However, we already have several candidates at our disposal which look to be quantum resistant. In public key encryption there are a number of complex problems which appear to be possible replacements for the one way functions at the heart of the likes of RSA and ECDSA.
These come from fields including:
- Subset-sum - known to many as the knapsack problem
- Combinatorial group theory
- Number ﬁelds
- Buchmann-Williams Key Establishment
- The NTRU Cryptosystem
- The Goldreich-Goldwasser-Halevi Cryptosystem
- The Ajtai-Dwork Cryptosystem
- The McEliece Cryptosystem
We even have some analysis of the levels of quantum resistance of each of these crypto schemes. Not all look hopeful, and some have been all but dismissed as post quantum candidates. However, some are showing considerable promise with NTRU and the McEliece schemes being particular favourites of mine. In general, lattice based cryptography looks like the most likely to be the successor to the currently popular crypto schemes.
I would encourage anyone with an interest in information security to become familiar with quantum resistant cryptography as I suspect we will all see a migration towards such schemes in the foreseeable future.