Bit Security of the CDH Problems over Finite Field, by Mingqiang Wang and Tao Zhan and Haibin Zhang

It is a long-standing open problem to prove the existence of (deterministic) hard-core predicates for the Computational Diffie-Hellman (CDH) problem over finite fields, without resorting to the generic approaches for any one-way functions (e.g., the Goldreich-Levin hard-core predicates). Fazio et al. (FGPS, Crypto '13) make important progress on this problem by defining a weaker Computational Diffie-Hellman problem over $\mathbb{F}_{p^2}$, i.e., Partial-CDH problem, and proving, when allowing changing field representations, the unpredictability of every single bit of one of the coordinates of the secret Diffie-Hellman value.