Linear threshold verifiable secret sharing in bilinear groups

In many pairing-based cryptosystems, the secret keys are elements of bilinear groups. For safeguarding such secret keys or decrypting or signing in a threshold manner, Verifiable Secret Sharing (VSS) in bilinear groups is required. In this paper, we show a method of verifiably sharing a random secret in a bilinear group. Our method is simple and practical. It can be regarded as a generalisation of threshold linear VSS in finite fields to the case when the secrets are in bilinear groups. We present a general scheme for verifiably sharing secrets in bilinear groups. A modified version of our general scheme with improved efficiency is also introduced.