ALL the CTFS of Crypto2025 finally

crypto-asimmetric/inferious_prime/Arithmetic.py

@@ -0,0 +1,97 @@
+#!/usr/bin/env python3
+
+'''
+Created on Dec 22, 2011
+
+@author: pablocelayes
+'''
+
+def egcd(a,b):
+    '''
+    Extended Euclidean Algorithm
+    returns x, y, gcd(a,b) such that ax + by = gcd(a,b)
+    '''
+    u, u1 = 1, 0
+    v, v1 = 0, 1
+    while b:
+        q = a // b
+        u, u1 = u1, u - q * u1
+        v, v1 = v1, v - q * v1
+        a, b = b, a - q * b
+    return u, v, a
+
+def gcd(a,b):
+    '''
+    2.8 times faster than egcd(a,b)[2]
+    '''
+    a,b=(b,a) if a<b else (a,b)
+    while b:
+        a,b=b,a%b
+    return a
+
+def modInverse(e,n):
+    '''
+    d such that de = 1 (mod n)
+    e must be coprime to n
+    this is assumed to be true
+    '''
+    return egcd(e,n)[0]%n
+
+def totient(p,q):
+    '''
+    Calculates the totient of pq
+    '''
+    return (p-1)*(q-1)
+
+def bitlength(x):
+    '''
+    Calculates the bitlength of x
+    '''
+    assert x >= 0
+    n = 0
+    while x > 0:
+        n = n+1
+        x = x>>1
+    return n
+
+
+def isqrt(n):
+    '''
+    Calculates the integer square root
+    for arbitrary large nonnegative integers
+    '''
+    if n < 0:
+        raise ValueError('square root not defined for negative numbers')
+
+    if n == 0:
+        return 0
+    a, b = divmod(bitlength(n), 2)
+    x = 2**(a+b)
+    while True:
+        y = (x + n//x)//2
+        if y >= x:
+            return x
+        x = y
+
+
+def is_perfect_square(n):
+    '''
+    If n is a perfect square it returns sqrt(n),
+
+    otherwise returns -1
+    '''
+    h = n & 0xF; #last hexadecimal "digit"
+
+    if h > 9:
+        return -1 # return immediately in 6 cases out of 16.
+
+    # Take advantage of Boolean short-circuit evaluation
+    if ( h != 2 and h != 3 and h != 5 and h != 6 and h != 7 and h != 8 ):
+        # take square root if you must
+        t = isqrt(n)
+        if t*t == n:
+            return t
+        else:
+            return -1
+
+    return -1