Identity-Based Encryption from LWE with More Compact Master Public Key

This paper presents an adaptively secure identity-based encryption (IBE) scheme from Learning With Errors (LWE) in the standard model. Compared to the previous LWE-based most compact construction of Yamada (CRYPTO17), one of the distinguishing properties of our IBE scheme is that the master public key size of our IBE scheme is significantly smaller, and our design is explicitly given, and thus all the IBE parameters can be instantiated. To achieve this, we design a more compact homomorphic equality test algorithm over LWE problems, which is significantly better than the previous bit-wise comparison of Yamada (CRYPTO17) and Katsumata (ASIACRYPT17). We show that our homomorphic equality test algorithms can pack a super-constant number of GSW-type bit encodings and thus may find other improvements in other LWE-based crypto schemes.