# Factorize RSA knowing several N and E

I did a CRT challenge yesterday and theres one problem I was unable to solve, probably due to my lack of understanding advanced crypto math.

Its about RSA. There are ten given pairs of N and E (modulo and exponent). E is always the standard exponent 10001 (hex). N is a 2048 bit number.

Well, I tried everything known to me (CRT, Wiener, p-1), no luck. Now it occurred to me that maybe 10 pairs aren't given to keep you busy but that maybe the vulnerability is located there?

Any ideas?

no, I don't have the data anymore. :)

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Did they publish an exponent pair (e,d)? –  CodesInChaos Dec 7 '12 at 11:21
i dont think so, only N and E like this: 10001 <...N1...> 10001 <...N2...> 10001 <...N3...> –  lonelyis Dec 7 '12 at 11:23
There is no solution to the problem as you describe it. Perhaps some of the moduli were badly created and contain common factors. –  CodesInChaos Dec 7 '12 at 11:26
For the deterministic algorithm, see $\:$ www.math.dartmouth.edu/~carlp/aks041411.pdf . $\hspace{.7 in}$ –  Ricky Demer Dec 7 '12 at 22:38
Why do you care if the factors are prime? RSA is always done using a product of two (probable) primes, so any nontrivial factor will be prime. –  Antimony Dec 10 '12 at 7:09