Abstract
We present a novel parallel one-more signature forgery against blind Okamoto-Schnorr and blind Schnorr signatures in which an attacker interacts some l times with a legitimate signer and produces from these interactions l + 1 signatures. Security against the new attack requires that the following ROS-problem is intractable: find an overdetermined,s olvable system of linear equations modulo q withrandom inhomogenities (right sides).
There is an inherent weakness in the security result of Pointcheval and Stern. Theorem 26[PS00] does not cover attacks with 4 parallel interactions for elliptic curves of order 2200. That would require the intractability of the ROS-problem, a plausible but novel complexity assumption. Conversely, assuming the intractability of the ROS-problem, we show that Schnorr signatures are secure in the random oracle and generic group model against the one-more signature forgery.
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Schnorr, C.P. (2001). Security of Blind Discrete Log Signatures against Interactive Attacks. In: Qing, S., Okamoto, T., Zhou, J. (eds) Information and Communications Security. ICICS 2001. Lecture Notes in Computer Science, vol 2229. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-45600-7_1
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DOI: https://doi.org/10.1007/3-540-45600-7_1
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