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In this paper, the authors propose two new Spatial Encryption (SE) schemes based on existing Inner Product Encryption (IPE) schemes. Both of their SE schemes are fully secure under simple assumptions and in prime order bilinear groups. Moreover, one of their SE schemes has constant-size ciphertexts. Since, SE implies Hierarchical Identity-Based Encryption (HIBE), they also obtain a fully secure HIBE scheme with constant-size ciphertexts under simple assumptions. Their second SE scheme is attribute-hiding (or anonymous). It has sizes of public parameters, secret keys and ciphertexts that are quadratically smaller than the currently known SE scheme with similar properties.
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