Albrecht Heeffer investigated Menzies'claim that Regiomontanus based his solution to the Chinese remainder theorem on the Chinese work " Mathematical Treatise in Nine Sections " from 1247.
32.
*PM : noncommutative case Chinese remainder theorem for rings, id = 9152 new !-- WP guess : noncommutative case Chinese remainder theorem for rings-- Status:
33.
*PM : noncommutative case Chinese remainder theorem for rings, id = 9152 new !-- WP guess : noncommutative case Chinese remainder theorem for rings-- Status:
34.
What I decided to do was to write a program that computes the determinants modulo some prime numbers and then use Mathematica to compute the determinants using the Chinese Remainder Theorem.
35.
In the treatise Qin included a general form of the Chinese remainder theorem that used " Da yan shu " ('YM?/ g ) or algorithms to solve it.
36.
The theoretical way solutions modulo the prime powers are combined to make solutions modulo " n " is called the Chinese remainder theorem; it can be implemented with an efficient algorithm.
37.
To decrypt a ciphertext " c " we compute the plaintext as m = c ^ d \ mod pq, which like for Rabin and RSA can be computed with the Chinese remainder theorem.
38.
The Chinese remainder theorem is widely used for computing with large integers, as it allows replacing a computation for which one knows a bound on the size of the result by several similar computations on small integers.
39.
Secret sharing using the Chinese remainder theorem uses, along with the Chinese remainder theorem, special sequences of integers that guarantee the impossibility of recovering the secret from a set of shares with less than a certain cardinality.
40.
Secret sharing using the Chinese remainder theorem uses, along with the Chinese remainder theorem, special sequences of integers that guarantee the impossibility of recovering the secret from a set of shares with less than a certain cardinality.
