Ramp Scheme Based on CRT for Polynomial Ring over Finite Field

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 ≤ r1< r2≤ n, the ramp scheme can be used to construct a(r1, n)-threshold scheme that is threshold changeable to(r′, n)-threshold scheme for all r′∈ {r1+ 1, r1+ 2, · · ·, r2}. The threshold changeable secret sharing(TCSS) scheme has a greater information rate than other existing TCSS schemes of this type.