feat: added a few algorithms that will be used for rewriting RSA algorithm that currently fails the tests (#288)

* feat: added a few algorithms that will be used for rsa algorithm

* fix: renamed the directory for better import string organisation

* fix: rename of a file

* updating DIRECTORY.md

* fix: corrected the mistakes in the documetation comments of some code

* fix: missplelling

* fix: spelling errors

* fix: reduced cyclomatic complexity

Co-authored-by: github-actions <${GITHUB_ACTOR}@users.noreply.github.com>

Author: tjgurwara99

DIRECTORY.md

@@ -104,15 +104,19 @@
   * Gcd
     * [Gcd](https://github.com/TheAlgorithms/Go/blob/master/math/gcd/gcd.go)
     * [Gcd Test](https://github.com/TheAlgorithms/Go/blob/master/math/gcd/gcd_test.go)
+    * [Gcditerative](https://github.com/TheAlgorithms/Go/blob/master/math/gcd/gcditerative.go)
+  * Lcm
+    * [Lcm](https://github.com/TheAlgorithms/Go/blob/master/math/lcm/lcm.go)
   * Modulararithmetic
     * [Modularexponentiation](https://github.com/TheAlgorithms/Go/blob/master/math/modulararithmetic/modularexponentiation.go)
     * [Modularexponentiation Test](https://github.com/TheAlgorithms/Go/blob/master/math/modulararithmetic/modularexponentiation_test.go)
   * Power
     * [Fastexponent](https://github.com/TheAlgorithms/Go/blob/master/math/power/fastexponent.go)
     * [Fastexponent Test](https://github.com/TheAlgorithms/Go/blob/master/math/power/fastexponent_test.go)
-  * Primecheck
-    * [Primecheck](https://github.com/TheAlgorithms/Go/blob/master/math/primecheck/primecheck.go)
-    * [Primecheck Test](https://github.com/TheAlgorithms/Go/blob/master/math/primecheck/primecheck_test.go)
+  * Prime
+    * [Millerrabinprimalitytest](https://github.com/TheAlgorithms/Go/blob/master/math/prime/millerrabinprimalitytest.go)
+    * [Prime Test](https://github.com/TheAlgorithms/Go/blob/master/math/prime/prime_test.go)
+    * [Primecheck](https://github.com/TheAlgorithms/Go/blob/master/math/prime/primecheck.go)
   * Pythagoras
     * [Pythagoras](https://github.com/TheAlgorithms/Go/blob/master/math/pythagoras/pythagoras.go)
     * [Pythagoras Test](https://github.com/TheAlgorithms/Go/blob/master/math/pythagoras/pythagoras_test.go)

ciphers/polybius/polybius_test.go

@@ -45,7 +45,7 @@ func TestNewPolybius(t *testing.T) {
 		wantErr    string
 	}{
 		{
-			name: "correct initalization", size: 5, characters: "HogeF", key: "abcdefghijklmnopqrstuvwxy", wantErr: "",
+			name: "correct initialization", size: 5, characters: "HogeF", key: "abcdefghijklmnopqrstuvwxy", wantErr: "",
 		},
 		{
 			name: "truncate characters", size: 5, characters: "HogeFuga", key: "abcdefghijklmnopqrstuvwxy", wantErr: "",

math/gcd/gcd.go

@@ -1,9 +1,9 @@
 package gcd
 
-// Gcd finds and returns the greatest common divisor of a given integer.
-func Gcd(a, b int) int {
+// Recursive finds and returns the greatest common divisor of a given integer.
+func Recursive(a, b int64) int64 {
 	if b == 0 {
 		return a
 	}
-	return Gcd(b, a%b)
+	return Recursive(b, a%b)
 }

math/gcd/gcd_test.go

@@ -2,30 +2,48 @@ package gcd
 
 import "testing"
 
+type testFunction func(int64, int64) int64
+
 var testCases = []struct {
 	name   string
-	a      int
-	b      int
-	output int
+	a      int64
+	b      int64
+	output int64
 }{
 	{"gcd of 10 and 0", 10, 0, 10},
 	{"gcd of 98 and 56", 98, 56, 14},
 	{"gcd of 0 and 10", 0, 10, 10},
 }
 
-func TestGCD(t *testing.T) {
+func TemplateTestGCD(t *testing.T, f testFunction) {
 	for _, tc := range testCases {
 		t.Run(tc.name, func(t *testing.T) {
-			actual := Gcd(tc.a, tc.b)
+			actual := f(tc.a, tc.b)
 			if actual != tc.output {
 				t.Errorf("Expected GCD of %d and %d to be: %v, but got: %d", tc.a, tc.b, tc.output, actual)
 			}
 		})
 	}
 }
 
