TOTP (Time-based One-Time Password) Algorithm is used in Two factor authentication. I understand the algorithm and that current time is used as a variable to generate a token. Wiki page for reference: http://en.wikipedia.org/wiki/Time-based_One-time_Password_Algorithm
My question is, can current time be faked?
Suppose you have tokens T(0),...,T(n) where T(0) was generated at time = 0 and T(n) was generated at time = n.
Suppose I have the initial seed value for the algorithm, and I know current time is k, is it possible to generate T(k) without having generated T(0),...,T(k-1)?
In other words, can time elapsed be 'faked'? Or is T(k) based on every token in the set of tokens, T(0),...,T(k-1). If it is based on every previous token, does generating T(k) require at least (block of time) * (k-1) time to generate or can the process of elapsed time be fed to the algorithm to generate T(k) in less time?