A multi-secret sharing scheme based on general linear groups

A threshold secret sharing scheme has many practical applications, such as opening a bank vault, launching a nuclear, or authenticating an electronic funds transfer. The known matrix projection secret sharing scheme needs a security channel which is unpractical. To overcome this problem, a multi-secret sharing scheme based on general linear groups over finite fields is proposed.In this scheme,each participant selects her/his secret shadow by herself/himself and the dealer need not deliver any secret information to each participant. So a secure channel among the dealer and participants is no longer needed and the cost of the system can be lowered.The security of the proposed scheme is based on the difficulty to solve the discrete logarithm problem on general linear groups over finite fields and difficulty to break Shamir´s secret sharing scheme.