On the modular inversion hidden number problem

Authors:
San Ling;Igor E. Shparlinski;Ron Steinfeld;Huaxiong Wang
Affiliations:
Div. of Mathematical Sciences, School of Physical and Mathematical Sciences, Nanyang Technological University, Singapore, 637371, Singapore;Department of Computing, Macquarie University, Sydney, NSW 2109, Australia;Department of Computing, Macquarie University, Sydney, NSW 2109, Australia;Div. of Mathematical Sciences, School of Physical and Mathematical Sciences, Nanyang Technological University, Singapore, 637371, Singapore
Venue:
Journal of Symbolic Computation
Year:
2012

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Abstract

We give a rigorous deterministic polynomial time algorithm for the modular inversion hidden number problem introduced by D. Boneh, S. Halevi and N.A. Howgrave-Graham in 2001. 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, S. Halevi and N.A. Howgrave-Graham 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.