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Bonsai trees, or how to delegate a lattice basis. (English) Zbl 1280.94043
Gilbert, Henri (ed.), Advances in cryptology – EUROCRYPT 2010. 29th annual international conference on the theory and applications of cryptographic techniques, French Riviera, May 30 – June 3, 2010. Proceedings. Berlin: Springer (ISBN 978-3-642-13189-9/pbk). Lecture Notes in Computer Science 6110, 523-552 (2010).
Summary: We introduce a new lattice-based cryptographic structure called a bonsai tree, and use it to resolve some important open problems in the area. Applications of bonsai trees include:
\(\bullet\) An efficient, stateless ‘hash-and-sign’ signature scheme in the standard model (i.e., no random oracles), and
\(\bullet\) The first hierarchical identity-based encryption (HIBE) scheme (also in the standard model) that does not rely on bilinear pairings. Interestingly, the abstract properties of bonsai trees seem to have no known realization in conventional number-theoretic cryptography.
For the entire collection see [Zbl 1188.94008].

94A60 Cryptography
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