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Monocypher is by far the best C/C++ crypto library, probably by far the best crypto library full stop.
It's a single pair of .c/.h files. The interface has easy to use implementations of sensible primitives and algorithms. The manual is absolutely wonderful, with really clear descriptions of what each function does and what guarantees they provide.
ATM I'm using it in Medfall to sign updates. I sign a manifest that lists all the game files and their hashes, and the public key is hardcoded in the client. It's less than 100 lines of code for everything. The keygen and signing utilities, and the client side verification code.
If you rip out arc4random from the portable LibreSSL and pair it with monocypher you have everything you need to make an encrypted game networking protocol. Something like:
crypto_key_exchangeand use that to encrypt messages to each other.
The client hasn't really proven its identity to the server because you have to ship the same private key with every client so it's easy to fake, but that's not a big deal. On the other hand the client does know it's talking to the correct server, so you don't have to worry about sending your login credentials to random hackers.
I don't think you need to care about replay attacks here. To impersonate the server, you would need to take a signed x25519 public key and crack the secret key and that should be impossible. But you can stick a (signed) timestamp in there if you want. (doesn't totally mitigate it but you can reduce the time they have to crack a key to like a few seconds)