First of all, I've seen a question marked as off topic because OP doesn't cover any issue related to cryptographic work, but the legal aspects, but I'm unsure where to attend to ask the following questions.
I've never thought I was going to ask such a question, since I always thought that cryptography should be an open field, because the majority of information I know is on the public domain. But advices received from partners and relatives encouraged me to experiment with the idea. I know that some schemes were patented in their beginning: DH, RSA, DES, NTRU, some schemes on ECC.
Imagine that I own various schemes that are based on existing ideas, but the construction of these schemes are different from the original description, resulting in a different scheme that is believed to have better security or it is more efficient (optimized). I haven't studied any subject related to patents since I started my career so I'm not very familiarized with the scenarios that can arise:
Can you patent a cryptographic scheme and publish a paper opening your method entirely, which is descriptive enough, so its security can be analyzed by the cryptographic community? Could I provide an implementation of the scheme?
Can you patent a cryptographic scheme based on an scheme/idea that was previously patented but lacks of patent nowadays, considering that this scheme is a modification of the original one?
I just don't want to hit a barrier considering this option. I'd like everyone to read and study the presented schemes, so I can still contribute onward with the community I've always thought that patenting make your idea less interesting or restrictive because you can't disclose any technical secret related to it, but maybe I'm wrong because I'm lacking of information. Thanks in advance.