Abstract
Boneh et al. showed a KDM secure public-key encryption scheme under the DDH assumption. The KDM security means that even when any affine function of the secret keys is encrypted, it is guaranteed to be secure. In this paper, we show a more tight proof. The reduction loss to the DDH assumption is \(2\slash 3\) times smaller in the KDM\(^{(1)}\)-security, and \(5\slash 6\) times smaller in the KDM\(^{(n)}\)-security, where n is the number of users. Our proof is also conceptually simpler.
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Notes
- 1.
It is tightly reduced to the DDH assumption if \(\ell =2\) or \(Q=2\). Otherwise, however, it is not.
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Tada, H., Ueda, A., Kurosawa, K. (2018). How to Prove KDM Security of BHHO. In: Inomata, A., Yasuda, K. (eds) Advances in Information and Computer Security. IWSEC 2018. Lecture Notes in Computer Science(), vol 11049. Springer, Cham. https://doi.org/10.1007/978-3-319-97916-8_18
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