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  Hidden Collisions on DSS

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by Uperieure S Ormale, N Ecole, Serge Vaudenay, Serge Vaudenay, Serge Vaudenay
http://www.dmi.ens.fr/ftp/pub/dmi/users/liens/liens-96-9.A4.ps.Z
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Abstract:

We explain how to forge public parameters for the Digital Signature Standard with two known messages which always produce the same set of valid signatures (what we call a collision). This attack is thwarted by using the generation algorithm suggested in the specifications of the Standard, so it proves one always need to check proper generation. We also present a similar attack when using this generation algorithm within a complexity 2 74, which is better than the birthday attack which seeks for collisions on the underlying hash function. Imagine you want to join to a brand new association which offers to provide useful services on the net. To allow electronic payment, this association provides a DSS implementation with public parameters p = 1007386175274283816733054843443587432664299802160928

Citations

788 A public key cryptosystem and a signature scheme based on discrete logarithms – Elgamal - 1985
413 Efficient signature generation for smart cards – Schnorr - 1991
210 Efficient identification and signatures for smart cards – Schnorr
172 Security proofs for signature schemes – Pointcheval, Stern
31 Generating ElGamal signatures without knowing the secret key – Bleichenbacher - 1996
1 Department of Commerce, National Institute of Standards and Technology – S - 1995