Minimal information about RSA prime factorization

farah · 2013-02-05, 23:03

Hi

I'm not mathematician and I have very basic knowledge of math. So sorry if my question is so simple.

I want to know is there some known facts about basic information on RSA prime factors? I mean like:

- Prime factors (p and q) of RSA keys have same length or
- You can guess (at least) length of P and Q from given public key or
- You can guess minimum length of one of prime factors
etc.

Is there some known basic information on RSA keys?

Thanks

Dubslow · 2013-02-05, 23:58

p and q have roughly the same length, so that neither is too small, but if they were very similar, they would also be easier to find. So for an RSA key of 1024 bits, p and q are around 512 bits each -- maybe plus or minus a few bits.

However, there are still 2^511 numbers with 512 bits, and so maybe ~2^502 prime numbers with 512 bits which are potentially p or q -- so even knowing the bit length of the factors doesn't help.

2013-02-05, 23:03	#1
farah Feb 2013 1₁₀ Posts	Minimal information about RSA prime factorization Hi I'm not mathematician and I have very basic knowledge of math. So sorry if my question is so simple. I want to know is there some known facts about basic information on RSA prime factors? I mean like: - Prime factors (p and q) of RSA keys have same length or - You can guess (at least) length of P and Q from given public key or - You can guess minimum length of one of prime factors etc. Is there some known basic information on RSA keys? Thanks

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2013-02-05, 23:58	#2
Dubslow Basketry That Evening! "Bunslow the Bold" Jun 2011 40<A<43 -89<O<-88 3·29·83 Posts	p and q have roughly the same length, so that neither is too small, but if they were very similar, they would also be easier to find. So for an RSA key of 1024 bits, p and q are around 512 bits each -- maybe plus or minus a few bits. However, there are still 2^511 numbers with 512 bits, and so maybe ~2^502 prime numbers with 512 bits which are potentially p or q -- so even knowing the bit length of the factors doesn't help.