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A Deterministic Algorithm for Computing Divisors in an Interval

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Information Security and Privacy (ACISP 2018)

Part of the book series: Lecture Notes in Computer Science ((LNSC,volume 10946))

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Abstract

We revisit the problem of finding a nontrivial divisor of a composite integer when it has a divisor in an interval \([\alpha , \beta ]\). We use Strassen’s algorithm to solve this problem. Compared with Kim-Cheon’s algorithms (Math Comp 84(291): 339–354, 2015), our method is a deterministic algorithm but with the same complexity as Kim-Cheon’s probabilistic algorithm, and our algorithm does not need to impose that the divisor is prime. In addition, we can further speed up the theoretical complexity of Kim-Cheon’s algorithms and our algorithm by a logarithmic term \(\log (\beta -\alpha )\) based on the peculiar property of polynomial arithmetic we consider.

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Acknowledgements

This research was supported the National Natural Science Foundation of China (Grants 61702505, 61472417, 61732021, 61772520), National Cryptography Development Fund (MMJJ20170115, MMJJ20170124) and the Fundamental Theory and Cutting Edge Technology Research Program of Institute of Information Engineering, CAS (Grants Y7Z0341103, Y7Z0321102), JST CREST Grant Number JPMJCR14D6, JSPS KAKENHI Grant Number 16H02780.

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Authors and Affiliations

  1. State Key Laboratory of Information Security, Institute of Information Engineering, Chinese Academy of Sciences, Beijing, 100 093, China

    Liqiang Peng, Yao Lu, Rui Zhang & Lei Hu

  2. Data Assurance and Communication Security Research Center, Chinese Academy of Sciences, Beijing, 100 093, China

    Liqiang Peng, Yao Lu & Lei Hu

  3. The University of Tokyo, Tokyo, Japan

    Yao Lu & Noboru Kunihiro

Authors
  1. Liqiang Peng
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  2. Yao Lu
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  3. Noboru Kunihiro
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  4. Rui Zhang
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  5. Lei Hu
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Editor information

Editors and Affiliations

  1. University of Wollongong, Wollongong, NSW, Australia

    Willy Susilo

  2. University of Wollongong, Wollongong, NSW, Australia

    Guomin Yang

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Peng, L., Lu, Y., Kunihiro, N., Zhang, R., Hu, L. (2018). A Deterministic Algorithm for Computing Divisors in an Interval. In: Susilo, W., Yang, G. (eds) Information Security and Privacy. ACISP 2018. Lecture Notes in Computer Science(), vol 10946. Springer, Cham. https://doi.org/10.1007/978-3-319-93638-3_1

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  • DOI: https://doi.org/10.1007/978-3-319-93638-3_1

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-93637-6

  • Online ISBN: 978-3-319-93638-3

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