International Conference on Smart Card Research and Advanced Applications

CARDIS 2010: Smart Card Research and Advanced Application pp 164-181

Improved Fault Analysis of Signature Schemes

  • Christophe Giraud
  • Erik W. Knudsen
  • Michael Tunstall
Conference paper

DOI: 10.1007/978-3-642-12510-2_12

Volume 6035 of the book series Lecture Notes in Computer Science (LNCS)


At ACISP 2004, Giraud and Knudsen presented the first fault analysis of DSA, ECDSA, XTR-DSA, Schnorr and ElGamal signatures schemes that considered faults affecting one byte. They showed that 2304 faulty signatures would be expected to reduce the number of possible keys to 240, allowing a 160-bit private key to be recovered. In this paper we show that Giraud and Knudsen’s fault attack is much more efficient than originally claimed. We prove that 34.3% less faulty signatures are required to recover a private key using the same fault model. We also show that their original way of expressing the fault model under a system of equations can be improved. A more precise expression allows us to obtain another improvement of up to 47.1%, depending on the values of the key byte affected.


Fault analysisSignature schemesSmart card
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Copyright information

© Springer-Verlag Berlin Heidelberg 2010

Authors and Affiliations

  • Christophe Giraud
    • 1
  • Erik W. Knudsen
    • 2
  • Michael Tunstall
    • 3
  1. 1.Oberthur TechnologiesPessacFrance
  2. 2.Alm. BrandKøbenhavn ØDenmark
  3. 3.Department of Computer ScienceUniversity of BristolBristolUnited Kingdom