Mathematical Foundations for Asymmetric
نویسنده
چکیده
1.2 Algorithm for GCD The Euclidean algorithm is a simple algorithm for finding the gcd of two numbers. The basis of the algorithm is the fact that if a = qb+ c, a, q, b, c ∈ Z,⇒ (a, b) = (b, c). (4) This is very easy to see. Let s = (a, b)⇒ s|a, s|b⇒ a = sa1, b = sb1 t = (b, c)⇒ t|b, t|c⇒ b = tb2, c = tc2 Also c = a− qb = s(a1 − qb1)⇒ s|c Also as s|b (as s is the gcd of (a, b), s divides b and c. As the greatest number to divide both b and c is t, we have s ≤ t. (5)
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