Abstract
We propose a new computational problem and call it the twin bilinear Diffie-Hellman inversion (BDHI) problem. Inspired by the technique proposed by Cash, Kiltz and Shoup, we have developed a new trapdoor test which enables us to prove that the twin BDHI problem is at least as hard as the ordinary BDHI problem even in the presence of a decision oracle that recognizes a solution to the problem. The relation between the two problems implies that many of the cryptographic constructions based on ordinary BDHI problem can be improved with a tighter security reduction. As one such application, we present a new variant of Sakai-Kasahara Identity-Based Encryption (SK-IBE) with a simple and efficient security proof in the random oracle model, under the computational BDHI problem. We also present a new Identity-Based Key Encapsulation Mechanism (ID-KEM) based on SK-IBE, which has a better security analysis than previous results.
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Chen, Y., Chen, L. (2011). The Twin Bilinear Diffie-Hellman Inversion Problem and Applications. In: Rhee, KH., Nyang, D. (eds) Information Security and Cryptology - ICISC 2010. ICISC 2010. Lecture Notes in Computer Science, vol 6829. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-24209-0_8
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DOI: https://doi.org/10.1007/978-3-642-24209-0_8
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