From de49afb7efe4710ff8e4f06f617dbf227b16c804 Mon Sep 17 00:00:00 2001
From: ABHIJIT MAGAPU <cb.en.p2cse19011@cb.students.amrita.edu>
Date: Tue, 28 Jul 2020 19:00:18 +0530
Subject: [PATCH] Upload New File
---
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create mode 100644 CB.EN.P2CSE19011-Diffie_Hellman_key_exchange.ipynb
diff --git a/CB.EN.P2CSE19011-Diffie_Hellman_key_exchange.ipynb b/CB.EN.P2CSE19011-Diffie_Hellman_key_exchange.ipynb
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@@ -0,0 +1,729 @@
+{
+ "cells": [
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "# Code for Finding a large prime number (min 20-digit) "
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {},
+ "outputs": [],
+ "source": [
+ "from random import randrange, getrandbits\n",
+ "def is_prime(n, k=128):\n",
+ " \"\"\" Test if a number is prime\n",
+ " Args:\n",
+ " n -- int -- the number to test\n",
+ " k -- int -- the number of tests to do\n",
+ " return True if n is prime\n",
+ " \"\"\"\n",
+ " # Test if n is not even.\n",
+ " # But care, 2 is prime !\n",
+ " if n == 2 or n == 3:\n",
+ " return True\n",
+ " if n <= 1 or n % 2 == 0:\n",
+ " return False\n",
+ " # find r and s\n",
+ " s = 0\n",
+ " r = n - 1\n",
+ " while r & 1 == 0:\n",
+ " s += 1\n",
+ " r //= 2\n",
+ " # do k tests\n",
+ " for _ in range(k):\n",
+ " a = randrange(2, n - 1)\n",
+ " x = pow(a, r, n)\n",
+ " if x != 1 and x != n - 1:\n",
+ " j = 1\n",
+ " while j < s and x != n - 1:\n",
+ " x = pow(x, 2, n)\n",
+ " if x == 1:\n",
+ " return False\n",
+ " j += 1\n",
+ " if x != n - 1:\n",
+ " return False\n",
+ " return True\n",
+ "def generate_prime_candidate(length):\n",
+ " \"\"\" Generate an odd integer randomly\n",
+ " Args:\n",
+ " length -- int -- the length of the number to generate, in bits\n",
+ " return a integer\n",
+ " \"\"\"\n",
+ " # generate random bits\n",
+ " p = getrandbits(length)\n",
+ " # apply a mask to set MSB and LSB to 1\n",
+ " p |= (1 << length - 1) | 1\n",
+ " return p\n",
+ "def generate_prime_number(length=60):\n",
+ " \"\"\" Generate a prime\n",
+ " Args:\n",
+ " length -- int -- length of the prime to generate, in bits\n",
+ " return a prime\n",
+ " \"\"\"\n",
+ " p = 4\n",
+ " # keep generating while the primality test fail\n",
+ " while not is_prime(p, 128):\n",
+ " p = generate_prime_candidate(length)\n",
+ " return p\n",
+ "print(generate_prime_number())"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "610292520201647"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "# Code for finding Primitive root "
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 1,
+ "metadata": {},
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "Smallest primitive root of 610292520201647 is 5\n"
+ ]
+ }
+ ],
+ "source": [
+ "# Python3 program to find primitive root \n",
+ "# of a given number n \n",
+ "from math import sqrt \n",
+ " \n",
+ "# Returns True if n is prime \n",
+ "def isPrime( n): \n",
+ " \n",
+ " # Corner cases \n",
+ " if (n <= 1): \n",
+ " return False\n",
+ " if (n <= 3): \n",
+ " return True\n",
