What is the Chinese remainder theorem explain with example?

What is the Chinese remainder theorem explain with example?

For example, if we know that the remainder of n divided by 3 is 2, the remainder of n divided by 5 is 3, and the remainder of n divided by 7 is 2, then without knowing the value of n, we can determine that the remainder of n divided by 105 (the product of 3, 5, and 7) is 23.

What is the main contribution of Chinese remainder theorem?

Chinese remainder theorem, ancient theorem that gives the conditions necessary for multiple equations to have a simultaneous integer solution. The theorem has its origin in the work of the 3rd-century-ad Chinese mathematician Sun Zi, although the complete theorem was first given in 1247 by Qin Jiushao.

How is Chinese remainder theorem used in cryptography?

The proposed encryption technique uses Chinese Remainder Theorem (CRT) and hash map to generate and distribute secret co-prime keys to participants. The proposed technique not only increases randomness in encrypted image but also compresses the image, resulting in easy storage and fast transmission.

Which of the following statement about Chinese remainder theorem is correct Mcq?

Explanation: To apply Chinese remainder theorem, moduli of linear congruence should be co-prime. Hence this is the correct statement. A number is called modulus if the sum or if a difference of two numbers is integrally divisible by that number.

What are the last two digits of 49 19 using Chinese remainder theorem?

The Chinese remainder theorem provides with a unique solution to simultaneous linear congruences with the coprime modulo. The modulo generally being 100. Hence, the last two digits of 49^19 is 49.

Is Chinese remainder theorem unique?

The Chinese remainder theorem is a theorem which gives a unique solution to simultaneous linear congruences with coprime moduli.

Is Chinese remainder theorem if and only if?

The Chinese remainder theorem (CRT) asserts that there is a unique class a + NZ so that x solves the system (2) if and only if x ∈ a + NZ, i.e. x ≡ a(mod N). Thus the system (2) is equivalent to a single congruence modulo N.

What is Chinese remainder theorem in cryptography and network security?

One of the most useful results of number theory is the Chinese remainder theorem (CRT). In essence, the CRT says it is possible to reconstruct integers in a certain range from their residues modulo a set of pairwise relatively prime moduli.

What is DES algorithm in cryptography?

The DES (Data Encryption Standard) algorithm is a symmetric-key block cipher created in the early 1970s by an IBM team and adopted by the National Institute of Standards and Technology (NIST). The algorithm takes the plain text in 64-bit blocks and converts them into ciphertext using 48-bit keys.

What is remainder theorem maths?

Remainder Theorem is an approach of Euclidean division of polynomials. According to this theorem, if we divide a polynomial P(x) by a factor ( x – a); that isn’t essentially an element of the polynomial; you will find a smaller polynomial along with a remainder.