The Research Of Several Special Threshold Signature Schemes

Threshold signature is a signature scheme based on digital signature which isdesigned to address the needs of decentralizes the over-concentration signature. Itsessence is the secret sharing technology applied to the digital signature, only when noless than t members use their sub-secret keys to sign the message, and merge thesesignatures can produce the final threshold signature. As the global informationizationdegree is increasing day and day, the rapid development of the network, the normalthreshold signature already cannot satisfy some new requirements in practical life.Therefore, a well performing threshold signature scheme not only base on a solidtheoretical foundation, but should be applied to the real life flexibly.This article mainly focuss on the threshold blind signature and threshold proxysignature, meanwhile, apply the signature scheme to the practical life. The mainresearch achievements are as following:1. Start with RSA cipher, EIGamal cipher and ECC cipher, study thresholdsignature based on the three typical public-key cryptosystem. Analyze the efficiencyand security of threshold signature and be a stepping stone to develop a new thresholdsignature.2. Combined with elliptic curve cryptosystem, partially blind signature, secretsharing technology, a new threshold partially blind signature scheme is constructed.By analyzing the existing threshold blind signature schemes, found that these schemesgenerally have some defects, i.e. low efficiency, narrow scope of application. On thepremise of ensuring safety of scheme, combined with the feature of partially blind,this paper construct a new threshold partially blind signature which makes up for thatany third party can verify the signature which a common threshold blind signaturelacks. Comparing and analyzing the proposed scheme with the existing schemes onefficiency, we could know that the former is more efficient.3. Using the Lagrange formula, and certificateless public key cryptography, anew threshold proxy signature scheme is constructed. Through the study of thesecurity analysis of scheme [85], found that the scheme has public-key replacementattack of the original signer or proxy signer’s. After improving the original scheme, the public key substitution attack disappeared. And reduces the computational costsand communication costs of the scheme.4. By using the new proposed threshold partially blind signature scheme in theelectronic voting system, we can better apply theory to practice. Analyze the safety ofelectronic voting system, found that the system have the characteristcs of legitimacy,anonymity, uniqueness, verifiability, robustness, etc.