Research On The Forward-secure Threshold Digital Signature Scheme

The forward secure threshold digital signature is mainly analyzed and studied in this paper. The main idea of threshold digital signature is to divide the secret key into several participants. Each participant has a share of the secret, only the specific numbers of participants can reconstruct the secret. So it cannot breach the system security even some participants expose their shares. The use of secret sharing and threshold digital signature reduce the probability of the exposure of secret key. Unlike the general digital scheme, the forward secure digital signature scheme can ensure the adversary couldn't forge any signature pertaining to the past, even if he had obtained the present key. In the key evolution paradigm: the user produces signatures using different secret keys during different time periods while the public key remains fixed. An improved forward-secure threshold digital signature was formed based on the ELGamal signaturesystem in this thesis. Through using w = (SK_j^w/h(m)g^R' mod p)mod q in each period time signing process to hide the secret key in the signing process while the time parameter j is anavailable parameter in the verifying process w=(g^1/h(m)y ^-w/h(m)w^'2T-j mod p)mod q ,therefore,the scheme has the genuine forward-secure property.Morever,we put forward a new forward-secure threshold digital signature based on the Schnorr signature system, we hide thesecret key in the signing process by using r'=X_jg^K' mod p in each period time signing process while the time parameter j is an available parameter in the verifying processR = g^sy^er^'2T-je mod p .By implementing the two signature into practice, it is infeasible for anattacker to forge any valid signature pertaining to the past even if he has corrupted up to more than or equal to the threshold members and has obtained the current key. This scheme has the genuine forward-secure property which reduce the potential damage in case secrets are exposed to the minimum degree.The thesis is composed of the following chapters:Chapterl the overview of the aim and significance of digital signature, the general situation of domestic and foreign research and knowledge related to cryptograph as well as some math preparatory knowledge.Chapter2 generally introduces the situation and the actuality of the threshold digital signature. Besides this, we analysis some famous threshold digital signature scheme. Based on this, we put forward our expectation of the threshold digital signature scheme. The overview of forward secure digital signature scheme is presented and generic constructions and security models of forward secure digital signature are described, at the same time, the merit and applied foreground of forward secure digital signature scheme are analyzed.Chapter3 an improved forward-secure digital signature is presented based on the predecessor. This scheme is not only the secret key has the forward-secure property but also the signature. As a result, the attacker can't obtain X_j-1 from X_j, that is to say the secret key has forward-secureproperty which reduce the potential damage in case secrets are exposed to the minimum degree.Chapter 4 Based on the Schnorr cryptosystem, a new forward-secure threshold signature scheme was proposed Which ensure that the signature's secret key and the signature are simultaneously secure through hiding the current secret key in the signature process while using the time-parameter effectively in the verification process. This scheme has the new property that it is infeasible for an attacker to forge any signature valid pertaining to the past even if he has taken control of more than or equal threshold members and obtained the current key.Chapter 5 We summarize and expect the paper. Both threshold signature and forward-secure signature are signatures which are designed to reduce the potential damage in case secrets are exposed to the minimum. Therefore, they have practicality utilize value.