The existing certificateless signcryption schemes were designed mainly based on the traditional public key cryptography, in which the security relies on the hard problems, such as factor decomposition and discrete logarithm. However, these problems will be easily solved by the quantum computing. So the existing certificateless signcryption schemes are vulnerable to the quantum attack. Multivariate public key cryptography (MPKC), which can resist the quantum attack, is one of the alternative solutions to guarantee the security of communications in the post-quantum age. Motivated by these concerns, we proposed a new construction of the certificateless multi-receiver signcryption scheme (CLMSC) based on MPKC. The new scheme inherits the security of MPKC, which can withstand the quantum attack. Multivariate quadratic polynomial operations, which have lower computation complexity than bilinear pairing operations, are employed in signcrypting a message for a certain number of receivers in our scheme. Security analysis shows that our scheme is a secure MPKC-based scheme. We proved its security under the hardness of the Multivariate Quadratic (MQ) problem and its unforgeability under the Isomorphism of Polynomials (IP) assumption in the random oracle model. The analysis results show that our scheme also has the security properties of non-repudiation, perfect forward secrecy, perfect backward secrecy and public verifiability. Compared with the existing schemes in terms of computation complexity and ciphertext length, our scheme is more efficient, which makes it suitable for terminals with low computation capacity like smart cards.

Certificateless multi-receiver signcryption scheme provides the sender with the ability to send the same message to multiple authorized receivers contemporaneously, and at the same time, it can avoid the key escrow problem in the existing identity-based multi-receiver signcryption schemes, which makes it get great attention in the field of one-to-many communication. However, in the existing certificateless multi-receiver signcryption schemes, a secure channel is essential for their key extract algorithm, which brings some troubles in practical applications. On one hand, the security of the partial private key depends on the secure channel. Once the secure channel is broken by an attacker, the user’s partial private key may be leaked. On the other hand, maintaining the secure channel increases the economic cost and implementation complexity of the application systems. Motivated by these concerns, we propose a new anonymous certificateless multi-receiver signcryption scheme, in which the key generation center only utilizes a public channel to send the pseudo partial private key to the user during key extract algorithm, and the designated user can work out the real partial private key from the pseudo partial private key while others cannot. The avoidance of the secure channel improves the security of the proposed scheme and makes the communication system much lighter.

Anonymity, which is more and more important to multi-receiver schemes, has been taken into consideration by many researchers recently. To protect the receiver anonymity, in 2010, the first multi-receiver scheme based on the Lagrange interpolating polynomial was proposed. To ensure the sender’s anonymity, the concept of the ring signature was proposed in 2005, but afterwards, this scheme was proven to has some weakness and at the same time, a completely anonymous multi-receiver signcryption scheme is proposed. In this completely anonymous scheme, the sender anonymity is achieved by improving the ring signature, and the receiver anonymity is achieved by also using the Lagrange interpolating polynomial. Unfortunately, the Lagrange interpolation method was proven a failure to protect the anonymity of receivers, because each authorized receiver could judge whether anyone else is authorized or not. Therefore, the completely anonymous multi-receiver signcryption mentioned above can only protect the sender anonymity. In this paper, we propose a new completely anonymous multi-receiver signcryption scheme with a new polynomial technology used to replace the Lagrange interpolating polynomial, which can mix the identity information of receivers to save it as a ciphertext element and prevent the authorized receivers from verifying others. With the receiver anonymity, the proposed scheme also owns the anonymity of the sender at the same time. Meanwhile, the decryption fairness and public verification are also provided.

Ciphertext-Policy Attribute-Based Proxy Reencryption (CP-ABPRE) has found many practical applications in the real world, because it extends the traditional Proxy Reencryption (PRE) and allows a semitrusted proxy to transform a ciphertext under an access policy to the one with the same plaintext under another access policy. The existing CP-ABPRE schemes were proven secure only in the selective security model, a limited model, which is an unnatural constraint on the attacker. The scheme proved in this model can only be called selectively secure one. However, from a security perspective, the adaptively secure CP-ABPRE scheme is more desirable. In this paper, an adaptively secure CP-ABPRE scheme is proposed, which is based on Waters’ dual system encryption technology. The proposed scheme is constructed in composite order bilinear groups and proven secure under the complexity assumptions of the subgroup decision problem for 3 primes (3P-SDP). Analyses show that our proposal provides higher computational efficiency compared with the existing schemes.