A (t, n) threshold quantum secret sharing scheme is proposed, in which the secret is a quantum state, and the dealer encodes the secret through the phase shift operation. The participants perform the phase shift operations on the quantum state according to their private keys, and any t out of the n participants can use the Lagrange interpolation to recover the original quantum state. Compared to the existing schemes, the proposed scheme is simpler and more efficient.

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An identity-based threshold signcryption scheme for multiple receivers is proposed. For the n specified receivers, the ciphertext can be decrypted and verified when arbitrary t or more receivers work together. The steps of the private keys extraction, the signcryption, the decryption, and the verification are introduced in detail. The chosen-ciphertext security of the scheme is proved formally. The comparisons to the existing schemes show that the proposed scheme is more secure, more flexible, and the simulative game of the security proof in the scheme is more perfect.