Louis de Branges posted a 124-page paper recently, purporting to solve mathematics' “greatest unsolved problem,” the Riemann Hypothesis, that may simplify efforts to derive prime numbers.
The hypothesis, formulated by Bernhard Riemann in a 1859 paper titled “On the Number of Prime Numbers Less Than a Given Quantity,” essentially suggests that, because an equivalent exists between the distribution of zeros in Riemann’s zeta function and the disbursement of prime numbers among integers, it is possible to predict the position of prime numbers.
“De Branges’ work deserves attention from the mathematics community,” said Leonard Lipshitz, head of Purdue’s mathematics department. “It will obviously take time to verify his work, but I hope that anyone with the necessary background will read his paper so that a useful discussion of its merits can follow.”
Wide-spread discussion followed de Branges’ announcement, with security experts and mathematicians speculating that it might mean an end to current public-key encryption methods. London newspaper the Guardian even trumpeted the news with an article titled “Math’s Holy Grail Could Bring Disaster for Internet.”
“Suddenly all cryptic codes would be breakable,” the article reads. “No internet transaction would be safe.”
Public-key encryption, is, in essence, based upon prime numbers and the products that result when two are multiplied together. While it is very easy to get the product of two prime numbers, reverse engineering the product into its factors is exceptionally difficult.
Finding those factors would be significantly easier if a set of prime numbers could be specified instead of using the classical method to generate prime numbers, which is basically picking a random odd number and see if it is prime.
Some security experts believe that the discovery might not present a huge problem for cryptographers to overcome, though.
“I don’t think it’s the end of the world,” Bruce Schneier, chief technology officer at Counterpane Internet Security Inc., told eWeek.
“Just because something is possible doesn’t mean it’s easy,” Schneier said. “It might mean we have to increase key size or move to a different algorithm, but I doubt it.”