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Ramp Scheme Based on CRT for Polynomial Ring over Finite Field
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作者 DING Jian KE Pinhui +1 位作者 LIN Changlu WANG Huaxiong 《Journal of Systems Science & Complexity》 SCIE EI CSCD 2023年第1期129-150,共22页
Chinese Reminder Theorem(CRT)for integers has been widely used to construct secret sharing schemes for different scenarios,but these schemes have lower information rates than that of Lagrange interpolation-based schem... Chinese Reminder Theorem(CRT)for integers has been widely used to construct secret sharing schemes for different scenarios,but these schemes have lower information rates than that of Lagrange interpolation-based schemes.In ASIACRYPT 2018,Ning,et al.constructed a perfect(r,n)-threshold scheme based on CRT for polynomial ring over finite field,and the corresponding information rate is one which is the greatest case for a(r,n)-threshold scheme.However,for many practical purposes,the information rate of Ning,et al.scheme is low and perfect security is too much security.In this work,the authors generalize the Ning,et al.(r,n)-threshold scheme to a(t,r,n)-ramp scheme based on CRT for polynomial ring over finite field,which attains the greatest information rate(r−t)for a(t,r,n)-ramp scheme.Moreover,for any given 2≤r_(1)<r_(2)≤n,the ramp scheme can be used to construct a(r_(1),n)-threshold scheme that is threshold changeable to(r′,n)-threshold scheme for all r′∈{r_(1)+1,r_(1)+2,···,r_(2)}.The threshold changeable secret sharing(TCSS)scheme has a greater information rate than other existing TCSS schemes of this type. 展开更多
关键词 chinese reminder theorem polynomial ring ramp scheme threshold changeable secret sharing
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