Generating verifiable random numbers without a trusted party

Verifiable random number requires that the number is not only random but also its randomness can be verified. It has many applications in cryptographic protocols, such as key management, digital signature and authentication. In 2010, Liu et al. have introduced an efficient scheme to generate verifiable random numbers using polynomial interpolation. This scheme has inspired several other works recently. In this paper, we show that the computational efficiency of Liu´s protocol can be further improved by replacing Lagrange interpolation with Barycentric interpolation. Moreover, we introduce a new method to generate verifiable random numbers based on verifiable secret sharing. Compared with Liu´s scheme, our work has removed the assumption for a trusted party. Hence, it is suitable for circumstances where the players cannot agree with a trusted entity.