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RSA and Elliptic Curve Least Significant Bit Security

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Progress in Cryptology - LATINCRYPT 2014 (LATINCRYPT 2014)

Part of the book series: Lecture Notes in Computer Science ((LNSC,volume 8895))

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Abstract

The security of the least significant bit (LSB) of the secret key in the Elliptic Curve Diffie-Hellman protocol (and of the message in the RSA) is related to the security of the whole key (and of the whole message, respectively). Algorithms to invert these cryptographic algorithms, making use of oracles that predict the LSB, have been published. We implement two of these algorithms, identify critical parameters, and modify the sampling to achieve a significant improvement in running times.

D. Nakamura—Partially funded by Coordenadoria de Aperfeiçoamento de Pessoal de Nível Superior (CAPES).

R. Terada—Partially funded by Fundação de Amparo à Pesquisa (FAPESP) grant 2011/50761-2.

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Notes

  1. 1.

    This requirement is NOT explicitly written in [1].

  2. 2.

    http://csrc.nist.gov/groups/ST/toolkit/key_management.html.

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Authors and Affiliations

  1. Computer Science Department, University of São Paulo, São Paulo, Brazil

    Dionathan Nakamura & Routo Terada

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  1. Dionathan Nakamura
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  2. Routo Terada
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Correspondence to Routo Terada .

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Editors and Affiliations

  1. University of Campinas, Campinas, Brazil

    Diego F. Aranha

  2. University of Waterloo, Waterloo, Ontario, Canada

    Alfred Menezes

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Nakamura, D., Terada, R. (2015). RSA and Elliptic Curve Least Significant Bit Security. In: Aranha, D., Menezes, A. (eds) Progress in Cryptology - LATINCRYPT 2014. LATINCRYPT 2014. Lecture Notes in Computer Science(), vol 8895. Springer, Cham. https://doi.org/10.1007/978-3-319-16295-9_8

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  • DOI: https://doi.org/10.1007/978-3-319-16295-9_8

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