Prime numbers guru 'factors' down success

[William Knowles]

http://timesofindia.indiatimes.com/cms.dll/html/comp/articleshow?artid=34707852

SIDDHARTHA D KASHYAP
TIMES NEWS NETWORK
JANUARY 18, 2003
 
PUNE: Computer scientist Manindra Agrawal, who hit global headlines 
last year by unravelling a long-standing mystery of prime numbers, 
does not plan to patent his method.

The problem of conclusively identifying enormous prime numbers 
(hundreds of digits long) had baffled mathematicians across centuries 
until the Kanpur-based IIT-ian and two of his undergraduate students - 
Neeraj Kayal and Nitin Saxena - developed a simple method of cracking 
it.

Prime numbers (such as 1, 5, 11, 37...) are divisible only by 
themselves or 1. While smaller prime numbers are easy to make out, for 
very large numbers, there never had been a formula for "primality 
testing" until August 2002.

"I'm not keen on restricting mathematicians and other people from 
using this method," says Agrawal,who will soon be leaving for a 
year-long stint at the Institute for Advanced Studies in Princeton, 
New Jersey.

Felicitated for his mathematical breakthrough by Tata Consultancy 
Services here on Friday afternoon, Agrawal delivered a lecture on the 
subject. The primality formula opened up new vistas to decode Internet 
encryption, besides offering a new ray of hope to other problems in 
Mathematics.

"What we've so far achieved is a foolproof method of identifying large 
prime numbers," he said, adding that the factoring problem is yet to 
be solved. "So why not allow people to work on this technique and 
unravel the further problem," he asked, while explaining the reason 
for not opting for a patent.

While Agrawal's discovery has fascinated people,who have gone to the 
extent of heralding an end to the use of the Internet, Agrawal humbly 
accepts it is presently of little or no commercial value. 

"The algorithm we discovered will not set new world records because of 
its innate lack of speed," he admits. A 100-digit number takes at 
least a year to determine its primality, he adds.

"All those reports are misleading and inconsequential now," he said, 
adding that the race is, however, on to arrive at new approaches to 
primality testing. "We hope to achieve some results at the end of two 
years."

Does the discovery hold any relevance to cryptography? "No, not at the 
moment. Again because our algorithm is not fast enough for practical 
applications," he said. Presently, information security on the 
Internet is based on the difficulty of factoring an enormous number. 

"For anybody to decrypt such a number, one has to figure out the two 
prime numbers (factors) used, which are 250 digits each, or more 
long," he said. "Besides, factoring is the key to many other 
mathematical problems too."
 

 
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