+ " \n",
+ " # This is checked so that we can skip \n",
+ " # middle five numbers in below loop \n",
+ " if (n % 2 == 0 or n % 3 == 0): \n",
+ " return False\n",
+ " i = 5\n",
+ " while(i * i <= n): \n",
+ " if (n % i == 0 or n % (i + 2) == 0) : \n",
+ " return False\n",
+ " i = i + 6\n",
+ " \n",
+ " return True\n",
+ " \n",
+ "\"\"\" Iterative Function to calculate (x^n)%p \n",
+ " in O(logy) */\"\"\"\n",
+ "def power( x, y, p): \n",
+ " \n",
+ " res = 1 # Initialize result \n",
+ " \n",
+ " x = x % p # Update x if it is more \n",
+ " # than or equal to p \n",
+ " \n",
+ " while (y > 0): \n",
+ " \n",
+ " # If y is odd, multiply x with result \n",
+ " if (y & 1): \n",
+ " res = (res * x) % p \n",
+ " \n",
+ " # y must be even now \n",
+ " y = y >> 1 # y = y/2 \n",
+ " x = (x * x) % p \n",
+ " \n",
+ " return res \n",
+ " \n",
+ "# Utility function to store prime \n",
+ "# factors of a number \n",
+ "def findPrimefactors(s, n) : \n",
+ " \n",
+ " # Print the number of 2s that divide n \n",
+ " while (n % 2 == 0) : \n",
+ " s.add(2) \n",
+ " n = n // 2\n",
+ " \n",
+ " # n must be odd at this po. So we can \n",
+ " # skip one element (Note i = i +2) \n",
+ " for i in range(3, int(sqrt(n)), 2): \n",
+ " \n",
+ " # While i divides n, print i and divide n \n",
+ " while (n % i == 0) : \n",
+ " \n",
+ " s.add(i) \n",
+ " n = n // i \n",
+ " \n",
+ " # This condition is to handle the case \n",
+ " # when n is a prime number greater than 2 \n",
+ " if (n > 2) : \n",
+ " s.add(n) \n",
+ "\n",
+ "def findPrimitive( n) : \n",
+ " s = set() \n",
+ " \n",
+ " # Check if n is prime or not \n",
+ " if (isPrime(n) == False): \n",
+ " return -1\n",
+ " \n",
+ " # Find value of Euler Totient function \n",
+ " # of n. Since n is a prime number, the \n",
+ " # value of Euler Totient function is n-1 \n",
+ " # as there are n-1 relatively prime numbers. \n",
+ " phi = n - 1\n",
+ " \n",
+ " # Find prime factors of phi and store in a set \n",
+ " findPrimefactors(s, phi) \n",
+ " \n",
+ " # Check for every number from 2 to phi \n",
+ " for r in range(2, phi + 1): \n",
+ " \n",
+ " # Iterate through all prime factors of phi. \n",
+ " # and check if we found a power with value 1 \n",
+ " flag = False\n",
+ " for it in s: \n",
+ " \n",
+ " # Check if r^((phi)/primefactors) \n",
+ " # mod n is 1 or not \n",
+ " if (power(r, phi // it, n) == 1): \n",
+ " \n",
+ " flag = True\n",
+ " break\n",
+ " \n",
+ " # If there was no power with value 1. \n",
+ " if (flag == False): \n",
+ " return r \n",
+ " \n",
+ " # If no primitive root found \n",
+ " return -1\n",
+ "\n",
+ "n = 610292520201647\n",
+ "print(\"Smallest primitive root of\",n, \"is\", findPrimitive(n)) "
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "# Code for Diffie–Hellman"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 2,
+ "metadata": {},
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "g: 3 (a shared value), n: 610292520201647 (a prime number)\n",
+ "\n",
+ "Alice calculates:\n",
+ "a (Alice random): 37856\n",
+ "Alice value (A): 23079533594046 (g^a) mod p\n",
