to actually prove it is random, or "normal," as mathematicians like to call it.

The long-sought proof of pi's randomness has plagued mathematicians for hundreds of years. Little progress has been made since the 19th century.

Bailey, who worked for 14 years at NASA Ames Research Center, has made progress on proving pi's randomness. In 1996 Bailey, along with Canadian mathematicians Peter Borwein and Simon Plouffe, found a formula-named BBP in honor of its authors-that could calculate a given digit of pi without having to calculate any of the previous digits.

Bailey and his colleague, Richard Crandall, director of the Center of Advanced Computation at Reed College, found a relationship between the BBP formula and the chaos theory-evidence needed to prove that pi is a normal number.

"We found a link between the digits of pi and the theory of chaotic dynamics," Bailey said. "And it's possibly a step towards a proof of normality."

In order to complete the puzzle, the scientists must concretely prove that the equation they developed is a random-number generator.

Although other colleagues in the field believe this may be too difficult to prove, Crandall and Bailey are nonetheless determined to try.

Defined as the circumference of a circle divided by its diameter, pi is an irrational constant, meaning its digits run on indefinitely-without a set pattern.

Tags:






Comments (0) »

Comment Policy
The Daily Cal encourages readers to voice their opinions respectfully in regards to both the readers and writers of The Daily Californian. Comments are not pre-moderated, but may be removed if deemed to be in violation of this policy. Comments should remain on topic, concerning the article or blog post to which they are connected. Brevity is encouraged. Posting under a pseudonym is discouraged, but permitted. Click here to read the full comment policy.
White space
Left Arrow
News
Image Student regent resigns after sex crime allegations
Jesse Cheng officially announced his resignation from his positio...Read More»
News
Image Pet shop may occupy planned Goodwill
After failed negotiations with the landlord and resistance from the busines...Read More»
News
Image Campus graduate takes new first steps
UC Berkeley's graduation day this year was symbolic for graduate Austin Whi...Read More»
News
Image Regents rescind part of approval
The ongoing legal battle surrounding revisions to the building plans for th...Read More»
News
Image UC spared additional cuts in budget revision
While the University of California escaped further funding reductions M...Read More»
News
Image UC Board of Regents wary of unreliable state funds
SAN FRANCISCO - Following the release of Gov. Jerry Brown's revis...Read More»
Right Arrow




Job Postings

White Space