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Question about the Residual Pseudorandomness property in Verifiable Random Function paper, written by Micali, Rabin, Vadhan, in 1998

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I am reading a paper named Verifiable Random Function, written by Micali, Rabin, Vadhan in 1998. In Residual Pseudo randomness propoerty of a VRF, it is written that If T runs for at most s(k) steps, it succeeds in the experiment with probability 1/2 + 1/s(k). I do not understand the exact meaning of s(k). If it is polynomial, then the scheme is not safe. It is exponential, T cannot run s(k), because it is an efficient algorithm.

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