An Id-Based Proxy Signature Without Trusted PKG

With the rapid development of modern communication technique and computer technique,our society has come into information age.How to communicate conveniently and securely becomes more and more important.Digital Signatures play an important role in electronic commerce for its various applications.After public key cryptography was proposed,many digital signatures and schemes are designed for various use in different fields.At the same time,these digital signatures are attacked by outside.How to design a safe and practical signature has been a main subject of many experts.In our life,people often delegate some rights to a trusted proxy,who exerts these rights for him.In these entrusted rights,signing right is included.The traditional method of right delegation is to use print,as it can be passed easily.Signing right also will be encountered in virtual information world.Being a legal replacement for handwritten signatures,digital signature dose not have agential function at first.In 1996,Mambo,Usuda and Okamoto proposed the concept of proxy digital signature,and in this scheme,an original signer is allowed to delegate his signing power to a designed person or group,who is called the proxy signer and can sign messages on behalf of the original signer.Also,Mambo and some researchers later pointed that the proxy signature must satisfy the so-called distinguishability,verifiability, strong non-forgeability,strong non-deniability,strong identifiability,prevention of misuse,etc.Proxy signature plays an important role in some applications such as electronic commerce,electronic voting,electronic auction etc.Because of the fascinating blueprint of the proxy signature's application,once it was proposed it has become the hotspot of the research.Furthermore,various extensions of the basic proxy signature primitive have been considered.These include proxy multisignature, threshold signature,ID-based proxy signature,blind proxy signature, proxy signature with warrant recovery,one-time proxy signature,and proxy anonymous proxy signaturesIdentity-based cryptography was proposed by Shamir in 1984.In such a cryptography, users can take their public information,such as their email address,as their public key.So in an ID-based cryptography,verifier doesn't need obtain signer's public key certificate first when he wants to verify a signature.It can distinctly simplify. the key management procedure of CA-based PKI.The bilinear pairings,namely the Weil pairing and Tate pairing of algebraic curves,are important tools for research on algebraic geometry.They also are important tools for construction of a bilinear map,which have three properties such as bilinear property,non-degenerate property,and computable property.Based on the bilinear pairings's various applications,many new proxy signatures were proposed, whose security and efficiency were improved.In a traditional ID-based cryptography,If the Private Key Generater(PKG) is dishonest,then he can forge a valid signature.The security of the scheme will be threatened.Also,in a proxy signature,If original signer can forge a signature as proxy signer dose,It is unfair for the proxy signer.The proxy signature proposed in our paper can prevent the hidden trouble.In the paper,We first review some proxy signatures,then based on an ID-based signature without trusted PKG,we propose an efficient proxy signature.Chaos control is one of the important subjects in the research of chaos,which has been developed so far mainly in two different directions:control of chaos and anti-control of chaos.A process of making a chaotic system nonchaotic or stable is called control of chaos.Over the last decade,chaotic motions are regarded as harmful,so the traditional control engineering design always tries to stabilize a chaotic system,therefore, research on control of chaos has been rapidly developed(cf.[1～4]).Anti-control of chaos(or called Chaotification) is a process of making an originally non-chaotic dynamical system chaotic,or enhancing a chaotic system to present stronger or different type of chaos.Recently,it has been found that chaos can actually be very useful under some circumstances,such as in encryption[5],digital communications [6],human brain analysis[7],and heartbeat regulation[8].