When designing a protocol based on zero knowledge proofs, be it based on the discrete log problem, or on a Hamiltonian cycle in a graph, or something else, I assume there are security considerations, like there are security considerations in the use of conventional ciphers.
For example, when using AES (or any block cipher for that matter), one has to make sure that the IV is random, and a good block cipher mode is chosen.
When using RSA, one has to use a secure padding scheme, pick a high, but not too high exponent (
0x10001, for example).
I wonder whether there exist this kind of considerations for several ZKP systems too; e.g., on how to generate a "good" graph for the Hamiltonian path problem.
I.e. I wonder how to make sure that Victor cannot gain Peggy's knowledge, using side channels, timing attacks, statistical attacks, or something alike? Has there been interesting publications to read upon this topic?