+ "\n",
+ "Bob calculates:\n",
+ "b (Bob random): 50018\n",
+ "Bob value (B): 69387698405719 (g^b) mod p\n",
+ "\n",
+ "Alice calculates:\n",
+ "Key: 573821206942293 (B^a) mod p\n",
+ "Key: f4cb54ce1c55e40a6482af8ee396da4f565d243f4532ad83d006dcf526499322\n",
+ "\n",
+ "Bob calculates:\n",
+ "Key: 573821206942293 (A^b) mod p\n",
+ "Key: f4cb54ce1c55e40a6482af8ee396da4f565d243f4532ad83d006dcf526499322\n"
+ ]
+ }
+ ],
+ "source": [
+ "import random\n",
+ "import hashlib\n",
+ "import sys\n",
+ "\n",
+ "g=3\n",
+ "p=610292520201647\n",
+ "\n",
+ "a=random.randint(10000,99999)\n",
+ "\n",
+ "b=random.randint(10000,99999)\n",
+ "\n",
+ "A = (g**a) % p\n",
+ "B = (g**b) % p\n",
+ "\n",
+ "print('g: ',g,' (a shared value), n: ',p, ' (a prime number)')\n",
+ "\n",
+ "print('\\nAlice calculates:')\n",
+ "print('a (Alice random): ',a)\n",
+ "print('Alice value (A): ',A,' (g^a) mod p')\n",
+ "\n",
+ "print('\\nBob calculates:')\n",
+ "print('b (Bob random): ',b)\n",
+ "print('Bob value (B): ',B,' (g^b) mod p')\n",
+ "\n",
+ "print('\\nAlice calculates:')\n",
+ "keyA=(B**a) % p\n",
+ "print('Key: ',keyA,' (B^a) mod p')\n",
+ "print('Key: ',hashlib.sha256(str(keyA).encode()).hexdigest())\n",
+ "\n",
+ "print('\\nBob calculates:')\n",
+ "keyB=(A**b) % p\n",
+ "print('Key: ',keyB,' (A^b) mod p')\n",
+ "print('Key: ',hashlib.sha256(str(keyB).encode()).hexdigest())"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "# Code to Find an integer k such that where a and m are relatively prime."
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 17,
+ "metadata": {},
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "2\n",
+ "1\n"
+ ]
+ }
+ ],
+ "source": [
+ "# Python3 program to calculate \n",
+ "# discrete logarithm \n",
+ "import math; \n",
+ "\n",
+ "# Iterative Function to calculate \n",
+ "# (x ^ y)%p in O(log y) \n",
+ "def powmod(x, y, p): \n",
+ "\n",
+ "\tres = 1; # Initialize result \n",
+ "\n",
+ "\tx = x % p; # Update x if it is more \n",
+ "\t\t\t# than or equal to p \n",
+ "\n",
+ "\twhile (y > 0): \n",
+ "\t\t\n",
+ "\t\t# If y is odd, multiply x with result \n",
+ "\t\tif (y & 1): \n",
+ "\t\t\tres = (res * x) % p; \n",
+ "\n",
+ "\t\t# y must be even now \n",
+ "\t\ty = y >> 1; # y = y/2 \n",
+ "\t\tx = (x * x) % p; \n",
+ "\treturn res; \n",
+ "\n",
+ "# Function to calculate k for given a, b, m \n",
+ "def discreteLogarithm(a, b, m): \n",
+ "\tn = int(math.sqrt(m) + 1); \n",
+ "\n",
+ "\tvalue = [0] * m; \n",
+ "\n",
+ "\t# Store all values of a^(n*i) of LHS \n",
+ "\tfor i in range(n, 0, -1): \n",
+ "\t\tvalue[ powmod (a, i * n, m) ] = i; \n",
+ "\n",
+ "\tfor j in range(n): \n",
+ "\t\t\n",
+ "\t\t# Calculate (a ^ j) * b and check \n",
+ "\t\t# for collision \n",
+ "\t\tcur = (powmod (a, j, m) * b) % m; \n",
+ "\n",
+ "\t\t# If collision occurs i.e., LHS = RHS \n",
+ "\t\tif (value[cur]): \n",
+ "\t\t\tans = value[cur] * n - j; \n",
+ "\t\t\t\n",
+ "\t\t\t# Check whether ans lies below m or not \n",
+ "\t\t\tif (ans < m): \n",
+ "\t\t\t\treturn ans; \n",
+ "\t\n",
+ "\treturn -1; \n",
+ "\n",
