Reference : Practical Cryptanalysis of ISO/IEC 9796-2 and EMV Signatures
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Practical Cryptanalysis of ISO/IEC 9796-2 and EMV Signatures
Coron, Jean-Sébastien mailto [University of Luxembourg > Faculty of Science, Technology and Communication (FSTC) > Computer Science and Communications Research Unit (CSC) >]
Naccache, David [École Normale Supérieure]
Tibouchi, Mehdi [École Normale Supérieure]
Weinmann, Ralf-Philipp [University of Luxembourg > Interdisciplinary Centre for Security, Reliability and Trust (SNT) > >]
Proceedings of CRYPTO 2009
August 16-20, 2009
Santa Barbara
[en] digital signatures ; forgery ; RSA ; public-key cryptanalysis ; ISO/IEC 9796-2 ; EMV
[en] In 1999, Coron, Naccache and Stern discovered an existential signature forgery for two popular RSA signature standards, ISO/IEC 9796-1 and 2. Following this attack ISO/IEC 9796-1 was withdrawn. ISO/IEC 9796-2 was amended by increasing the message digest to at least 160 bits. Attacking this amended version required at least 2^{61} operations. In this paper, we exhibit algorithmic refinements allowing to attack the amended (currently valid) version of ISO/IEC 9796-2 for all modulus sizes. A practical forgery was computed in only two days using 19 servers on the Amazon EC2 grid for a total cost of $\simeq$ US$800. The forgery was implemented for e?= 2 but attacking odd exponents will not take longer. The forgery was computed for the RSA-2048 challenge modulus, whose factorization is still unknown. The new attack blends several theoretical tools. These do not change the asymptotic complexity of Coron et al.’s technique but significantly accelerate it for parameter values previously considered beyond reach. While less efficient (US$45,000), the acceleration also extends to EMV signatures. EMV is an ISO/IEC 9796-2-compliant format with extra redundancy. Luckily, this attack does not threaten any of the 730 million EMV payment cards in circulation for operational reasons. Costs are per modulus: after a first forgery for a given modulus, obtaining more forgeries is virtually immediate.
<br />Advances in Cryptology - CRYPTO 2009, 29th Annual International Cryptology Conference

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