Certificateless signature scheme without random oracles

The security of certificateless signature schemes can be proved under the random oracle model.However，any implementation of the random oracle may result in insecure schemes.Some certificateless signature schemes without random oracles are not secure against key replacement attack.In order to solve this problem，a new certificateless signature scheme in the standard model had constructed.Based on the NGBDH and Many-DH assumption，the scheme was proved secure against existentially unforgeable under adaptive chosen message attack.In addition，the proposed scheme enjoys less computation cost and lower communication bandwidth and can resist against key replacement attack.