In-My-Opinion.org

»193-digit no: RSA-640 factored in challenge for $20,000«


(No don't pass over this article thinking it's just a buncha boring numbers..)

Most of you know what prime numbers are , I presume.

(I'm going to be a bit tedious here so, if you just want the article and news I'm talking about, look lower down.)

Numbers that do not have factors other than 1 and themselves = they cannot be factorized .
Eg. 2, 3, 5, 7, 11...


Factorization = breaking down a composite number into its (prime, but not necessarily) factors.
Eg. 12 = 2 x 2 x 3

Composite number = any number that can be factorized into numbers other than 1 and itself.
Eg. 4, 6, 8, 9, 10...

1 is neither prime nor composite.

Now, RSA numbers are composite numbers that have exactly 2 prime factors (called "semi primes). Numbers can get really big, if you've noticed. Factorizing becomes harder, as numbers get higher.

So, if you're given a product 'p', it can be extremely difficult to find the factors.

Imagine you're given a 100-digit number 'p', and you have to find out exactly two prime numbers 'a' and 'b' such that

p = a x b


i.e., 6 = 2 x 3 on a much larger scale.

So, you realize it would be extremely hard to factor an RSA number. Which is why these numbers can be used in encrypting data with 'keys'.

RSA Security issued a factoring challenge, inviting anyone to factorize certain RSA numbers they listed, for a certain cash-award. A German team has announced that they have factorized the 193-digit number RSA-640 :

3107418240490043721350750035888567930037346022842727545720161948823206440 5180815045563468296717232867824379162728380334154710731085019195485290 07337724822783525742386454014691736602477652346609

(Why is it called RSA-640? We follow the decimal system in arithmetic. Computer algorithms run on the binary system. This 193-digit number has 640 binary digits, hence the name. )

into these two 97-digit [prime] factors :

(1634733645809253848443133883865090859841783670033092312181110852389 333100104508151212118167511579)

x

(1900871281664822113126851573935413975471896789968515493666638539088 027103802104498957191261465571)

and, according to the challenge, they win $20,000 .

Awesome, innit?

There are several challenges still left open, 6 numbers from RSA-704 to RSA-2048, for awards ranging from $30,000 to $200,000.

Any math geeks here? Yes, oh yes.. keep going

You can get the full article on this, if you're interested, at




posted by ryder
  All your base are belong to us


in-my-opinion.org -> Technology, Computers, Science, Internet -> Language, Math and Names -> 193-digit no: RSA-640 factored in challenge for $20,000



I learned something new, I guess

Wow. If I actually had money, I'd be out buying a calculator with a really big screen right now.

posted by Sharaith
  



They say, that some scientist has already found a solution how to calculate these numbers in a fraction of time, but keeps it secret, because the secret services use the knowledge to crack encrypted emails etc...

posted by knn
  



Pfft I see the lack of popularity of math topics here.. time to go digging..
Sharaith:
If I actually had money

You need money to make money, interesting point you make Very Happy
knn:
some scientist has already found a solution how to calculate these numbers in a fraction of time, but keeps it secret, because the secret services use the knowledge to crack encrypted emails etc...

Sure, and they feed this solution into a machine that is constantly working on cracking codes.. and the scientist goes public with the knowledge..

Have you read Digital Fortress by Dan Brown Θ knn? It's a very boring book.


posted by ryder
  





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