The invention discloses a certificateless multi-
receiver signcryption method with a multivariate-based
cryptosystem. The certificateless multi-
receiver signcryption method is used for solving the technical problem of poor security of an existing certificateless
signcryption method. The technical scheme includes that the method includes: firstly, using a
key generation center to generate
system parameters, and selecting a secure multivariable
encryption algorithm to generate keys; and enabling a user U to obtain
system private keys of the
key generation center and generate the private keys to user keys prior to that a user Alice with the identity IDA sends signcryption messages to a
user group L={ID1, ID2,...,IDt}, and accepting or refusing
ciphertext sigma by means of un-signcryption. By the aid of the multivariate-based
cryptosystem,
high security of anti-
quantum computation is achieved, and the certificateless multi-
receiver signcryption method is still high in security facing
attack of a
quantum computer. Compared with the background art, the certificateless multi-receiver signcryption method is small in computation and high in security, has the advantages of completeness,
confidentiality, unforgeability, forward security, backward security, receiver
privacy protection and the like and is capable of resisting existing known
attack.