Abstract：Heterogeneous signcryption can be used to guarantee the confidentiality and unforgeability in the different cryptography. In 2016, between traditional public key cryptography and certificateless public key cryptography, the mutual signcryption schemes including PCHS and CPHS were proposed by Liu et al. However, via the security analysis, it is shown that the above schemes are not secure. Firstly, the processes of attack performed by the second type of adversary are described. Secondly, the possible reasons why the second type of adversary can perform these attacks are analyzed. In the end, the original schemes are improved. The improved schemes can overcome the security weakness of the original schemes, and can also ensure the security of data transmission between traditional public key cryptographic and certificateless public key cryptography.
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