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 .

Read more about this topic:  Secret Sharing Using The Chinese Remainder Theorem

Famous quotes containing the words remainder and/or theorem:

    “Most personal correspondence of today consists of letters the first half of which are given over to an indexed statement of why the writer hasn’t written before, followed by one paragraph of small talk, with the remainder devoted to reasons why it is imperative that the letter be brought to a close.”
    —Robert Benchley (1889–1945)

    “To insure the adoration of a theorem for any length of time, faith is not enough, a police force is needed as well.”
    —Albert Camus (1913–1960)