Encryption algorithms and the "One-Time pad"
There is an entire class of ciphers that do exactly this. They're called stream ciphers. At their most basic, they pretend to be a one-time pad. You give them a small key and they generate a stream of seemingly random bits. You then XOR these bits with your plain-text to make ciphertext. 

You can add bells and whistles to this basic behaviour but what I've described is the essence of the stream-cipher.

The most famous of these stream ciphers is probably RC4. If you ever used SSL at all then you will have used this steam cipher. 

Equally, if you've ever used a mobile phone you've probably had your voice traffic "protected" with A5/1.

There are people who are experts in just this area of cipher design. 

There's nothing more to say really other than that this is a well established branch of cryptography with a very well developed body of research and many fielded designs.