With its use, the scarcity of numbers remain, that is, finding a clash that would allow to forge a transaction stays infeasible, and mining stays hard.
BTW while mining is so important with Bitcoin and Etherium, it's not a necessary part of a cryptocurrency. Mining is an incentive to keep doing blockchain validation. Some currencies exist without it (e.g. NXT).
To date the only practical replacements for RSA and EC achieve key derivation but not signatures. Without signatures we're not really 'complete' since certificates are hard to do with only key derivation.
Post-quantum cryptograph research is a very active area right now. If these researchers do not find a practical signature algorithm, PKI as we know it will change very significantly.
Ironically, blockchains might elevate in importance as a result, since the evolving blockchain is a useful construct for quantum resistance. It has cryptographic agility built in.
All crypto becomes easier (well, except for the one time pad). But some algorithms (AES, SHA) only require doubling the number of bits to achieve the same security level, which is rather trivial to do.
With its use, the scarcity of numbers remain, that is, finding a clash that would allow to forge a transaction stays infeasible, and mining stays hard.
BTW while mining is so important with Bitcoin and Etherium, it's not a necessary part of a cryptocurrency. Mining is an incentive to keep doing blockchain validation. Some currencies exist without it (e.g. NXT).