Efficient Identity-Based Encryption and Public-Key Signature from Trapdoor Subgroups

We present a new Identity-Based Encryption (IBE) scheme from a trapdoor subgroup of $\mathbb{Z}^*_{n}$ for an RSA modulus $n$. In a trapdoor subgroup of $\mathbb{Z}^*_{n}$, a subgroup order is hidden and can be used as a trapdoor. Our IBE scheme is efficient in both performance and space. Compared to practical pairing-based IBE schemes, ours is more efficient particularly in terms of computational performance. Following Naor\u27s observation, we also suggest a new Public-Key Signature (PKS) scheme from a trapdoor subgroup of $\mathbb{Z}^*_{n}$. A favorable feature of our PKS scheme is that signing algorithm is exponentiation-free and requires only one modular inversion. This enables our PKS scheme to provide the fastest signing, compared to practical signature schemes such as RSA and ECDSA. We prove the security of our schemes in the random oracle model under new computational hardness problems that arguably hold in the trapdoor subgroup of $\mathbb{Z}^*_{n}$