Breaking Big Numbers
One of the mathematical pursuits that will have long-lasting effects on future computing and data management is the factoring of large numbers - discovering what the most basic components are that combine to produce the large number.
This is important because each and every non-prime number can be broken down into prime factors. For relatively small numbers, this process is straight forward - for example, 27 can be expressed as 3 x 3 x 3, the product of three primes. For much larger numbers, the process is a lot more involved, especially when none of the factors are known ahead of time.
A number of encryption methods rely upon this increasing difficulty to create the lengthy keys used to encrypt and protect data. When the prime numbers used to create the larger number are also large, it becomes an extremely difficult process to crack.
That is changing.
It was recently disclosed that a 307 digit 'special' number (number conforming to a specific rule) has been factored, and the researchers believe that it is now only a few years until they can factor any given 1024-bit number. This is a problem because the most popular strong encryption is usually handled by 1024-bit RSA keys - which will be available for defeating once a general factoring solution has been developed.
Noted cryptographic experts are already suggesting that users consider moving to a stronger encryption setting, such as 2048-bit encryption, or change to symmetric encryption models, rather than asymmetric models (which are at greatest risk at the moment).
Of course, it doesn't matter how long it takes to defeat an encryption method. So long as the information it is protecting becomes worthless before the encryption can be cracked, it has achieved its goal.
26 May 2007
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