Editing Secret sharing (section)

=== Using the Chinese remainder theorem ===
{{main|Secret sharing using the 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 <math>m_1, m_2, ..., m_k</math>, given that <math>S < \prod_{i=1}^k m_i</math>. 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 <math>m_i</math>, and the secret is recovered by essentially solving the system of congruences using the Chinese remainder theorem.