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Elliptic Curve Cryptography in Practice

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Abstract

In this paper we perform a review of elliptic curve cryptography (ECC) as it is used in practice today in order to reveal unique mistakes and vulnerabilities that arise in implementations of ECC. We study four popular protocols that make use of this type of public-key cryptography: Bitcoin, secure shell (SSH), transport layer security (TLS), and the Austrian e-ID card. We are pleased to observe that about 1 in 10 systems support ECC across the TLS and SSH protocols. However, we find that despite the high stakes of money, access and resources protected by ECC, implementations suffer from vulnerabilities similar to those that plague previous cryptographic systems.

Joppe W. Bos—This work was conducted while this author was at Microsoft Research, Redmond, USA.

Jonathan Moore—Unaffiliated.

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Notes

  1. 1.

    This invalid curve attack onsecp256k1 using fault injection has been mentioned before, for example by Paulo S.L.M. Barreto (@pbarreto):“In other words: given 13 faults and a good PC, one can break secp256k1 (and Bitcoin) in 1 min.”, October 21, 2013, 10:20 PM, Tweet.

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Acknowledgments

We thank Jaap W. Bos for valuable discussions about the financial market, Andy Modell for support in TLS scanning, Sarah Meiklejohn for sharing her knowledge about Bitcoin, and Felipe Voloch for pointing out the existence of the private keys\(1\) and\(2\) in Bitcoin. We thank the Microsoft Security Vulnerability Research team for their help with responsibly disclosing the vulnerabilities we found to affected companies.

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Authors and Affiliations

  1. Microsoft Research, Redmond, USA

    Michael Naehrig

  2. University of Michigan, 2260 Hayward Street, Ann Arbor, MI, 48109, USA

    J. Alex Halderman & Eric Wustrow

  3. University of Pennsylvania, Philadelphia, USA

    Nadia Heninger

  4. NXP Semiconductors, Leuven, Belgium

    Joppe W. Bos

Authors
  1. Joppe W. Bos

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  2. J. Alex Halderman

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  4. Jonathan Moore

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  5. Michael Naehrig

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  6. Eric Wustrow

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Corresponding author

Correspondence toJ. Alex Halderman.

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Editors and Affiliations

  1. Carnegie Mellon University, Pittsburgh, Pennsylvania, USA

    Nicolas Christin

  2. University of Calgary, Calgary, Alberta, Canada

    Reihaneh Safavi-Naini

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© 2014 International Financial Cryptography Association

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Bos, J.W., Halderman, J.A., Heninger, N., Moore, J., Naehrig, M., Wustrow, E. (2014). Elliptic Curve Cryptography in Practice. In: Christin, N., Safavi-Naini, R. (eds) Financial Cryptography and Data Security. FC 2014. Lecture Notes in Computer Science(), vol 8437. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-45472-5_11

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