The Research Of Weighted Threshold Secret Sharing Based On General Chinese Remainder Theorem

Secret sharing is a most important branch in cryptology, which improves therobustness and security of systems. There is great importance in protecting secretinformation and transmitting data.In this dissertation, the research background and current situation of secretsharing is summarized, and some related important knowledge of number theory isintroduced. Some typical schemes on threshold secret sharing are studied, and theresearch production as well as typical schemes on weighted threshold secret sharingis emphatically analyzed. To resolve the problems and deficiencies of theseschemes, a weighted threshold secret sharing scheme based on general ChineseRemainder Theorem is proposed, in which participants can recover the secret whentheir sum of weight is equal to or larger than the threshold, but can’t get anyinformation if the sum is less than the threshold. Our contributions are as follows:1. The quantity of big prime numbers generated is equal to the sum ofparticipants’ weight in Iftene’s scheme. However, the Asmuth-Bloom sequence isextended in accord with participants’ weight, so the quantity of prime numbers isequal to the number of participants, but not the sum of participants’ weight.Therefore, the quantity of big prime numbers is decreased, the calculation cost ofgenerating prime numbers is lowered, and the initialization process is simplified.2. Generally, the quantity of every participant’s secret shares is equal to itsweight. However, the equivalence property of extended parameters is used, so thesecret shares can be obtained even if they are calculated only once, therefore, thecalculation cost is reduced.3. Based on the difficulty to solve the problem of discrete logarithm, a methodof verifying secret shares is given. The secret shares can be verified withparticipants’ private keys and some public parameters.Finally, the properties of prime numbers are introduced, a prototype system isdesigned with VC++6.0in Windows XP, and some critical module functions areanalyzed. The experimental results show that the scheme is correct and available.