Am I allowed to send encrypted traffic via any medium or any frequency, or is this completely barred (and thus everything has to be open with no exceptions?)
11(2) The Licensee shall only address Messages to other Amateurs or to the stations of those Amateurs and shall not encrypt these Messages for the purpose of rendering the Message unintelligible to other radio spectrum users.
From the terms and conditions spelt out by OFCOM (pdf), the UK communications regulator.
Alternately, in the license guidelines:
1(4) The Licensee shall address Messages only to other licensed amateurs or the stations of licensed amateurs and shall send only:
(a) Messages relating to technical investigations or remarks of a personal character; or
(b) Signals (not enciphered) which form part of, or relate to, the transmission of Messages.
If you are in the USA, check
§ 97.113 Prohibited transmissions of the FCC rules.
(4) Music using a phone emission except as specifically provided elsewhere in this section; communications intended to facilitate a criminal act; messages encoded for the purpose of obscuring their meaning, except as otherwise provided herein; obscene or indecent words or language; or false or deceptive messages, signals or identification.
As it stands now, encryption is prohibited regardless of your frequency.
It is prohibited in the US, with one exception. One is allowed to encrypt commands to an amateur satellite (Send from the ground to the satellite). Aside from that, encryption is prohibited.
Encryption on amateur radio is prohibited in most countries. There are some exceptions, in some countries, and for some specific use cases. You'll need to consult your local rules.
Some countries (Australia being an example) allow encryption in emergency communications and relevant training activities.
Some countries (US, for example) allow encryption for transmitting control commands to satellites, so that unauthorized stations can be prevented from causing harm to the satellite.
Some protocols used in digital networking (IPSEC, SSL/TLS) allow you to disable traffic encryption (using a "none" cipher), but still use cryptographic algorithms such as HMAC to do strong authentication and tampering prevention. Doing that does not conceal the contents of the traffic, so it's allowed, and sufficient for many use cases such as remote commands to satellites, or other restricted-access services.
Don N2IRZ wrote an article in CQ Magazine's August 2006 edition which made the case that data encryption is legal when it is used for the purpose of preventing unauthorized access. The context he's referring to is when using modified commercial WiFi routers which have channels that overlap with the amateur band (e.g. HSMM-Mesh/Broadband-Hamnet) and preventing part 15 users from joining part 97 mesh networks through the use of encrypted passwords such as WPA/WEP.
I'm not sure if his logic has held up in light of the recent FCC dismissal of a rulemaking petition to provide an exception for encryption for during disaster/public service operations, but it is an interesting read.
In India, the Indian Wireless Telegraph Act (Amateur Service) rules mandate the operator transmit in plain language. Unfortunately I'm unable to locate a copy on the WPC web-site; hence a link to a copy by a fellow ham OM vu2mue.
Defining the conduct of an Amateur Station in Annexure I - Section II.1.b
(b) Transmissions shall be made in plain language and limited to messages of a technical nature relating to tests and to remarks of personal character (excluding business affairs or transactions) in which the licensee, or the person with whom he is in communication, are directly concerned and for which, by reason of their unimportance, recourse to the public telecommunication service is not justified.
I am going to repeat the answer I just put on a similar question.
If you want to do this kind of stuff in the USA, hiding and such, please stay off our ham bands. These bands are reserved for those of us who have been properly licensed and follow the rules.