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The authors propose a new cryptographic primitive, called extractable perfectly one-way (EPOW) functions. Like perfectly One-Way (POW) functions, EPOW functions are Probabilistic functions that reveal no information about their input, other than the ability to verify guesses. In addition, an EPOW function, f, guarantees that any party that manages to compute a value in the range of f "Knows" a corresponding preimage. They capture "Knowledge of Preimage" by way of algorithmic extraction. They formulate two main variants of extractability, namely non-interactive and interactive.
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