+ "# Driver code \n",
+ "a = 610292520201647; \n",
+ "b = 12542369; \n",
+ "m = 5; \n",
+ "print(discreteLogarithm(a, b, m)); \n",
+ "\n",
+ "a = 610292520201647; \n",
+ "b = 1852642; \n",
+ "m = 5; \n",
+ "print(discreteLogarithm(a, b, m)); \n",
+ "\n",
+ "# This code is contributed by mits \n"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "# Applying this code to see how long it takes to break your chosen 3 keys. Record your observation as shown in the table(min 3 (p,g) values and for each (p,g) 3 private keys (weak, medium strong and strong) "
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 1,
+ "metadata": {},
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "2\n",
+ "1\n"
+ ]
+ }
+ ],
+ "source": [
+ "# Python3 program to calculate \n",
+ "# discrete logarithm \n",
+ "import math; \n",
+ "\n",
+ "# Iterative Function to calculate \n",
+ "# (x ^ y)%p in O(log y) \n",
+ "def powmod(x, y, p): \n",
+ "\n",
+ "\tres = 1; # Initialize result \n",
+ "\n",
+ "\tx = x % p; # Update x if it is more \n",
+ "\t\t\t# than or equal to p \n",
+ "\n",
+ "\twhile (y > 0): \n",
+ "\t\t\n",
+ "\t\t# If y is odd, multiply x with result \n",
+ "\t\tif (y & 1): \n",
+ "\t\t\tres = (res * x) % p; \n",
+ "\n",
+ "\t\t# y must be even now \n",
+ "\t\ty = y >> 1; # y = y/2 \n",
+ "\t\tx = (x * x) % p; \n",
+ "\treturn res; \n",
+ "\n",
+ "# Function to calculate k for given a, b, m \n",
+ "def discreteLogarithm(a, b, m): \n",
+ "\tn = int(math.sqrt(m) + 1); \n",
+ "\n",
+ "\tvalue = [0] * m; \n",
+ "\n",
+ "\t# Store all values of a^(n*i) of LHS \n",
+ "\tfor i in range(n, 0, -1): \n",
+ "\t\tvalue[ powmod (a, i * n, m) ] = i; \n",
+ "\n",
+ "\tfor j in range(n): \n",
+ "\t\t\n",
+ "\t\t# Calculate (a ^ j) * b and check \n",
+ "\t\t# for collision \n",
+ "\t\tcur = (powmod (a, j, m) * b) % m; \n",
+ "\n",
+ "\t\t# If collision occurs i.e., LHS = RHS \n",
+ "\t\tif (value[cur]): \n",
+ "\t\t\tans = value[cur] * n - j; \n",
+ "\t\t\t\n",
+ "\t\t\t# Check whether ans lies below m or not \n",
+ "\t\t\tif (ans < m): \n",
+ "\t\t\t\treturn ans; \n",
+ "\t\n",
+ "\treturn -1; \n",
+ "\n",
+ "# Driver code \n",
+ "a = 610292520201647; \n",
+ "b = 12542369; \n",
+ "m = 5; \n",
+ "print(discreteLogarithm(a, b, m)); \n",
+ "\n",
+ "a = 610292520201647; \n",
+ "b = 1852642; \n",
+ "m = 5; \n",
+ "print(discreteLogarithm(a, b, m)); \n",
+ "\n",
+ "# This code is contributed by mits "
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 4,
+ "metadata": {},
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "54\n",
+ "49\n"
+ ]
+ }
+ ],
+ "source": [
+ "# Python3 program to calculate \n",
+ "# discrete logarithm \n",
+ "import math; \n",
+ "\n",
+ "# Iterative Function to calculate \n",
+ "# (x ^ y)%p in O(log y) \n",
+ "def powmod(x, y, p): \n",
+ "\n",
+ "\tres = 1; # Initialize result \n",
+ "\n",
+ "\tx = x % p; # Update x if it is more \n",
+ "\t\t\t# than or equal to p \n",
+ "\n",
+ "\twhile (y > 0): \n",
+ "\t\t\n",
+ "\t\t# If y is odd, multiply x with result \n",
+ "\t\tif (y & 1): \n",
+ "\t\t\tres = (res * x) % p; \n",
