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What is the application of extended Euclidean algorithm?
The extended Euclidean algorithm is also the main tool for computing multiplicative inverses in simple algebraic field extensions. An important case, widely used in cryptography and coding theory, is that of finite fields of non-prime order.
What is the difference between Euclidean and extended Euclidean algorithm?
The Euclidean Algorithm is used to calculate the greatest common divisor of two numbers. The major difference between the two algorithms is that the Euclidean Algorithm is primarily used for manual calculations whereas the Extended Euclidean Algorithm is basically used in computer programs.
What is extended Euclidean algorithm RSA?
The extended Euclidean algorithm is essentially the Euclidean algorithm (for GCD’s) ran backwards. Your goal is to find d such that ed≡1(modφ(n)). And it’s easy to see that in this case, x=d. The value of y does not actually matter, since it will get eliminated modulo φ(n) regardless of its value.
How does extended algorithm work?
The extended Euclidean algorithm can be viewed as the reciprocal of modular exponentiation. By reversing the steps in the Euclidean algorithm, it is possible to find these integers x x x and y y y. The whole idea is to start with the GCD and recursively work our way backwards.
What is Euclidean algorithm used for?
In mathematics, the Euclidean algorithm, or Euclid’s algorithm, is an efficient method for computing the greatest common divisor (GCD) of two integers (numbers), the largest number that divides them both without a remainder.
How is Euclidean algorithm used in cryptography?
The Euclidean Algorithm finds the greatest common divisor of two integers a and b. We know that for integers a, b and c, if a | b and a | c, then a | (b + c). Therefore, any divisor of 287 and 91 must also be a divisor of 287 – 91*3 = 14.