Pieter_Arntz
March 10th, 2003, 10:09 AM
How does that hurt you?
I copied al lot of the article since the page is not readable for everyone.
Many of the world's foremost mathematicians will gather in Palo Alto, California, this month to investigate a recent breakthrough in number theory that could have enormous implications for cryptography and the security of communications and economic transactions on the Internet.
While the details of the mathematics may be understood by relatively few people, anyone who has ever bought something online and paid by credit card - or anyone who has sent an encrypted message - should pay attention to these developments and what comes next. The security of online communications may be at stake.
Prime numbers - like 7, 13 and 29 - are evenly divisible only by themselves and 1. Here again, if the number is small, it is relatively easy to determine whether it is prime or not by trying all possible divisors. But when the number is very large, there are too many possibilities to try all of them, and there hasn't been any other way to determine with certainty whether the number is prime. Until now.
The Indian team's solution was completely unexpected, and it turned out to be relatively simple - only 12 lines of computer code. Its simplicity stunned mathematicians, many of whom wondered aloud how they could have overlooked it all these years.
As it happens, the RSA cryptosystem, which is most often used to protect Internet communications, uses both prime numbers and factoring. To encrypt a message or a credit card number using RSA, your computer manipulates it using an extremely large number that is the product of two extremely large primes, both of which are kept secret.
To decrypt the message, you have to know what those two prime factors are. The product of the two primes can be and is made public - hence the name, public-key cryptography - and that is how people are able to send encrypted messages. But only those who know the two prime factors can decrypt it. As long as those two prime factors remain secret, the code is uncrackable, and eavesdroppers can't read the message.
Public-key cryptography based on primes and factoring has been unbreakable. But the recent achievement in primality testing has made people look again.
Source: http://www.iht.com/articles/89163.html
I copied al lot of the article since the page is not readable for everyone.
Many of the world's foremost mathematicians will gather in Palo Alto, California, this month to investigate a recent breakthrough in number theory that could have enormous implications for cryptography and the security of communications and economic transactions on the Internet.
While the details of the mathematics may be understood by relatively few people, anyone who has ever bought something online and paid by credit card - or anyone who has sent an encrypted message - should pay attention to these developments and what comes next. The security of online communications may be at stake.
Prime numbers - like 7, 13 and 29 - are evenly divisible only by themselves and 1. Here again, if the number is small, it is relatively easy to determine whether it is prime or not by trying all possible divisors. But when the number is very large, there are too many possibilities to try all of them, and there hasn't been any other way to determine with certainty whether the number is prime. Until now.
The Indian team's solution was completely unexpected, and it turned out to be relatively simple - only 12 lines of computer code. Its simplicity stunned mathematicians, many of whom wondered aloud how they could have overlooked it all these years.
As it happens, the RSA cryptosystem, which is most often used to protect Internet communications, uses both prime numbers and factoring. To encrypt a message or a credit card number using RSA, your computer manipulates it using an extremely large number that is the product of two extremely large primes, both of which are kept secret.
To decrypt the message, you have to know what those two prime factors are. The product of the two primes can be and is made public - hence the name, public-key cryptography - and that is how people are able to send encrypted messages. But only those who know the two prime factors can decrypt it. As long as those two prime factors remain secret, the code is uncrackable, and eavesdroppers can't read the message.
Public-key cryptography based on primes and factoring has been unbreakable. But the recent achievement in primality testing has made people look again.
Source: http://www.iht.com/articles/89163.html