Cheon\u27s algorithm, pairing inversion and the discrete logarithm problem

We relate the fixed argument pairing inversion problems (FAPI) and the discrete logarithm problem on an elliptic curve. This is done using the reduction from the DLP to the Diffie-Hellman problem developed by Boneh, Lipton, Maurer and Wolf. This approach fails when only one of the FAPI problems can be solved. In this case we use Cheon\u27s algorithm to get a reduction

Theory and application of computationally independent one-way functions: Interactive proof of ability - Revisited

We introduce the concept of computationally independent pair of one-way functions (CI-OWF). We also provide two rich classes of examples of such functions based on standard assumptions. We revisit two-party interactive protocols for proving possession of computational power and existing two-flow challenge-response protocols. We analyze existing protocols for proof of computation power and propose a new two-flow protocol using CI-OWF based on square Diffie-Hellman problem