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466 Yibing Kong et al.(c) A Decryption function D: m = D K −1(c), where K −1 means private key(decryption key).• A Modulus Generator MG: ∀s i ∈ S, MG generates a modulus n si , such thatn s1 ,n s2 , ..., n sl are pairwise relatively prime. Please note, these moduli arepublicly known and will be used as the CRT moduli.• A Shared DataBase (or file system) SDB that stores shared data.4.3 Cryptographic Access ControlOur data based solution is depicted by a scenario as follows. Assume that a subjects i wants to share a message m with k subjects s i1 ,s i2 , ..., s ik ∈ S, s i performsthe following operations (for simplicity, we assume that m
A Cryptographic Solution for General Access Control 467x ′ mod n si1 =(m e mod n si1 n si2 ...n sik )modn si1=(m e − qn si1 n si2 ...n sik )modn si1= m e mod n si1= E Ksi1 (m) .where m e = qn si1 n si2 ...n sik +r for some integers q and r (r
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