In earlier multi-receiver signcryption schemes, in order to help the authorised receivers to find the corresponding information for decryption from the ciphertext, the list of identities of all authorised receivers should be included in the ciphertext as a necessary element. However, this method has directly led to the privacy leakage problem of receivers. Later, several anonymous multi-receiver signcryption schemes use the Lagrange interpolation method to mix and hide the real identities of all receivers, so that the ciphertext does not expose identities of the receivers any longer.

Therefore the Lagrange interpolation method is considered to be a perfect solution to the receiver anonymity problem, and multiple anonymous multi-receiver signcryption schemes have been proposed based on it. However, recently, this method has been proven to be insecure because it cannot assure the anonymity of receivers either. In fact, in any of the existing anonymous schemes based on the Lagrange interpolation method, it is easy for one authorised receiver to judge whether anyone is an authorised receiver or not, which badly violates the receiver anonymity. Motivated by these concerns, the authors propose a new multi-receiver signcryption scheme to solve this problem. Analyses show that the proposed scheme meets confidentiality, unforgeablity and the sender and receivers’ anonymity.