Secret Sharing Using The Chinese Remainder Theorem - Chinese Remainder Theorem

Chinese Remainder Theorem

Let, and . The system of equations

\begin{cases} x \equiv & b_1 \ \bmod \ m_1 \\ & . \\ & . \\ & . \\ x \equiv & b_k \ \bmod \ m_k \\ \end{cases}

has solutions in if and only if for all, where denotes the greatest common divisor (GCD) of and . Furthermore, under these conditions, the system has a unique solution in where, which denotes the least common multiple (LCM) of .

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