## What is the application of extended Euclidean algorithm?

This process is called the extended Euclidean algorithm . It is used for finding the greatest common divisor of two positive integers a and b and writing this greatest common divisor as an integer linear combination of a and b .

## How do you use extended Euclidean algorithm for polynomials?

The Polynomial Euclidean Algorithm computes the greatest common divisor of two polynomials by performing repeated divisions with remainder. The algorithm is based on the following observation: If a = b q + r , then gcd ( a , b ) = gcd ( b , r ) .

**Is extended Euclidean algorithm polynomial time?**

Similarly, the polynomial extended Euclidean algorithm allows one to compute the multiplicative inverse in algebraic field extensions and, in particular in finite fields of non prime order. It follows that both extended Euclidean algorithms are widely used in cryptography.

**What is the significance of Extended Euclidean Algorithm with reference to RSA algorithm?**

Euclid algorithm and extended Euclid algorithm are the best algorithms to solve the public key and private key in RSA. Extended Euclid algorithm in IEEE P1363 is improved by eliminating the negative integer operation, which reduces the computing resources occupied by RSA, hence has an important application value.

### How do you find the HCF of two polynomials?

How to find the Highest Common Factor of Polynomials by Division Method?

- Let us take two polynomials f(x), g(x).
- Divide the polynomials f(x) / g(x) to get f(x) = g(x) * q(x) + r(x).
- If the remainder r(x) is zer0, then g(x) is the highest common factor of polynomials.

### Is GCD of polynomials unique?

It is unique up to a constant, i.e. if f,g are two polynomials, then there exist a unique “monic” gcd h such that any other gcd is a constant times h. Not quite, you can multiply the gcd with any non-zero element of the field and still have a gcd, but upto this association, the gcd is unique.

**What is Euclidean algorithm give example?**

The Euclidean algorithm is a way to find the greatest common divisor of two positive integers, a and b. First let me show the computations for a=210 and b=45. Divide 210 by 45, and get the result 4 with remainder 30, so 210=4·45+30. Divide 45 by 30, and get the result 1 with remainder 15, so 45=1·30+15.

**What is the use of extended Euclidean algorithm in RSA?**

#### Can the GCD of two polynomials be a constant?

#### What is the division algorithm for polynomials?

Quotient = x 2 − 7 x + 12 and remainder = 0. where r ( x ) = 0 or. The above result is called the Division Algorithm of Polynomials. If r ( x ) = 0 , then is called a factor of.

**What is Extended Euclidean Algorithm in cryptography?**

Extended Euclidean Algorithm is an extension of the Euclidean Algorithm that computes the greatest common divisor (GCD) of integers a and b. GCD is the largest integer that divides both a and b without any remainder.

**Where is RSA used?**

RSA is still seen in a range of web browsers, email, VPNs, chat and other communication channels. RSA is also often used to make secure connections between VPN clients and VPN servers. Under protocols like OpenVPN, TLS handshakes can use the RSA algorithm to exchange keys and establish a secure channel.

## What are the advantages of RSA algorithm?

Advantages of RSA It is very easy to implement RSA algorithm. RSA algorithm is safe and secure for transmitting confidential data. Cracking RSA algorithm is very difficult as it involves complex mathematics. Sharing public key to users is easy.

## How do you find the highest common factor of two polynomials?

Divide the polynomials f(x) / g(x) to get f(x) = g(x) * q(x) + r(x). Here the degree of g(x) > degree of r(x). If the remainder r(x) is zer0, then g(x) is the highest common factor of polynomials. If the remainder is not equal to zero, then again divide g(x) by r(x) to obtain g(x) = r(x) * q(x) + r1(x).