Updated

Signed-off-by: Marcin Woźniak <y0rune@aol.com>

2-lab/module1.py

@@ -0,0 +1,145 @@
+import random
+
+def extendedEuclidean(x, N):
+    A, B = N, x
+    U, V = 0, 1
+    while True:
+        q = A//B
+        temp1, temp2 = B, A + (-q * B)
+        A, B = temp1, temp2
+        temp1, temp2 = V, U + (-q * V)
+        U, V = temp1, temp2
+        if B == 0:
+            break
+    d, u = A, U
+    v = (d - x * u) // N
+    return (u, v, d)
+
+print(extendedEuclidean(10,13))
+
+# Zadanie 1
+def generateRandomInteger(n, k):
+    try:
+        assert k > 0, "You need at least one bit to write an integer"
+        assert n > 0, "Cannot divide by 0"
+        if k == 1:
+            minValue = 0
+            maxValue = 1
+        else:
+            assert 2**(k-1) < n, "No numbers to choose from"
+            minValue = 2**(k-1)
+            maxValue = (2**k)-1
+        generator = random.SystemRandom()
+        while True:
+            randomNumber = generator.randint(minValue, maxValue)
+            if randomNumber < n:
+                break
+        print(randomNumber)
+    except AssertionError as error:
+        print("Error: {}".format(error))
+        main()
+
+# Zadanie 2
+def inverseValueInPhi(n, b):
+    value = 0
+    found = False
+    for i in range(1, n):
+        value = (i * b) % n
+        if value == 1:
+            if extendedEuclidean(n, value)[2] == 1:
+                found = True
+                value = i
+                break
+    if found:
+        print("Result: {}".format(value))
+    else:
+        print("Result: No inverse number exists")
+
+# Zadanie 3
+def exponentialSquaring(n, k, b):
+    temp = 1
+    while (k > 0):
+        if (k % 2 != 0):
+            temp = (temp * b) % n
+        b = (b * b) % n
+        k = k // 2
+    return(temp % n)
+
+# Zadanie 4
+def quadricResidue(p, b):
+    try:
+        assert p > 2, "p must be higher than 2"
+        if exponentialSquaring(p, (p-1)/2, b) == 1:
+            return True
+        else:
+            return False
+    except AssertionError as error:
+        print("Error: {}".format(error))
+        main()
+
+# Zadanie 5
+def squareRoot(p, b):
+    try:
+        assert p % 4 == 3, "p mod 4 != 3"
+        assert quadricResidue(p, b), "b is not a quadric residue in p"
+        print("{}" . format(p))
+        for i in range(0, p):
+            a = exponentialSquaring(p, (p+1)//4, i)
+            print("%d %d %d" % (i, a, b, ))
+            if a == b:
+                return("Result: {}".format(i))
+        return False
+    except AssertionError as error:
+        print("Error: {}".format(error))
+        main()
+
+# Zadanie 6
+def primalityTest(n):
+    if n == 1:
+        return False
+    if n == 2 or n == 3:
+        return True
+    generator = random.SystemRandom()
+    counter = generator.randint(n//2, n)
+    while(counter != 0):
+        b = generator.randint(2, n-2)
+        if exponentialSquaring(n, n-1, b) != 1:
+            return False
+        counter = counter - 1
+    return True
+
+# User interface
+def main():
+    while True:
+        print("""
+              Choose function:
+              Type "1 n k" for generateRandomInteger(n,k)
+              Type "2 n b" for inverseValueInPhi(n, b)
+              Type "3 n k b" for exponentialSquaring(n, k, b)
+              Type "4 p b" for quadricResidue(p, b)
+              Type "5 p b" for squareRoot(p,b)
+              Type "6 n" for primalityTest(n)
+              Type "exit" to end program's execution
+              """)
+        userInput = input("Choose desired action: ")
+        if userInput == "exit":
+                exit()
+        userInput = list(map(int, userInput.split(" ")))
+        if userInput[0] == 1:
+            for i in range(0, int(input("How many times to run the function?: "))):
+                  generateRandomInteger(userInput[1], userInput[2])
+        elif userInput[0] == 2:
+            inverseValueInPhi(userInput[1], userInput[2])
+        elif userInput[0] == 3:
+            print("Result: {}".format(exponentialSquaring(userInput[1], userInput[2], userInput[3])))
+        elif userInput[0] == 4:
+            print("Result: {}".format(quadricResidue(userInput[1], userInput[2])))
+        elif userInput[0] == 5:
+            print(squareRoot(userInput[1], userInput[2]))
+        elif userInput[0] == 6:
+            print("Result: {}".format(primalityTest(userInput[1])))
+        else:
+            print("Error: Wrong instruction. Try again")
+
+if __name__ == "__main__":
+    main()