A Study Of Secure And Efficient Certificateless Signature Scheme In The Standard Model

In recent years, certificateless cryptography has been widely studied owing to the characteristics that it not only enjoys many advantages of identity-based cryptography (IBC) but also eliminates the fatal drawback which is called the key escrow in IBC. But, there still exists some problem in the certificateless cryptography. First, most of the schemes of certificateless cryptography are built in the random model in which the hash functions are regarded as ideal random functions. And it has been demonstrated that the schemes in this model does not always present secure when implementing random oracles by concrete cryptographic hash functions. Besides, there isn’t anything to bind the public key of users and part of the secret key of users is produced by the key generation center (KGC). Thus, certificateless cryptography is vulnerable to the malicious-but-passive KGC attack and the public-key-replace attack. Finally, according to the concept of M. Girault’s trust level, almost all the schemes of certificateless cryptography just can achieve trust level 2 in which the authority can impersonate a user without knowing the user’s secret key. Therefore, this paper is to solve the above problems. Specific work is shown as follows.1. Study the present certificateless algorithm model in the standard model. According to the concept of M. Girault’s trust level, I discover that all the scheme which is based on the present certificateless algorithm model in the standard model just can achieve trust level 2 at which the KGC can impersonate any user without knowing the user’s secret key. Therefore, the present certificateless algorithm model in the standard model is unsafe. In this paper, I modify this model to make the scheme based on the modified model can achieve trust level 3 in which the frauds of the KGC can be detected. Thus the schemes based on the modified model don’t have to be over-dependent on the honest of the KGC.2. Analyze a scheme of certificateless signature in the standard model proposed by Yu et al. in 2012. After the analysis, I draw the conclusion that there are some drawbacks in the scheme. I can deduce that this scheme is vulnerable to the malicious-but-passive KGC attack and the public-key-replace attack after specific attacks on this scheme.3. Based on the schnorr signature, I propose an efficient certificateless signature which provides stronger security and higher computational efficiency than the existing schemes. In addition, according to the concept of M. Girault’s trust level, my scheme can achieve trust level 3. Finally, I make use of the Non-pairing-based generalized bilinear DH(NGBDH) assumption and NGB-Many-DH assumption to prove that my scheme can withstand the public key replacement attack and the malicious-but-passive KGC attack.