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Feb 17, 2021 at 21:00 comment added Todd Lehman @MaartenBodewes — Well, there's quite an easy way around the problem of generating primes much smaller than 2^1024: Simply require that the high bit of the 1024-bit integer is 1. (Either generate a new random number if you chose one with a high bit of 0, or just plain always set it to 1.) You lose 1 bit of entropy, but you still have 1023 bits of entropy driving each prime factor.
Sep 24, 2018 at 13:03 comment added Maarten Bodewes Yes, you can certainly rewrite RSA key pair generation from scratch. But please beware that this is fraught with danger. For instance, you might be generating primes that are much smaller than 1024 bit if each bit is random. Therefore I'd recommend taking a known good implementation and using that.
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May 1, 2018 at 12:30 history answered Richard Ellicott CC BY-SA 3.0