Abstract
It has recently been proved by Nguyen and Shparlinski that the Digital Signature Algorithm (DSA) is insecure when a few consecutive bits of the random nonces k are known for a reasonably small number of DSA signatures. This result confirmed the efficiency of some heuristic lattice attacks designed and numerically verified by Howgrave-Graham and Smart. Here, we extend the attack to the Nyberg-Rueppel variants of DSA. We use a connection with the hidden number problem introduced by Boneh and Venkatesan and new bounds of exponential sums which might be of independent interest.
Part of this work is an output of the “Turbo-signatures” project, supported by the French Ministry of Research.
Work supported in part by the Australian Research Council.
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Mahassni, E.E., Nguyen, P.Q., Shparlinski, I.E. (2001). The Insecurity of Nyberg-Rueppel and Other DSA-Like Signature Schemes with Partially Known Nonces. In: Silverman, J.H. (eds) Cryptography and Lattices. CaLC 2001. Lecture Notes in Computer Science, vol 2146. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-44670-2_9
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DOI: https://doi.org/10.1007/3-540-44670-2_9
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