於隨機稀疏矩陣架構下的分散式金鑰產生機制

Abstract

分散式金鑰產生(Distributed Key Generation)在門檻式密碼系統(Threshold Cryptosystem)中扮演很重要的角色，而關於建立在離散對數模式下的分散式金鑰產生機制之相關研究已行之有年，由於它所帶來實用的性質因素，而使此議題廣泛且熱切地探討著。儘管這些年來，研究學者們分別提出為數不少的各種架構，但總是在效率上遇到難以突破的瓶頸，尤其是當我們將分散式金鑰產生機制著眼於有著大規模成員數量的系統上時，在成員們為了達到“可驗證之秘密分享(VSS)“之要求，而所需相互傳送的通訊量是很可觀的；因此，在此實際的情形下，各方所提出架構之效能皆不是很出色。 因此，為克服上述的瓶頸，我們提出一個架構於隨機稀疏矩陣的分散式金鑰產生機制，並提出在此架構下有非常高的成功機率以及完整的安全性證明；此外，我們所提的架構亦符合R.Gennaro等人於[GJKR99]探討分散式金鑰產生時所提出更嚴謹的安全性定義。

Distributed key generation (DKG) plays a very important role in the threshold cryptosystem and the interrelated researches in the distributed key generation protocol for discrete-log based cryptosystem have been lasted for several years. Due to their realistic factors in all kinds of applications, the discussions for these interrelated research topics are always hot and extensive. In spite of there are so many distributed key generation protocols proposed by scholars, the performances of these DKG protocols are still not very efficient. Especially when we implement these DKG protocols for the need of achieving “Verifiable Secret Sharing” in some large scale system, the necessary sharing messages sent between members will be very huge. Therefore, the communication load remains so heavy that there are still hard to conquer the bottleneck in efficiency. To this end, we will propose a new distributed key generation protocol which is constructed on “random sparse matrix”. Then we will also put forward the complete security proof and we claim that there would be very high successful probability in our random sparse matrix DKG. Furthermore, our random sparse matrix DKG also corresponds with the stricter security definition proposed by R.Gennaro etc. in [GJKR99] for distributed key generation.