# The history of the chinese remainder theorem

Some visual proofs of Pythagoras' Theorem My favourite proof of the look-and-see variety is on the right. The public key can be known by everyone, and it is used for encrypting messages. The intention is that messages encrypted with the public key can only be decrypted in a reasonable amount of time by using the private key.

The public key is represented by the integers n and e; and, the private key, by the integer d although n is also used during the decryption process. Thus, it might be considered to be a part of the private key, too. The keys for the RSA algorithm are generated the following way: Choose two distinct prime numbers p and q.

For security purposes, the integers p and q should be chosen at random, and should be similar in magnitude but differ in length by a few digits to make factoring harder. Its length, usually expressed in bits, is the key length.

The Chinese Remainder Theorem Evan Chen∗ February 3, The Chinese Remainder Theorem is a \theorem" only in that it is useful and requires proof. Chinese Remainder Theorem SHEN KANGSHENG Communicated by C. TRUESDELL 1. Source of the Problem This statement is called the SuN Z~ Theorem, or the Chinese Remainder Theo- rem. Indeed, in imitation of the theorem, YANa History df Hindu Mathematics, , Lahole, Vol. 2, pp. RSA (Rivest–Shamir–Adleman) is one of the first public-key cryptosystems and is widely used for secure data transmission. In such a cryptosystem, the encryption key is public and it is different from the decryption key which is kept secret (private). In RSA, this asymmetry is based on the practical difficulty of the factorization of the product of two large prime numbers, the "factoring.

This value is kept private. However, much smaller values of e such as 3 have been shown to be less secure in some settings.

The public key consists of the modulus n and the public or encryption exponent e. The private key consists of the private or decryption exponent d, which must be kept secret.

That the Euler totient function can be used can also be seen as a consequence of the Lagrange's theorem applied to the multiplicative group of integers modulo pq.

## Chinese remainder theorem - Wikipedia

Since it is beneficial to use a small value for e e. If they decide to use RSA, Bob must know Alice's public key to encrypt the message and Alice must use her private key to decrypt the message.

To enable Bob to send his encrypted messages, Alice transmits her public key n, e to Bob via a reliable, but not necessarily secret, route. Alice's private key d is never distributed. He then computes the ciphertext c, using Alice's public key e, corresponding to c.Oct 08,  · This feature is not available right now.

Please try again later. The Chinese remainder theorem is a theorem of number theory, which 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..

The theorem was first discovered in the 3rd century AD by the. The Chinese remainder theorem is a theorem of number theory, which 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. History; Actions. Chinese remainder theorem.

## Propositional Logic | Internet Encyclopedia of Philosophy

From Encyclopedia of Mathematics. Jump to: navigation, search. In this form the Chinese remainder theorem was known in . We know by the theory of Chinese Remainder Theorem that this solution is unique congruent modulo (3x5x7=). Hence + 8 x = is also a solution and indeed the most likely one since it is estimated that soldiers died.

RSA (Rivest–Shamir–Adleman) is one of the first public-key cryptosystems and is widely used for secure data transmission. In such a cryptosystem, the encryption key is public and it is different from the decryption key which is kept secret (private).

In RSA, this asymmetry is based on the practical difficulty of the factorization of the product of two large prime numbers, the "factoring.

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