Security analysis and improvement of some proxy signature schemes

In 1996, Mambo et al introduced the concept of proxy signature. Proxy signature can be applied to mobile agent, e-vote etc. Recently, Sun and Hsieh showed that Lee et al's strong proxy signature scheme and its application to multi-proxy signature scheme, Shum and Wei's privacy-protected strong proxy signature scheme, and Park and Lee's nominative proxy signature scheme were all insecure against the original signer's forgery attack. In this paper, we show those proxy signature schemes don't withstand public key substitution attack and give some slight but important modifications for those proxy signature schemes such that the resulting schemes are secure against the original signer's forgery attack and public key substitution attack. In addition, we show that Park and Lee's nominative proxy signature scheme don't satisfy strong nonrepudiation and strong identifiability. Improved schemes satisfy all properties of strong proxy signature scheme, and doesn't use secure channel between the original signer and the proxy signer.