Which cryptographic protocols are secure against quantum computer attacks?

Are there any cryptosystems that we know that would be secure against an attack by a quantum computer?

Are there problems which are known or suspected to be hard for quantum computers, and can these be utilized to yield cryptographic protocols which are secure against quantum computers?

• The key search term for that literature is “post-quantum cryptography”. Jun 29 '18 at 5:02
• Intuitively, the protocols that utilize problems not in $\mathrm{BQP}$... (I do not know too much about either crypto or complexity theory, though)
– xrq
Jun 30 '18 at 19:24
• I am no expert, but I think lattice cryptography, like schemes based on the Learning with Errors problem, are conjectured to be secure against quantum attacks. This would follow from worst-case quantum hardness of variants of the shortest vector problem. Jul 31 '18 at 13:30
• Note that Cryptography protocols and Cryptosystems are not the same. Sep 11 '19 at 7:21