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(Hierarchical) identity-based encryption from affine message authentication. (English) Zbl 1345.94044
Garay, Juan A. (ed.) et al., Advances in cryptology – CRYPTO 2014. 34th annual cryptology conference, Santa Barbara, CA, USA, August 17–21, 2014. Proceedings, Part I. Berlin: Springer (ISBN 978-3-662-44370-5/pbk). Lecture Notes in Computer Science 8616, 408-425 (2014).
Summary: We provide a generic transformation from any affine message authentication code (MAC) to an identity-based encryption (IBE) scheme over pairing groups of prime order. If the MAC satisfies a security notion related to unforgeability against chosen-message attacks and, for example, the $$k$$-linear assumption holds, then the resulting IBE scheme is adaptively secure. Our security reduction is tightness preserving, i.e., if the MAC has a tight security reduction so has the IBE scheme. Furthermore, the transformation also extends to hierarchical identity-based encryption (HIBE). We also show how to construct affine MACs with a tight security reduction to standard assumptions. This, among other things, provides the first tightly secure HIBE in the standard model.
For the entire collection see [Zbl 1292.94002].

##### MSC:
 94A60 Cryptography 94A62 Authentication, digital signatures and secret sharing
##### Keywords:
IBE; HIBE; standard model; tight reduction
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