I've read about different signature schemes which for the same bits of security differ largely in the size of the public key: The ones proven in the standard oracle model perform worse than the ones proven in the random oracle model. I understand that a difference in the size of a signature is important in case the signature is sent along the data which was signed.

However, what are the negative effects of a large public key? What comes to my mind is that this could be an issue in embedded hardware which is limited in storing capacity. Might this be an issue in other scenarios as well? E.g. are there protocols in which public keys are included in packets and thus take up important space?

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    $\begingroup$ Smart Cards and card verifiable certificates is one... With an APDU command size of 255 bytes using a signature of 256 bytes (RSA 2048) requires some thought - and I would not call that a large key size. $\endgroup$ – Maarten Bodewes Apr 5 '17 at 9:54
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    $\begingroup$ For reference: keylength.com $\endgroup$ – Maarten Bodewes Apr 5 '17 at 9:55

Larger public keys (in the same scheme) lead to

  • larger signatures
  • larger certificates
  • slower signature computation
  • much slower key generation

All of these might be a problem, especially for embedded devices, as you already mentioned. As for your last question: Yes, there are a lot of protocols which transfer a public key, usually in the form of a (X.509) certificate. A TLS handshake is just the most prominent example.

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    $\begingroup$ While for the same scheme a larger public key will mean all of the above, note that (other) schemes with larger public keys (for the same security level) may still be faster. $\endgroup$ – SEJPM Apr 5 '17 at 9:34
  • $\begingroup$ That's right, but I understood the question in a way, that means "larger public key in the same scheme" $\endgroup$ – mat Apr 5 '17 at 9:46

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