- #1
- 1,120
- 1
http://mathworld.wolfram.com/news/2005-05-10/rsa-200/
Damn, my record stands at factoring a semiprimes of about 95 digits lol.
Damn, my record stands at factoring a semiprimes of about 95 digits lol.
Last edited:
You can factor Mersenne numbers from the formulae alone assume the exponent isn't prime. Also there is a specific test for testing the primality of Mersenne numbers: http://mathworld.wolfram.com/Lucas-LehmerTest.htmlgazzo said:How much different are these to factoring mersenne numbers?
What makes them so much harder? :S
gazzo said:How much different are these to factoring mersenne numbers?
What makes them so much harder? :S
The factors p and q will have the probably have the properties:saltydog said:I believe also they're chosen to be as far apart as possible. Correct me if I'm wrong, but the closer they are together, the easier (relatively speaking), it is to factor the composite.
Zurtex said:The factors p and q will have the probably have the properties:
[tex](pq)^{\frac{1}{3}} < p < q[/tex]
Also it is highly likely that:
[tex]\alpha p < q < \beta p \quad \text{where} \quad \alpha \approx 2 \, \, \text{and} \, \, \beta \approx 10[/tex]
These are 2 properties I found highly useful to reduce chance of factorization, or at least when I studied factoring such numbers.
Well actually for large numbers the 2nd one implies the 1st one and a lot stronger conditions, however the 1st one is more logically important, the 2nd one makes sense when you try and think about how people might attack it. You will see that my inequalities hold for RSA-200.saltydog said:Very nice Zurtex. Think I'll check your properties out with RSA-200. Thanks.
Zurtex said:The factors p and q will have the probably have the properties:
[tex](pq)^{\frac{1}{3}} < p < q[/tex]
Also it is highly likely that:
[tex]\alpha p < q < \beta p \quad \text{where} \quad \alpha \approx 2 \, \, \text{and} \, \, \beta \approx 10[/tex]
These are 2 properties I found highly useful to reduce chance of factorization, or at least when I studied factoring such numbers.
RSA-200 is a number with 200 decimal digits that is the product of two large prime numbers. It is important because it is used as a benchmark for testing the efficiency of factoring algorithms, which are crucial for cryptography and data security.
The factoring of RSA-200 was accomplished in 17 days using a combination of distributed computing and specialized factoring algorithms.
The factoring of RSA-200 was a collaborative effort involving mathematicians and computer scientists from various institutions, including the University of Bonn, the University of California Berkeley, and the University of Michigan.
The previous record for factoring large numbers was the factoring of RSA-180, which had 180 decimal digits and was achieved in 1999 using the Number Field Sieve algorithm.
The factoring of RSA-200 is considered a significant achievement because it demonstrates the continuous progress in factoring algorithms and highlights the importance of constantly updating and improving methods for securing data and information.