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This might be a very simple question. However, I am just learning the concept, so just excuse me.

I am wondering why there is not any attempt to generate all semiprime numbers? (as an dict. attack to RSA-xxx algorithms). Because as far as I can see, all one is to do is as following:

  1. get a database of prime numbers
  2. multiply each prime number with each one. (which will require O(n^2) space)
  3. save the product.

  4. Of course, you will not do this for all of the prime numbers:)

    You will do this to prime numbers which will fall to the domain of RSA's random prime generator. In other words, which will create a $x$-bit number for RSA-$x$ (2048 bit for RSA-2048, for example).

I am sure one of these steps is impractical. Can you tell which one?

Paŭlo Ebermann
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Sumer Cip
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    Hint: based on this answer, compute how large your dictionary would need to be. – fgrieu Jun 12 '13 at 16:34
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    The problem is that there more than $2^{1000}$ primes that fall into the range of RSA-2048. Totally infeasible to find them all. – CodesInChaos Jun 12 '13 at 17:29
  • @CodesInChaos: Oh, come on, that's only $2.743 \times 10^{279}$ yottabytes! (Just to store the semiprimes, that is. You'd need approximately double the space to store the factors too.) – Reid Jun 12 '13 at 18:25
  • @Reid no, you would need to store $2^{1999}$ multiples of those primes, which is quite a bit more. For each of them you would want both factors. – Paŭlo Ebermann Jun 13 '13 at 05:27
  • That's okay. I'm sure a few external hard drives will be more than enough... perhaps not. – Thomas Jun 13 '13 at 06:07
  • @PaŭloEbermann: I was envisioning storing each 2048-bit semiprime plus the two factors, each around 1024 bits. – Reid Jun 13 '13 at 13:03

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