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I think you are referring to Colin Percival's Everything you need to know about Cryptography, in one hour in which he observes: An asymmetric authentication scheme is considered to be broken if an attacker with access to the verification key can generate any valid ciphertext, even if he can convince you to sign arbitrary other plaintexts. This is ...

Mathematically, it can probably be done. There has been research into trapdoor block ciphers. See, e.g., A family of trapdoor ciphers by Rijmen and Preneel, and follow-up papers. In practice, though, the problem statement is not realistic. The assumptions are just not realistic. Today, there's no reason why Red would be limited to using Blue's ciphers. ...

I think the thing you are looking for is "escrow" as in http://en.wikipedia.org/wiki/Key_escrow. Be aware though that the security of your system is reduced to the hardness for an attacker to find the master password which might be much easier than breaking the disk encryption scheme

Schneier's "A Self-study Course in Block-Cipher Cryptanalysis" is an excellent resource for what you are looking for. In particular, FEAL-4 would be a promising cipher to look at as it is breakable by almost every cryptanalysis technique. One thing you will notice when going through Schneier's course (or when looking at cryptanalysis research in general) is ...

The design of DES might give some insight into the problem. The NSA altered the S-box of DES. Many people thought they planted a backdoor. It wasn't until later that differential cryptanalysis was independently discovered by Biham and Shamir that people realized that the NSA actually made DES stronger. So the lesson to learn from this is: clearly the NSA ...

You've asked two different questions here: Q1: how to put a trapdoor in a block cipher, and Q2: examples of block ciphers that are good for learning block cipher cryptanalysis. @mikeazo has answered question Q2 well. I'm going to answer question Q1. For an example of how to put a hidden backdoor (trapdoor) in a block cipher, see the following research ...

A good solution would be to hold the master password encrypted by a N+P sharing scheme, where a certain amount of perhaps board members, or third parties, would need to come together to be able to reconstruct the master password. c++ cryptopp does secret sharing (http://en.wikipedia.org/wiki/Shamir%27s_Secret_Sharing) through ...

This manuscript by Warren Smith claims to outline an approach to having a (otherwise very good) block cipher with a trapdoor. The idea is something like the following: Linear cryptanalysis has you make linear approximations of the S-boxes and then solve a noisy system of equations by getting lots of samples (known plaintext pairs). But this linear system of ...