refactoring II

LP/utils.py

@@ -0,0 +1,122 @@
+#!/usr/bin/env python3
+# -*- coding: UTF-8 -*-
+import math
+
+
+def is_prime(num):
+    if isinstance(num, str):
+        num = int(num)
+    if num in [2, 3, 5]:
+        return True
+    if num & 1 and num % 5 > 0:
+        for i in range(2, math.floor(math.sqrt(num)) + 1):
+            if i & 1 and (num % i) == 0:
+                return False
+        return True
+    return False
+
+
+def rev(num):  # or int(str(num)[::-1])
+    if isinstance(num, str):
+        num = int(num)
+    revs = 0
+    while (num > 0):
+        remainder = num % 10
+        revs = (revs * 10) + remainder
+        num = num // 10
+    return revs
+
+
+def is_emirp(num):
+    return is_prime(rev(num))
+
+
+def power(x, y, p):
+    res = 1
+    x %= p
+    while (y > 0):
+        if (y & 1):
+            res = (res * x) % p
+        y = y >> 1
+        x = (x * x) % p
+    return res
+
+
+def sqrtNormal(n, p):
+    n %= p
+    for x in range(2, p):
+        if ((x * x) % p == n):
+            return x
+    return None
+
+
+# Assumption: p is of the form 3*i + 4 where i >= 1
+def sqrtFast(n, p):
+    if (p % 4 != 3):
+        # raise ValueError('Invalid Input')
+        return sqrtNormal(n, p)
+    # Try "+(n ^ ((p + 1)/4))"
+    n = n % p
+    x = power(n, (p + 1) // 4, p)
+    if ((x * x) % p == n):
+        return x
+    # Try "-(n ^ ((p + 1)/4))"
+    x = p - x
+    if ((x * x) % p == n):
+        return x
+    return None
+
+
+def elliptic_curve(x, a, b, r):
+    y2 = (x ** 3 + a * x + b) % r
+    y = sqrtFast(y2, r) if y2 > 0 else 0
+    if y is None:
+        return None, None
+    return y, -y % r
+
+
+AFFINE_INV = None
+
+
+def affine_inverse(s, n=29):
+    def fn(s, n):
+        g = [n, s]
+        u = [1, 0]
+        v = [0, 1]
+        y = [None]
+        i = 1
+        while g[i] != 0:
+            y.append(g[i - 1] // g[i])
+            g.append(g[i - 1] - y[i] * g[i])
+            u.append(u[i - 1] - y[i] * u[i])
+            v.append(v[i - 1] - y[i] * v[i])
+            i += 1
+        return v[-2] % n
+
+    global AFFINE_INV
+    if AFFINE_INV is None:
+        AFFINE_INV = [fn(x, n) for x in range(n)]
+    return AFFINE_INV[s]
+
+
+def affine_decrypt(x, key, n=29):  # key: (s, t)
+    return ((x - key[1]) * affine_inverse(key[0], n)) % n
+
+
+def autokey_reverse(data, keylen, pos, search_term):
+    ret = [29] * keylen
+    for o in range(len(search_term)):
+        plain = search_term[o]
+        i = pos + o
+        while i >= 0:
+            plain = (data[i] - plain) % 29
+            i -= keylen
+        ret[i + keylen] = plain
+    return ret
+
+
+if __name__ == '__main__':
+    alphabet = 'ABCDEFGHIJKLMNOPQRSTUVWXYZ'
+    cipher = 'YDIDWYASDDJVAPJMMBIASDTJVAMD'
+    indices = [affine_decrypt(alphabet.index(x), (5, 9), 26) for x in cipher]
+    print(''.join(alphabet[x] for x in indices))