Chinese remainder theorem
Proper noun
Meaning
the Chinese remainder theorem
(number theory) A theorem stating 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.
Examples
Each of the shares is represented in a congruence, and the solution of the system of congruences using the Chinese remainder theorem is the secret to be recovered.
Encryption Most implementations of RSA use the Chinese remainder theorem during signing of HTTPS certificates and during decryption.
Over principal ideal domains In main, the Chinese remainder theorem has been stated in three different ways: in terms of remainders, of congruences and of a ring isomorphism.
Practical implementations use the Chinese remainder theorem to speed up the calculation using modulus of factors (mod pq using mod p and mod q).
Range ambiguity resolution main The range ambiguity resolution techniques used with medium pulse repetition frequency radar can be seen as a special case of the Chinese remainder theorem.
See Section 31.5: The Chinese remainder theorem, pp. 873–876.