@article {IOPORT.06030302, author = {Ling, San and Shparlinski, Igor E. and Steinfeld, Ron and Wang, Huaxiong}, title = {On the modular inversion hidden number problem.}, year = {2012}, journal = {Journal of Symbolic Computation}, volume = {47}, number = {4}, issn = {0747-7171}, pages = {358-367}, publisher = {Elsevier Science (Academic Press), London}, doi = {10.1016/j.jsc.2011.09.002}, abstract = {Summary: We give a rigorous deterministic polynomial time algorithm for the modular inversion hidden number problem introduced by {\it D. Boneh, S. Halevi} and {\it N. A. Howgrave-Graham} in 2001 [Advances in cryptology -- ASIACRYPT 2001. Lect. Notes Comput. Sci. 2248, 36-51 (2001; Zbl 1062.94545]. For our algorithm, we need to be given about 2/3 of the bits of the output, which matches one of the heuristic algorithms of D. Boneh et al. and answers one of their open questions. However their more efficient algorithm that requires only 1/3 of the bits of the output still remains heuristic.}, identifier = {06030302}, }