Research On Special Digital Signatures

Digital signature, which can provide authentication, integrity and non-repudiation of message, is one of key techniques of information security and has wide application in every field of society and life such as business, politics and military. With a rapid development of Internet, e-commerce and e-government, and the deeper research of digital signature technology, normal digital signatures cannot satisfy the need and people have paid more and more attention to digital signatures with additional properties. Researching on it has an important theoretical significance and practical values.In this thesis, research is focused on several special digital signatures:blind signature, threshold signature, proxy signature, and forward secure signature. New safe and efficient signature schemes have been presented. The main contributions are as follows.1. Research on secure and efficient blind signature primitives.Works have been done around the blind signature primitives with only one bilinear pairing without trusted Private Key Generator (PKG). Based on l-SDHP problem, an ID-based signature scheme with only one bilinear pairing without trusted PKG is presented. Based on the scheme, two schemes have been presented which one is blind signature scheme with only one bilinear pairing without trusted PKG and the other is partially blind signature scheme with only one bilinear pairing without trusted PKG. Their strong blindness and unforgeability under the random oracle model have been proved, and their efficiencies have been analyzed. Three schemes all remove key escrow problem in ID-based cryptographic primitives by using un-trusted PKG technology; They can not only resist attack from un-trusted PKG by using "zero-knowledge proof" but also resist forgery on adaptively chosen message and ID attack basing on the hardness of l-SDHP; The last scheme can resist the changing agreed information attack by using public key ginf, and can achieve the authenticity verification of agreed information. Besides, they are all more efficient than other likely schemes because they have only one bilinear pairing.Around certificate-based signature, based on discrete logarithm problem, two schemes with strong secure properties without bilinear pairing are presented which one is certificate-based efficient signature scheme and the other one is certificate-based efficient blind signature schem. Two schemes have higher efficiency, as they are mainly based on modular exponentiation arithmetic in the finite field instead of pairings and messages are blinded by affine transformation in the second scheme. The validities of public key and certificate are verified before verifying signature, so the mutual authentication of both public key and certificate are achieved. Under the random oracle model, it have been proved that schemes are blind and existentially unforgeable against user forgery attack, CA forgery attack and public key replacing attack. Efficiency analysis shows that, compared with other similar schemes, schemes have shorter signature length, smaller computation and communication complexity, so they are suitable for application fields of lower computing power and limited bandwidth.2. Research on secure threshold signature primitives.Works have been done around the threshold signature primitives with anonymity, traceability and resisting conspiracy attack and other forgery attacks. The security of a provably secure threshold signature scheme presented by Jing Xu (Xu scheme for short) is first analyzed, and then conspiracy attack and adaptive chosen message attack to Xu scheme are realized. It is found that Xu scheme not only is vulnerable to conspiracy attack when members of the signer group are more than t members, but also has another more serious weakness:because of bad structure of the signature (σ1,σ2), distributed key generation protocol can’t provide unknowability of the group’s secret key and attacker can realize adaptive chosen message attack easily.In order to overcome the weaknesses of Xu scheme, a new (t, n) threshold signature scheme with anonymity, traceability, partial signature verifiability is presented and its security analysis has been given. The scheme can resist conspiracy attack and other forgery attacks. Moreover, by employing the secure Gennaro’s distributed key generation protocol, the partial private keys λ1and the group private key λ=F (0) are generated by all members, so the scheme realizes the unknowability of the group’s secret key. Then a new (t, n) threshold blind signature scheme with anonymity, traceability, partial signature verifiability and a practical (t, n) threshold proxy signature scheme with the same secure properties are presented and their security analyses have been done. Analyses show that the three threshold schemes have more secure than other likely schemes:cheat from either key manage center or members can be detected; partial signatures are verifiable by using verifiable secret sharing technology; schemes can not only resist the conspiracy attack and forgery attack essentially, but also provide anonymity and traceability simultaneously. Those three threshold signature schemes can be used in different applying areas.3. Research on proxy multi-signature primitives.Based on discrete logarithm problem, strong RSA problem and fork lemma, two proxy multi-signature schemes are presented:one is blind proxy multi-signature scheme and the other is proxy multi-signature scheme, and their unforgeability and blindness (only the first scheme has) have been proved. Two schemes are more secure than general proxy multi-signatures as the facts exist that they both avoid the attacking way in some documents, the proofs of validation of partial proxy keys and partial proxy signatures are realized, and any attacker including original signer has no any information about important parameter M so any attacker including original signer can’t forge valid proxy multi-signature of any message m.4. Research on forward secure signature primitives. After a research on forward security signature, two forward secure signature schemes based on polynomial key evolving are presented, and their security and efficiency analyses have been given. Two schemes both have infinite recovery power.Based on factoring problem and quadratic residue problem, two forward secure proxy blind signature schemes are presented, and their security and efficiency analyses have been given. Advantages of two schemes exist that the proofs of validation of proxy authority can be realized, schemes are strong blind, forward secure and proxy schemes, and they are both more efficient than other general schemes.