From 10105585e5272f301a1101986ad9927a8d646c12 Mon Sep 17 00:00:00 2001
From: Sandesh C <sandeshc13@gmail.com>
Date: Sat, 12 Nov 2016 03:13:47 +0530
Subject: [PATCH] pollard rho - 1 attack impl, basic version

---
 .gitignore          |  5 ++++
 README.md           |  3 ++
 pollardRhoAttack.py | 70 +++++++++++++++++++++++++++++++++++++++++++++
 3 files changed, 78 insertions(+)
 create mode 100644 .gitignore
 create mode 100644 README.md
 create mode 100644 pollardRhoAttack.py

diff --git a/.gitignore b/.gitignore
new file mode 100644
index 0000000..0df48dd
--- /dev/null
+++ b/.gitignore
@@ -0,0 +1,5 @@
+# compiled python files
+*.pyc
+
+# Ignored folders
+old/
\ No newline at end of file
diff --git a/README.md b/README.md
new file mode 100644
index 0000000..af002da
--- /dev/null
+++ b/README.md
@@ -0,0 +1,3 @@
+# Pollard's Rho - 1 Attack
+
+__Cryptography__ course, Term Project. Python implementation.
\ No newline at end of file
diff --git a/pollardRhoAttack.py b/pollardRhoAttack.py
new file mode 100644
index 0000000..87f9a69
--- /dev/null
+++ b/pollardRhoAttack.py
@@ -0,0 +1,70 @@
+import sys
+
+# Message Codes
+CODE_ARG     = 0
+CODE_FAIL    = 1
+
+# Message Texts
+MSG = []
+MSG.append('Number of Arguments does not match the Expected.' + \
+    '\nUsage: python pollardRhoAttack.py <N> <B>')
+MSG.append('FAILURE.' + \
+    '\nUnable to factorize the large prime.')
+
+if len(sys.argv) != 3:
+    exit(MSG[CODE_ARG])
+
+def gcd(a, b):
+    """ Returns gcd(a, b) """
+    """ Complexity: O( lg(max(a,b)) ) """
+    if a > b:
+        return gcd(b, a)
+
+    if a == 0:
+        return b
+
+    return gcd(b % a, a)
+
+def moduloPower(a, i, N):
+    """ Returns a**i (mod N) """
+    """ Complexity: O(  ) """
+    val = 1
+    while i > 0:
+        if i % 2:
+            val *= a
+            val %= N
+        a *= a
+        a %= N
+        i /= 2
+    return val
+
+def pollardRhoAttack(a, N, B):
+    """ Implementation of Pollard's Rho - 1 Attack """
+
+    # computing a**(B!) (mod N)
+    for i in range(2, B + 1):
+        a = moduloPower(a, i, N)
+
+    # computing gcd(a - 1, N)
+    d = gcd(a - 1, N)
+
+    if 1 < d and d < N:
+        print 'Prime Factorization of', N
+        print '(', d, ',', N/d, ')'
+        return True
+
+    # d = 1 or d = N
+    return False
+
+if __name__ == '__main__':
+    ### "base" for the attack
+    a = 2
+
+    ### large prime to factorize
+    N = int( sys.argv[1] )
+
+    ### "bound" for the attack
+    B = int( sys.argv[2] )
+
+    if not pollardRhoAttack(a, N, B):
+        print MSG[CODE_FAIL]
\ No newline at end of file