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Trading time for space: Towards an efficient IBE scheme with short(er) public parameters in the standard model. (English) Zbl 1184.94235
Won, Dongho (ed.) et al., Information security and cryptology – ICISC 2005. 8th international conference, Seoul, Korea, December 1–2, 2005. Revised selected papers. Berlin: Springer (ISBN 3-540-33354-1/pbk). Lecture Notes in Computer Science 3935, 424-440 (2006).
Summary: At Eurocrypt 2005, B. Waters [“Efficient identity-based encryption without random oracles”, Lect. Notes Comput. Sci. 3494, 114–127 (2005; Zbl 1137.94360)] proposed an efficient identity-based encryption scheme which is secure in the standard model. One drawback of this scheme is that the number of elements in the public parameter is rather large. Here we propose a generalisation of Waters’ scheme. In particular, we show that there is an interesting trade-off between the tightness of the security reduction and the smallness of the public parameter. For a given security level, this implies that if one reduces the number of elements in the public parameter then there is a corresponding increase in the computational cost due to the increase in group size. This introduces a flexibility in choosing the public parameter size without compromising security. In concrete terms, to achieve 80-bit security for 160-bit identities we show that compared to Waters’ protocol the public parameter size can be reduced by almost \(90\%\) while increasing the computation cost by \(30\%\). Our construction is proven secure in the standard model without random oracles. Additionally, we show that CCA security can also be achieved through reduction to the oracle decision bilinear Diffie-Hellman problem (OBDH).
For the entire collection see [Zbl 1103.68012].

94A60 Cryptography
94A62 Authentication, digital signatures and secret sharing
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