Until recently, explicit constructions of identity-based encryption (IBE) required considerably more structure or stronger assumptions than public key encryption from similar assumptions. In this talk, a framework is presented, which significantly facilitates the construction of IBE schemes and leads to new constructions from weaker assumptions. The central tool is a new primitive called compact One-Time Signatures with Encryption (OTSE), which turns out to be equivalent with IBE. This primitive can be built from weak assumptions such as the computational Diffie-Hellman problem (in groups without pairings), the Factoring problem, the Learning-with-Errors problem (with the same parameters as Regev-encryption) and the sub-exponentially hard Learning-Parity-with-Noise problem. The main technique of our framework is a novel non-black-box transformation from compact OTSE to both fully secure IBE and selectively secure hierarchical IBE. This new technique critically relies on garbled circuits and suggests new applications for this versatile primitive.
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