Flaw Found in an Online Encryption Method

By JOHN MARKOFF
February 14, 2012

SAN FRANCISCO - A team of European and American mathematicians and 
cryptographers have discovered an unexpected weakness in the 
encryption system widely used worldwide for online shopping, banking, 
e-mail and other Internet services intended to remain private and 
secure.

The flaw - which involves a small but measurable number of cases - 
has to do with the way the system generates random numbers, which are 
used to make it practically impossible for an attacker to unscramble 
digital messages. While it can affect the transactions of individual 
Internet users, there is nothing an individual can do about it. The 
operators of large Web sites will need to make changes to ensure the 
security of their systems, the researchers said.

The potential danger of the flaw is that even though the number of 
users affected by the flaw may be small, confidence in the security 
of Web transactions is reduced, the authors said.

The system requires that a user first create and publish the product 
of two large prime numbers, in addition to another number, to 
generate a public "key." The original numbers are kept secret. To 
encrypt a message, a second person employs a formula that contains 
the public number. In practice, only someone with knowledge of the 
original prime numbers can decode that message.

For the system to provide security, however, it is essential that the 
secret prime numbers be generated randomly. The researchers 
discovered that in a small but significant number of cases, the 
random number generation system failed to work correctly.

The importance in ensuring that encryption systems do not have 
undetected flaws cannot be overstated. The modern world's online 
commerce system rests entirely on the secrecy afforded by the public 
key cryptographic infrastructure.

The researchers described their work in a paper that the authors have 
submitted for publication at a cryptography conference to be held in 
Santa Barbara, Calif., in August. They made their findings public 
Tuesday because they believe the issue is of immediate concern to the 
operators of Web servers that rely on the public key cryptography 
system.

...

http://www.nytimes.com/2012/02/15/technology/researchers-find-flaw-in-an-online-encryption-method.html

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