#StackBounty: #post-quantum-cryptography #lattice-crypto #hardness-assumptions Error Correcting Code VS Lattice

Bounty: 50

I’m not an expert in PQ-Crypto. As I understood Error Correcting Code and Lattice based crypto.
The cryptographic assumptions are very similar. And the key-difference for me is the nature of the noise. In one case the noise is inspired of the "physical noise", and in the other one, it’s more mathematical and consider a more complex distance (euclidean distance instead hamming distance).

Intuitively, this reason makes sense about the fact that in every apllications I know lattice-based crypto is more efficient than Error-correcting based crypto.

  1. Is my intuition seems correct to you?
  2. If yes, is there a theorem which certify that every cryptographic protocol based on an error-correcting code assumption could be transformed in a more efficient protocol based on lattice (i.e with the same level of security and based on a weaker lattice assumption)?
  3. If No, is there more informal claim of known researcher which consider this question. Or it just doesn’t make sens to compare these two families of assumptions?

Get this bounty!!!

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