Pairing-based cryptography for homomorphic cryptography

This paper introduces pairing-based cryptography focusing on homomorphic cryptography. Pairing is a bilinear map from two rational point groups to a multiplicative group in extension field. The bilinearity is used for realizing recent innovative cryptographies. In these years, it is applied to some homomorphic encryptions though it needs a heavy calculation. This paper introduces some related approaches from the view-point of pairing-based cryptography.