One of the things that I have come to like about elliptic curve cryptography is that the key only needs to be twice as long as the desired security level. That's a very small expansion (I also like it aesthetically). The sizes for the public key and private key are also the same. Unfortunately, ECC is not secure against quantum algorithms and quantum computers capable of breaking uses of elliptic curves seem to be coming up within a decade or two. What is more is that many post-quantum cryptosystems—the ones I am familiar with, at least—have idiotically huge keys and signatures. The best key sizes seem to be acghieved by lattice-based cryptosystems and one variant of code-based cryptography. Are there any candidates with smaller key and signature sizes? Any as small 10 times larger than the desired security level? Any as small as ECC ones?

  • $\begingroup$ csrc.nist.gov/projects/post-quantum-cryptography/… $\endgroup$ – user10653 Dec 26 '17 at 19:22
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    $\begingroup$ You can browse through the NIST pqcrypto submissions, but it's pretty clear that it's too early to say which ones with small keys/signatures/ciphertext overheads/agreement costs are going to stand to scrutiny! $\endgroup$ – Squeamish Ossifrage Dec 26 '17 at 19:43
  • $\begingroup$ SIDH can be used with the same key size as regular DH. $\endgroup$ – forest Aug 19 '18 at 3:09

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