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Predicting truncated multiple recursive generators with unknown parameters

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Abstract

Pseudorandom sequences are widely used in cryptography. Multiple recursive generators are an important class of pseudorandom sequence generators. A typical application is to obtain truncated sequences by truncating partial bits of the sequences output by the generators. This paper studies the predictability of truncated multiple recursive generators with unknown parameters. Given a few truncated digits of high-order bits output by a multiple recursive generator, we give a method based on lattice reduction to recover the parameters and the initial state of the generator. Our method is an extension of Stern’s algorithm which was proposed to predict the truncated sequences of linear congruential generators.

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Acknowledgements

This work was supported by NSF of China (Nos. 61872383, 61402524 and 61602510). The work of Qun-Xiong Zheng was also supported by Young Elite Scientists Sponsorship Program by CAST (2016QNRC001) and by National Postdoctoral Program for Innovative Talents (BX201600188) and by China Postdoctoral Science Foundation funded project (2017M611035).

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Correspondence to Qun-Xiong Zheng.

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Sun, H., Zhu, X. & Zheng, Q. Predicting truncated multiple recursive generators with unknown parameters. Des. Codes Cryptogr. (2020). https://doi.org/10.1007/s10623-020-00729-8

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Keywords

  • Multiple recursive generator
  • Truncated sequence
  • Lattice reduction
  • Predictability

Mathematics Subject Classification

  • 11H06
  • 11K45
  • 11B50
  • 94A60