Scientists Envision Applications for Pi In Encrypted Internet Transactions
Friday, August 10, 2001
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.
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