some math scripts

Cryptography/tools/finding_gcd.py

@@ -0,0 +1,26 @@
+#!/usr/bin/python
+
+
+def finding_gcd(a, b):
+    ''' implements the greatest common divider algorithm '''
+    while(b != 0):
+        result = b
+        a, b = b, a % b        
+    return result
+
+
+def test_finding_gcd():
+    number1 = 21
+    number2 = 12
+    assert(finding_gcd(number1, number2) == 3)
+    print('Tests passed!')
+
+if __name__ == '__main__':
+    test_finding_gcd()
+
+
+
+    
+    
+    
+    

Cryptography/tools/finding_if_prime.py

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+#!/usr/bin/python
+
+import math
+import random
+
+def finding_prime(number):
+    ''' find whether a number is prime in a simple way'''
+    num = abs(number)
+    if num < 4 : return True
+    for x in range(2, num):
+        if num % x == 0:
+            return False
+    return True
+       
+
+def finding_prime_sqrt(number):
+    ''' find whether a number is prime as soon as it rejects all candidates up to sqrt(n) '''
+    num = abs(number)
+    if num < 4 : return True
+    for x in range(2, int(math.sqrt(num)) + 1):
+        if number % x == 0:
+            return False
+    return True
+
+
+def finding_prime_fermat(number):
+    ''' find whether a number is prime with Fermat's theorem, using probabilistic tests '''
+    if number <= 102:
+        for a in range(2, number):
+            if pow(a, number- 1, number) != 1:
+                return False
+        return True
+    else:
+        for i in range(100):
+            a = random.randint(2, number - 1)
+            if pow(a, number - 1, number) != 1:
+                return False
+        return True
+
+
+
+def test_finding_prime():
+    number1 = 17
+    number2 = 20
+    assert(finding_prime(number1) == True)
+    assert(finding_prime(number2) == False)
+    assert(finding_prime_sqrt(number1) == True)
+    assert(finding_prime_sqrt(number2) == False)
+    assert(finding_prime_fermat(number1) == True)
+    assert(finding_prime_fermat(number2) == False)
+    print('Tests passed!')
+
+
+if __name__ == '__main__':
+    test_finding_prime()
+
+

Cryptography/tools/generate_prime.py

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+#!/usr/bin/python
+
+import math
+import random
+import sys
+from finding_prime import finding_prime_sqrt
+
+
+def generate_prime(number=3):
+    ''' return a n-bit prime '''
+    while 1:
+        p = random.randint(pow(2, number-2), pow(2, number-1)-1)
+        p = 2 * p + 1
+        if finding_prime_sqrt(p):
+            return p
+
+
+if __name__ == '__main__':
+    if len(sys.argv) < 2:
+        print ("Usage: generate_prime.py number")
+        sys.exit()
+    else:
+        number = int(sys.argv[1])
+        print(generate_prime(number))
+
+
+
+
+
+
+
+
+

Cryptography/tools/quick_select.py

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+def quickSelect(seq, k):
+    # this part is the same as quick sort
+    len_seq = len(seq)
+    if len_seq < 2: return seq
+
+    ipivot = len_seq // 2
+    pivot = seq[ipivot]
+
+    smallerList = [x for i,x in enumerate(seq) if x <= pivot and  i != ipivot]
+    largerList = [x for i,x in enumerate(seq) if x > pivot and  i != ipivot]
+
+    # here starts the different part
+    m = len(smallerList)
+    if k == m:
+        return pivot
+    elif k < m:
+        return quickSelect(smallerList, k)
+    else:
+        return quickSelect(largerList, k-m)
+
+
+
+
+if __name__ == '__main__':
+    # Checking the Answer
+    seq = [10, 60, 100, 50, 60, 75, 31, 50, 30, 20, 120, 170, 200]
+
+    # we want the middle element
+    k = len(seq) // 2
+
+    # Note that this only work for odd arrays, since median in
+    # even arrays is the mean of the two middle elements
+    print(quickSelect(seq, k))
+    import numpy
+    print numpy.median(seq)