Possible mission idea: MD5 and MD5 collision (maybe MD4)
Coding content of the mission: you are asked to calculate MD5 of some string, and then asked to provide an MD5 collision.
Possible plot ties:
- a secluded society working illegally on AI problems doesn't want to have any communication with undeserving people; «for last century or so a few megacorps cannot manage to migrate off MD5, so even knowing there are MD5 collisions is illegal — we only care to talk to people who prefer illegal truth to officially-sanctioned falsehood»
- broken password verification:
MD5(username) xor MD5(password)
has to be in the list and username should not be the same as password. You get read-only access to the list and see zero there
Another possible variation is a password database leak with unsalted SHA256 values — one of the passwords is actually the test vector from the official standard. The hash is very searchable in the real life (maybe you could have the text of the NIST standard available in-universe just in case)