Solving a class of modular polynomial equations and its relation to modular inversion hidden number problem and inversive congruential generator

@article{Xu2018SolvingAC,
  title={Solving a class of modular polynomial equations and its relation to modular inversion hidden number problem and inversive congruential generator},
  author={Jun Xu and Santanu Sarkar and Lei Hu and Zhangjie Huang and Liqiang Peng},
  journal={Designs, Codes and Cryptography},
  year={2018},
  volume={86},
  pages={1997-2033}
}
In this paper we revisit the modular inversion hidden number problem (MIHNP) and the inversive congruential generator (ICG) and consider how to attack them more efficiently. We consider systems of modular polynomial equations of the form $$a_{ij}+b_{ij}x_i+c_{ij}x_j+x_ix_j=0~(\mathrm {mod}~p)$$aij+bijxi+cijxj+xixj=0(modp) and show the relation between solving such equations and attacking MIHNP and ICG. We present three heuristic strategies using Coppersmith’s lattice-based root-finding… 

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