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This question already has an answer here:

As far as I understand ECDSA keys are smaller than RSA because all of the value of the ECDSA (up to a high number) are valid private keys.

Is there any method of compressing RSA keys, based on some form of description of the key?

e.g. This is the $M^{\text{th}}$ possible value of $n$, given that $e = E$ and $A \leq n < B$.

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marked as duplicate by otus, e-sushi May 6 '16 at 2:02

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    $\begingroup$ Are you asking about compressing the public key or the private key? The latter can be compressed to a small seed used in a random number generator. $\endgroup$ – otus May 4 '16 at 9:14
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    $\begingroup$ In addition of otus' comment: for compression of an RSA public key, see this. Compression is not the same as enumeration. $\endgroup$ – fgrieu May 4 '16 at 11:03
  • $\begingroup$ @otus Both, ideally. $\endgroup$ – fadedbee May 4 '16 at 12:25
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    $\begingroup$ The easiest trick for creating a small private key is simply to regenerate it with a well seeded PRNG. That way you don't need to compress the key itself. For the public key you'd probably require to compress the modulus. That's not easily done. You might however get away with creating a unique identifier over the modulus (i.e. hashing the value). If you then trust that unique identifier you can ask another party for the modulus when required. $\endgroup$ – Maarten Bodewes May 4 '16 at 12:47

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