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I'm working on factorizing a ~450 bit key that I know has been generated with RSALib and thus is vulnerable to ROCA. Now reading the original paper, I can see that the primes are generated in the following form:

p=kM+(65537amod

where k and a are unknown value to us but where M is known and is in fact the product of the first j primes. Now in the original paper I was able to find that we know j for some intervals but I'm not quite sure how to derive it for key length that are below 512 bits. Is there a way to do it?

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  • \begingroup I'm a little bit confused, are you asking for the number of primes below a certain number, say the number of primes below 1000? \endgroup Commented Aug 31, 2018 at 9:09
  • \begingroup No, basically RSALib has a predefined method for generating primes but I couldn't find any documentation for primes where the keysize is < 512 bits. \endgroup
    – S. L.
    Commented Aug 31, 2018 at 16:04

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