Anonymous IBE From Quadratic Residuosity With Fast Encryption

We develop two variants of Cocks\u27 identity-based encryption. One variant has faster encryption, where the most time-consuming part only requires several modular multiplications. The other variant makes the first variant anonymous under suitable complexity assumptions, while its decryption efficiency is about twice lower than the first one. Both the variants have ciphertext expansion twice more extensive than the original Cocks\u27 identity-based encryption. To alleviate the issue of the second variant\u27s large ciphertext expansion, we consider using it to construct a public-key encryption with keyword search scheme with a fast encryption algorithm