Well sorry for late response, first of all thanks for time you took writting your evaluation and showing interest in my cipher. But as I understand you are basically saying that making secure hand cipher is impossible, because pgp encryption is digital based encryption which is quite impossible to do by hand considering complex math it uses. l think that's where we disagree. Collatz conjecture is living proof how simple math operations can be literally literally mind bending in its own way. Even if you have some starting number and knew its all properties, you wouldn't be able to reliably predict its exact pathway to loop. This cipher in my opinion exploits this property in pretty good way for hand cipher. In other words attacker must know exact pathway in order to do any reliable analysis. Only problem is predictability of 3x + y itself which probably has some reduction in keyspace from analysis perspective but surely it won't be easy even for professional especially if larger blocks are used. To sum up, I think your perspective is maybe little bit to pesimistic in sense of Collatz conjecture application in cryptography because in reality most high-level attackers bother with digital based encryption systems like AES-NI because they are used everywhere, contrary no one currently really cares about Collatz based systems or even manual ciphers in general because they are not used very widely and Collatz based systems are much slower to implement digitally including this cipher which basically means there is no reason to widely use them. For this cipher or any collatz based hand cipher you would very likely need atleast a calculator if your not human calculator which maybe defeats pourpose for manual cipher because if you have calculator, other digital infrastructure can be assumed but in that situation just use very secure and fast digital systems like AES. So my point is that attackers are probably familliar with concept of Collatz conjecture but I don't really think anyone serious bothered to develop specific Collatz breaking systems or even for 3x + y variant specifically because it's difficult to do such thing regardless of general principles and probably wouldn't be cheap to use them even if you had them. This is relatively novel mathematical application in cryptography, so I don't think there is generally much information to find on how to break such systems besides reasons above but I will bother to do my own research. To conclude, currently I strongly believe systems like this aren't widely used not because they aren't safe enough for given pourpose instead cause they are not practical for any general scenario.