Modern day cryptography involves some absolutely fascinating math, some of which I have been fortunate to have been exposed to while working in the field of digital video broadcast systems. The requirement that calls for the use of cryptography in video distribution is protection the content from pirates attempting to steal the video content. At the most fundamental level, the audio/video data that is transmitted is encrypted so that it is not in the clear for anybody and everybody to pick up. One has to apply the process of decryption in order to recover the original content from a data stream (or bitstream).
The nature of the encryption process determines how easy it is for somebody to break the code in order to obtain the clear version of the data that is being sent. When symmetric block ciphers are used for encryption, you need the encryption keys to figure out how to decrypt the data. To break the system one could try to guess at the encryption key, or try to intercept the key that is being sent to the receiver separately. In general, the shorter the encryption key, the quicker the guessing process is. The Data Encryption Standard (DES) that was more commonly used in the past has become easily breakable with the power of computers today. These days, the Advanced Encryption Standard (AES), with its longer block sizes and keys, is more commonly used. AES block ciphers are hard to crack using the brute force of computers even today. If you are trying to do this in real time with a stream of data that is being transmitted, it becomes close to impossible. (People used to think that the NSA had a backdoor into the AES algorithm. Nowadays people talk more about capability the NSA might have to break the standard using raw computer power rather than by using a backdoor.)
Protection of the content being transmitted does not depend simply on the fact that data is encrypted. The encryption only assures that nobody can make sense of the data easily as it is being sent. The security is actually in the knowledge of the key that is needed to decrypt the data, and most efforts to break a system focus on this aspect of the system design. In a real system there is some form of data exchange between the source and the destination related to the key, and security is compromised if this is discovered. In any case, when it comes to video distribution, there are many additional strategies applied along with the data stream encryption process itself in order to protect the content.
The Turing Award is being awarded this year to Whitfield Diffie and Martin Hellman for their invention of Public-Key Cryptography and Digital Signatures. The concept is quite brilliant! It is based on the use of an asymmetric cipher, something quite different from the symmetric block ciphers described earlier. When a symmetric block cipher is used, the same key is used in the processes for encryption and decryption. With an asymmetric cipher, the key being used for encryption is different from that used for decryption. There is a relationship between the encryption key (also called the public key) and the decryption key (also called the private key) that cannot be guessed because of the complexity of the math involved in generating the key pair. What this allows an entity to do is then distribute a public key in the clear to everybody for use in the communications process with itself, knowing that data that is generated during the communications process using this key pair cannot be made proper sense of by any other entity without the use of the correct decryption key, something which remains private.
The algorithms used for Public-key cryptography are more complex than those used for the block ciphers in use today and are ill-suited for real-time streaming of data. Today, public key cryptography is primarily used for digital authentication of content and the creation of digital signatures that can be used to confirm the identity of the entity that you are communicating with. In the case of video broadcasting, they generally tend to be used for protecting the keys that are used in association with the block cipher encrypted audio/video data that is transmitted.
This is a fascinating subject, but you really need to know your math to delve deeper. There is a great book, a bible if you will, on the subject of Cryptography by Bruce Schneier, that anybody who is interested in the topic should read.