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From researching post-quantum cryptographic schemes it seems hash-based and lattice-based algorithms are the most promising (MQ-based seem to be covered by patents and have more potential unknowns which could be used to exploit them.) Hash-based schemes seem like the most reliable, but lack certain features found in lattice-based algorithms like the ability to do blind signatures.

For these reasons I'm curious what the potential issues with lattice-based cryptographic systems are and how likely they are to result in practical issues for implementations (be it key and signature size increases to compensate or hard-stop issues where you simply can't work around them with lattice-based cryptosystems.)

What key and signature sizes are expected to be secure currently? What if new algorithms come along as a worst-case scenario? (Assuming 256 bits of security in both cases.)

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    $\begingroup$ This question deserves a much better title, at the very least. $\endgroup$ – zhenfei zhang Jan 11 '18 at 4:24
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    $\begingroup$ @zhenfeizhang What would you suggest? $\endgroup$ – CoryG Jan 11 '18 at 11:50

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