Secret sharing schemes are widely applied in various areas, and there are series of achievements, among which the verifiable multi-secret schemes are the most representative ones. A few verifiable multi-secret schemes own the following drawbacks: insensitive to the differences of security levels, lack of expandability, high computation complexity of verification process, and low efficiency of execution. Addressing the issues, an extensible cheat-proofing multi-secret sharing scheme with low computation complexity is proposed. With the security of RSA public key system and discrete logarithm puzzle, the proposed scheme can realize the following functions: first, the secret dealer can set relatively threshold values according to different security levels; second, the participants and secret combiner can verify the secret shares, which can guard against cheating problem, resist various kinds of attacks and improve the success rate of secret reconstruction; in addition, the secret shares are reusable in the situations of new group secret and new participant joining the group, which brings about good expandability. Moreover, compared with the previous schemes, the proposed scheme reduces the information content published by secret dealer and brings down the computation complexity of verification, which makes the efficiency of the scheme greatly improved. Copyright © 2013 John Wiley & Sons, Ltd.