We introduce the concept of anonymous identity-based hash proof system (IB-HPS), and show how to use it to construct identity-based encryption schemes providing anonymity in the presence of key leakage. We give four different constructions of anonymous IB-HPS based on: (1) the decision bilinear Diffie-Hellman assumption, (2) the decision truncated augmented bilinear Diffie-Hellman exponent assumption, (3) the quadratic residuosity assumption, and (4) the decision learning with errors assumption.
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