[PDF] chinese remainder theorem notes

In mathematics, the Chinese remainder theorem states that if one knows the remainders of the Euclidean division of an integer n by several integers, then one can determine uniquely the remainder of the division of n by the product of these integers, under the condition that the divisors are pairwise coprime (no two
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  • What is the Chinese remainder theorem in cryptography notes?

    The Chinese remainder theorem asserts that if the ni are pairwise coprime, and if a1, , ak are integers such that 0 ? ai < nifor every i, then there is one and only one integer x, such that 0 ? x < N and the remainder of the Euclidean division of x by niis ai for every i.

  • What is the general formula for the Chinese remainder theorem?

    Here is a more general form of the Chinese remainder theorem. x ? a1 mod m1, x ? a2 mod m2, , x ? ar mod mr, has a solution, and this solution is uniquely determined modulo m1m2 ···mr.

  • What is Chinese remainder theorem powers?

    The Chinese remainder theorem is a powerful tool to find the last few digits of a power.
    The idea is to find a number mod 5 n 5^n 5n and mod 2 n , 2^n, 2n, and then combine those results, using the Chinese remainder theorem, to find that number mod 1 0 n 10^n 10n.

  • What is Chinese remainder theorem powers?

    (2) The new Chinese remainder theorem I is a parallel algorithm in mixed radix format. The delay is reduced from O(n) to O(logn). (3) The new Chinese remainder theorem II reduces the modulo operation from the size M to a size less than /spl radic/M.

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