Fault Attacks on RSA Signatures with Partially Unknown Messages
CHES '09 Proceedings of the 11th International Workshop on Cryptographic Hardware and Embedded Systems
Choosing key sizes for cryptography
Information Security Tech. Report
Fault attacks against EMV signatures
CT-RSA'10 Proceedings of the 2010 international conference on Topics in Cryptology
On the joint security of encryption and signature in EMV
CT-RSA'12 Proceedings of the 12th conference on Topics in Cryptology
Detailed cost estimation of CNTW attack against EMV signature scheme
FC'11 Proceedings of the 2011 international conference on Financial Cryptography and Data Security
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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 Following this attack iso/iec 9796-1 was withdrawn.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 261 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 $\simeq\mbox{{\sc us\$800}}$. 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.