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On the Multiple Fault Attacks on RSA Signatures with LSBs of Messages Unknown

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Information Security and Cryptology (Inscrypt 2012)

Part of the book series: Lecture Notes in Computer Science ((LNSC,volume 7763))

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Abstract

In CHES 2009, Coron, Joux, Kizhvatov, Naccache and Paillier (CJKNP) introduced the multiple fault attack on RSA signatures with partially unknown messages. However, the complexity of their attack is exponential in the number of faulty signatures. At RSA 2010, this fault attack was improved, which runs in polynomial time in the number of faults. Both of the previous fault attacks deal with the general case. This paper considers the special situation that some least significant bits (LSBs) of messages are unknown. Because of this special case, our new multiple fault attack can handle a larger size of the unknown part of message. We provide two kinds of techniques to factor the RSA modulus N using the multiple faulty signatures. Comparisons between the previous attacks and the new attacks with a number of LSBs of the message unknown are given on the basis of the simulations.

Supported by the National Natural Science Foundation of China (Grant No.61133013) and the National Basic Research Program of China (Grant No. 2013CB834205).

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Author information

Authors and Affiliations

  1. School of Information Science and Engineering, Hangzhou Normal University, Hangzhou, 310036, China

    Lidong Han

  2. Institute for Advanced Study, Tsinghua University, Beijing, 100084, China

    Lidong Han, Wei Wei & Mingjie Liu

  3. Beijing International Center for Mathematical Research, Peking University, Beijing, 100084, China

    Mingjie Liu

Authors
  1. Lidong Han
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  2. Wei Wei
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  3. Mingjie Liu
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Editor information

Editors and Affiliations

  1. Department of Fundamental Problems of Technology, Wrocław University of Technology, Wybrzeże Wyspiańskiego 27, 50-370, Wrocław, Poland

    Mirosław Kutyłowski

  2. Computer Science Department, Columbia University and Google Inc., Amsterdam Avenue 1214, 10027, New York, NY, USA

    Moti Yung

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Han, L., Wei, W., Liu, M. (2013). On the Multiple Fault Attacks on RSA Signatures with LSBs of Messages Unknown. In: Kutyłowski, M., Yung, M. (eds) Information Security and Cryptology. Inscrypt 2012. Lecture Notes in Computer Science, vol 7763. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-38519-3_1

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  • DOI: https://doi.org/10.1007/978-3-642-38519-3_1

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-38518-6

  • Online ISBN: 978-3-642-38519-3

  • eBook Packages: Computer ScienceComputer Science (R0)

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