Chinese remainder theorem
The Chinese remainder theorem can also be used in secret sharing, for it provides us with a method to uniquely determine a number "S" modulo "k" many pairwise coprime integers formula_5, given that formula_6. There are two secret sharing schemes that make use of the Chinese Remainder Theorem, Mignotte's and Asmuth-Bloom's Schemes. They are threshold secret sharing schemes, in which the shares are generated by reduction modulo the integers formula_7, and the secret is recovered by essentially solving the system of congruences using the Chinese Remainder Theorem.