Abstract
In this paper, we construct the first tightly secure signature scheme against adaptive chosen message attacks (CMA) from the Decisional Composite Residuosity (DCR) Assumption. Moreover, the verification key in our scheme is of constant size. Based on the DCR assumption, we design a one-time secure signature scheme first, then we employ a flat tree structure to obtain a signature scheme that is secure against non-adaptive chosen message attacks (NCMA). By combining the one-time scheme and NCMA-secure scheme, we obtain the final CMA-secure signature scheme with a tight security reduction to the DCR assumption.
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Notes
- 1.
Since the q leaves are the leftmost ones, \(N_{i+1}^{(j)\text {left}}\) has already been determined.
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Acknowledgments
The authors are supported by the National Natural Science Foundation of China Grant (Nos. 61672346, 61373153, 61472250). We thank the anonymous reviewers for their comments and suggestions.
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Zhang, X., Liu, S., Gu, D. (2017). Tightly-Secure Signatures from the Decisional Composite Residuosity Assumption. In: Pieprzyk, J., Suriadi, S. (eds) Information Security and Privacy. ACISP 2017. Lecture Notes in Computer Science(), vol 10342. Springer, Cham. https://doi.org/10.1007/978-3-319-60055-0_24
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