I was wondering about whether there exists a scheme that would have the following properties:

  • Be asymmetric (Encrypt with public key, decrypt with private key)
  • Be secure by today's standards (as hard as RSA 2048)
  • Short public key

Real life application is to enable people to communicate the public key over the phone to the sender so that the sender can encrypt messages using the receiver's public key. There is no network between the sender and receiver.

Any ideas?

  • 6
    It might be more useful if you also describe your actual use case instead of only what you imagine are the requirements for this use case. – Steffen Ullrich Dec 18 '18 at 9:25
  • Let us continue this discussion in chat. – Curve25519 Dec 18 '18 at 11:41
  • I want a short public key. why is this on hold – Curve25519 Dec 18 '18 at 13:47

You want to use elliptic curve cryptography (ECC).

For example, curve 25519 has public keys of 128 bits or 32 bytes, while providing similar security as RSA 2048.

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  • I'm not sure this is correct... Curve25519 has a 32-bit public key but only has a 128-bit security target (actually more like 126), not 256. And in fact the actual security is even lower, since five of the bits is supposed to be a fixed value for performance. Please see Does Curve25519 only provide 112 bit security?. This means it provides similar security to RSA 2048, not 3072. Perhaps you are confused because Curve25519's base order is 252 bits? That does not mean the security is anywhere near 256 bits. – forest Dec 18 '18 at 12:05
  • @sjoerd from the chat, the OP wants to implement the scheme using humans to transmit the public key, and hence needs a short key ... – schroeder Dec 18 '18 at 12:06

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