-func BenchmarkGCD(b *testing.B) {
+func TestGCDRecursive(t *testing.T) {
+	TemplateTestGCD(t, Recursive)
+}
+
+func TestGCDIterative(t *testing.T) {
+	TemplateTestGCD(t, Iterative)
+}
+
+func TemplateBenchmarkGCD(b *testing.B, f testFunction) {
 	for i := 0; i < b.N; i++ {
-		Gcd(98, 56)
+		f(98, 56)
 	}
 }
+
+func BenchmarkGCDRecursive(b *testing.B) {
+	TemplateBenchmarkGCD(b, Recursive)
+}
+
+func BenchmarkGCDIterative(b *testing.B) {
+	TemplateBenchmarkGCD(b, Iterative)
+}

math/gcd/gcditerative.go

@@ -0,0 +1,9 @@
+package gcd
+
+// Iterative Faster iterative version of GcdRecursive without holding up too much of the stack
+func Iterative(a, b int64) int64 {
+	for b != 0 {
+		a, b = b, a%b
+	}
+	return a
+}

math/lcm/lcm.go

@@ -0,0 +1,12 @@
+package lcm
+
+import (
+	"math"
+
+	"github.com/TheAlgorithms/Go/math/gcd"
+)
+
+// Lcm returns the lcm of two numbers using the fact that lcm(a,b) * gcd(a,b) = | a * b |
+func Lcm(a, b int64) int64 {
+	return int64(math.Abs(float64(a*b)) / float64(gcd.Iterative(a, b)))
+}

math/modulararithmetic/modularexponentiation_test.go

@@ -66,12 +66,12 @@ func TestModularExponentiation(t *testing.T) {
 			result, err := ModularExponentiation(test.base, test.exponent, test.mod)
 			if err != test.expectedError {
 				t.Logf("Test Failed for %s", test.name)
-				t.Logf("Unexpected error occured")
-				t.Errorf("Expected error: %v, Recieved error: %v", test.expectedError, err)
+				t.Logf("Unexpected error occurred")
+				t.Errorf("Expected error: %v, Received error: %v", test.expectedError, err)
 			}
 			if result != test.expected {
 				t.Logf("Test Failed for %s", test.description)
-				t.Fatalf("Expected: %d, Recieved: %d", test.expected, result)
+				t.Fatalf("Expected: %d, Received: %d", test.expected, result)
 			}
 		})
 	}

math/prime/millerrabinprimalitytest.go

@@ -0,0 +1,73 @@
+package prime
+
+import (
+	"math/rand"
+
+	"github.com/TheAlgorithms/Go/math/modulararithmetic"
+)
+
+// findD accepts a number and returns the
+// odd number d such that num = 2^r * d - 1
+func findRD(num int64) (int64, int64) {
+	r := int64(0)
+	d := num - 1
+	for num%2 == 0 {
+		d /= 2
+		r++
+	}
+	return d, r
+}
+
+// MillerTest This is the intermediate step that repeats within the
+// miller rabin primality test for better probabilitic chances of
+// receiving the correct result.
+func MillerTest(d, num int64) (bool, error) {
+	random := rand.Int63n(num-1) + 2
+
+	res, err := modulararithmetic.ModularExponentiation(random, d, num)
+
+	if err != nil {
+		return false, err
+	}
+	// miller conditions checks
+	if res == 1 || res == num-1 {
+		return true, nil
+	}
+
+	for d != num-1 {
+		res = (res * res) % num
+		d *= 2
+		if res == 1 {
+			return false, nil
+		}
+		if res == num-1 {
+			return true, nil
+		}
+	}
+	return false, nil
+}
+
+// MillerRabinTest Probabilistic test for primality of an integer based of the algorithm devised by Miller and Rabin.
+func MillerRabinTest(num, rounds int64) (bool, error) {
+	if num <= 4 {
+		if num == 2 || num == 3 {
+			return true, nil
+		}
+		return false, nil
+	}
+	if num%2 == 0 {
+		return false, nil
+	}
+	d, _ := findRD(num)
+
+	for i := int64(0); i < rounds; i++ {
+		val, err := MillerTest(d, num)
+		if err != nil {
+			return false, err
+		}
+		if !val {
+			return false, nil
+		}
+	}
+	return true, nil
+}

math/primecheck/primecheck_test.go renamed to math/prime/prime_test.go

@@ -1,4 +1,4 @@
-package primecheck
+package prime
 
 import (
 	"testing"
@@ -49,6 +49,33 @@ func TestTablePairApproach(t *testing.T) {
 
 }
 
+func TestMillerRabinTest(t *testing.T) {
+	var tests = []struct {
+		name     string
+		input    int64
+		expected bool
+		rounds   int64
+		err      error
+	}{
+		{"smallest prime", 2, true, 5, nil},
+		{"random prime", 3, true, 5, nil},
+		{"neither prime nor composite", 1, false, 5, nil},
+		{"random non-prime", 10, false, 5, nil},
+		{"another random prime", 23, true, 5, nil},
+	}
+	for _, test := range tests {
+		t.Run(test.name, func(t *testing.T) {
+			output, err := MillerRabinTest(test.input, test.rounds)
+			if err != test.err {
+				t.Errorf("For input: %d, unexpected error: %v, expected error: %v", test.input, err, test.err)
+			}
+			if output != test.expected {
+				t.Errorf("For input: %d, expected: %v", test.input, output)
+			}
+		})
+	}
+}
+
 func BenchmarkNaiveApproach(b *testing.B) {
 	for i := 0; i < b.N; i++ {
 		NaiveApproach(23)

math/primecheck/primecheck.go renamed to math/prime/primecheck.go

@@ -1,4 +1,4 @@
-package primecheck
+package prime
 
 // A primality test is an algorithm for determining whether an input number is prime.Among other fields of mathematics, it is used for cryptography.
 //Unlike integer factorization, primality tests do not generally give prime factors, only stating whether the input number is prime or not.