Abstract. 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:-An efficient, stateless 'hash-and-sign' signature scheme in the standard model (i.e., no random oracles), and -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.

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Abstract. The existence of encryption and commitment schemes secure under selective opening attack (SOA) has remained open despite considerable interest and attention. We provide the rst public key encryption schemes secure against sender corruptions in this setting. The underlying tool is lossy encryption. We then show that no non-interactive or perfectly binding commitment schemes can be proven secure with blackbox reductions to standard computational assumptions, but any statistically hiding commitment scheme is secure. Our work thus shows that the situation for encryption schemes is very di erent from the one for commitment schemes.

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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 an efficient, stateless 'hash-and-sign' signature scheme in the standard model (i.e., no random oracles), and 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.