@inproceedings{97ceb4df91f740ff82837d17eb7bd5a3,
title = "Bit security of the CDH problems over finite fields",
abstract = "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 {\textquoteright}13) made important progress on this problem by defining a weaker Computational Diffie- Hellman problem over Fp2, 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. In this paper, we show that all the individual bits of the CDH problem over Fp2 and almost all the individual bits of the CDH problem over Fpt for t > 2 are hard-core.",
keywords = "CDH, D-th CDH problem, Diffie-Hellman problem, Finite fields, Hard-core bits, List decoding, Multiplication code, Noisy oracle, Partial-CDH problem",
author = "Mingqiang Wang and Tao Zhan and Haibin Zhang",
note = "Publisher Copyright: {\textcopyright} Springer International Publishing Switzerland 2016.; 22nd International Conference on Selected Areas in Cryptography, SAC 2015 ; Conference date: 12-08-2015 Through 14-08-2015",
year = "2016",
doi = "10.1007/978-3-319-31301-6_25",
language = "English",
isbn = "9783319313009",
series = "Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)",
publisher = "Springer Verlag",
pages = "441--461",
editor = "Liam Keliher and Orr Dunkelman",
booktitle = "Selected Areas in Cryptography - SAC 2015 - 22nd International Conference, 2015, Revised Selected Papers",
address = "Germany",
}