How mathematics can help in computing and encryptions.
Lets take OTP case.
If you design a software which develops one lakh passwords of lengths of 2000 bytes.
Then if you have one million users you can use any one of the transformations to transform this password for a specific user.
You could have a function like GetPassword( seedValue,TransformationId ). The individual transformations could be given to the user along with a algorithm to generate a random code from a seed value. If this seed value is also differed , it could add to the strength of the password.
We coudl hide the password number in the password itself and the software at the cloud could be used to generate the same password. As a appliance could have been used we can overcome the barrier or very large passwords which can be used to make the job of hacker a prespiring one.