Merge pull request #206 from Mukulbaid63/pf_2

Euclid's Algorithm added

Author: balapriyac

Java/Euclid's GCD Algorithm/Euclid.java

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+// Java program to demonstrate working of extended 
+import java.util.*; 
+import java.io.*; 
+
+class Euclid 
+{   
+    /*Recursive function to calculate gcd using Euclid's algo*/
+	public static int gcd(int a,int b) 
+	{ 
+		if (a==0) 
+			return b; 
+
+		return gcd(b%a, a); 
+	} 
+
+    public static void main(String[] args) 
+	{ 
+        Scanner sc=new Scanner(System.in);
+
+        /*Taking a & b as user input*/
+		int a=sc.nextInt();
+        int b=sc.nextInt(); 
+		
+		System.out.println("GCD : " + gcd(a,b)); //Output
+
+	} 
+    
+} 
+

Java/Euclid's GCD Algorithm/README.md

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+
+# Sample Input:
+
+10 15
+
+  
+
+# Sample Output:
+
+5
+
+  
+
+# Sample Input:
+
+20 48
+
+  
+
+# Sample Output:
+
+4
+
+  
+
+# Explaination:
+TC 1:         
+ 10 = 2 * 5
+
+15 = 3 * 5
+
+The Greatest common divisor is 5
+
+  
+
+TC 2: 
+20 = 2 * 2 * 5
+
+48 = 2 * 2 * 2 * 2 * 3
+
+The Greatest common divisor is 2 * 2 = 4
+
+  
+
+The algorithm is based on below facts:
+
+  
+
+--If we subtract smaller number from larger (we reduce larger number), GCD doesn’t change. So if we keep subtracting repeatedly the larger of two, we end up with GCD.
+
+--Now instead of subtraction, if we divide smaller number, the algorithm stops when we find remainder 0.
+
+  
+
+# Time Complexity:
+
+<h3>O(log min(a,b))</h3>

Java/Euclid's GCD Algorithm/RelevanceInCryptography.md

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+# Relevance in Cryptography:
+RSA, which based on the great difficulty of integer factorization, is the most widely-used public-key cryptosystem used in electronic commerce. 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.
+
+
+