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Partial Bits Exposure Attacks on a New Commitment Scheme Based on the Zagier Polynomial

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Information Security and Cryptology (Inscrypt 2016)

Part of the book series: Lecture Notes in Computer Science ((LNSC,volume 10143))

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Abstract

In Asiacrypt’14, Boneh et al. built a new statistically hiding and computationally binding commitment scheme based on the collision-resistant property of the Zagier polynomial \(f_{zag}(x,y)=x^7+3y^7\). In this paper, we describe several types of partial bits exposure attacks on this new commitment, that is, the most significant bits exposure attack, the least significant bits exposure attack and the middle parts exposure attack. Besides, we study the partial bits exposure attack on the situation that a message is committed twice. We mainly use the famous Coppersmith’s method in our analyses.

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Acknowledgements

During my visit to the University of California Irvine in 2015, Alice Silverberg et al. studied this new commitment scheme in their seminar, which drew my attention to this commitment scheme. We thank them for helpful conversations about this work. Our work was partially supported by the National Key Basic Research Program of China (2013CB834203).

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Authors and Affiliations

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

    Xiaona Zhang & Li-Ping Wang

  2. Data Assurance and Communications Security Research Center, Chinese Academy of Sciences, Beijing, China

    Xiaona Zhang & Li-Ping Wang

  3. University of Chinese Academy of Sciences, Beijing, China

    Xiaona Zhang

Authors
  1. Xiaona Zhang
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  2. Li-Ping Wang
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Correspondence to Li-Ping Wang .

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Editors and Affiliations

  1. School of Science, Hangzhou Normal University, Hangzhou, China

    Kefei Chen

  2. Institute of Information Engineering, SKLOIS, Beijing, China

    Dongdai Lin

  3. Snapchat Inc., Columbia University, New York, New York, USA

    Moti Yung

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Zhang, X., Wang, LP. (2017). Partial Bits Exposure Attacks on a New Commitment Scheme Based on the Zagier Polynomial. In: Chen, K., Lin, D., Yung, M. (eds) Information Security and Cryptology. Inscrypt 2016. Lecture Notes in Computer Science(), vol 10143. Springer, Cham. https://doi.org/10.1007/978-3-319-54705-3_22

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  • DOI: https://doi.org/10.1007/978-3-319-54705-3_22

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-54704-6

  • Online ISBN: 978-3-319-54705-3

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