Compact Identity Based Encryption Based on n^{th} - Residuosity Assumption

. Practical Identity Based Encryption (IBE) schemes use the costly bilinear pairing computation. Clifford Cock proposed an IBE based on quadratic residuosity in 2001 which does not use bilinear pairing but was not efficient in practice, due to the large ciphertext size. In 2007, Boneh et al. proposed the first space efficient IBE that was also based on quadratic residuosity problem. It was an improvement over Cock’s scheme but still the time required for encryption was quartic in the security parameter. In this paper, we propose a compact, space and time efficient identity based encryption scheme without pairing, based on a variant of Paillier Cryptosystem and prove it to be CPA secure. We have also proposed a CCA secure scheme based on the basic IBE scheme using the Fujisaki-Okamoto transformation. We have proved both the schemes in the random oracle model.

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