+ "\n",
+ "\t\t# y must be even now \n",
+ "\t\ty = y >> 1; # y = y/2 \n",
+ "\t\tx = (x * x) % p; \n",
+ "\treturn res; \n",
+ "\n",
+ "# Function to calculate k for given a, b, m \n",
+ "def discreteLogarithm(a, b, m): \n",
+ "\tn = int(math.sqrt(m) + 1); \n",
+ "\n",
+ "\tvalue = [0] * m; \n",
+ "\n",
+ "\t# Store all values of a^(n*i) of LHS \n",
+ "\tfor i in range(n, 0, -1): \n",
+ "\t\tvalue[ powmod (a, i * n, m) ] = i; \n",
+ "\n",
+ "\tfor j in range(n): \n",
+ "\t\t\n",
+ "\t\t# Calculate (a ^ j) * b and check \n",
+ "\t\t# for collision \n",
+ "\t\tcur = (powmod (a, j, m) * b) % m; \n",
+ "\n",
+ "\t\t# If collision occurs i.e., LHS = RHS \n",
+ "\t\tif (value[cur]): \n",
+ "\t\t\tans = value[cur] * n - j; \n",
+ "\t\t\t\n",
+ "\t\t\t# Check whether ans lies below m or not \n",
+ "\t\t\tif (ans < m): \n",
+ "\t\t\t\treturn ans; \n",
+ "\t\n",
+ "\treturn -1; \n",
+ "\n",
+ "# Driver code \n",
+ "a = 610292520201647; \n",
+ "b = 12542369; \n",
+ "m = 125; \n",
+ "print(discreteLogarithm(a, b, m)); \n",
+ "\n",
+ "a = 610292520201647; \n",
+ "b = 1852642; \n",
+ "m = 125; \n",
+ "print(discreteLogarithm(a, b, m)); \n",
+ "\n",
+ "# This code is contributed by mits "
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 5,
+ "metadata": {},
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "-1\n",
+ "-1\n"
+ ]
+ }
+ ],
+ "source": [
+ "# Python3 program to calculate \n",
+ "# discrete logarithm \n",
+ "import math; \n",
+ "\n",
+ "# Iterative Function to calculate \n",
+ "# (x ^ y)%p in O(log y) \n",
+ "def powmod(x, y, p): \n",
+ "\n",
+ "\tres = 1; # Initialize result \n",
+ "\n",
+ "\tx = x % p; # Update x if it is more \n",
+ "\t\t\t# than or equal to p \n",
+ "\n",
+ "\twhile (y > 0): \n",
+ "\t\t\n",
+ "\t\t# If y is odd, multiply x with result \n",
+ "\t\tif (y & 1): \n",
+ "\t\t\tres = (res * x) % p; \n",
+ "\n",
+ "\t\t# y must be even now \n",
+ "\t\ty = y >> 1; # y = y/2 \n",
+ "\t\tx = (x * x) % p; \n",
+ "\treturn res; \n",
+ "\n",
+ "# Function to calculate k for given a, b, m \n",
+ "def discreteLogarithm(a, b, m): \n",
+ "\tn = int(math.sqrt(m) + 1); \n",
+ "\n",
+ "\tvalue = [0] * m; \n",
+ "\n",
+ "\t# Store all values of a^(n*i) of LHS \n",
+ "\tfor i in range(n, 0, -1): \n",
+ "\t\tvalue[ powmod (a, i * n, m) ] = i; \n",
+ "\n",
+ "\tfor j in range(n): \n",
+ "\t\t\n",
+ "\t\t# Calculate (a ^ j) * b and check \n",
+ "\t\t# for collision \n",
+ "\t\tcur = (powmod (a, j, m) * b) % m; \n",
+ "\n",
+ "\t\t# If collision occurs i.e., LHS = RHS \n",
+ "\t\tif (value[cur]): \n",
+ "\t\t\tans = value[cur] * n - j; \n",
+ "\t\t\t\n",
+ "\t\t\t# Check whether ans lies below m or not \n",
+ "\t\t\tif (ans < m): \n",
+ "\t\t\t\treturn ans; \n",
+ "\t\n",
+ "\treturn -1; \n",
+ "\n",
+ "# Driver code \n",
+ "a = 610292520201647; \n",
+ "b = 12542369; \n",
+ "m = 63456456; \n",
+ "print(discreteLogarithm(a, b, m)); \n",
+ "\n",
+ "a = 610292520201647; \n",
+ "b = 1852642; \n",
+ "m = 465464; \n",
+ "print(discreteLogarithm(a, b, m)); \n",
+ "\n",
+ "# This code is contributed by mits "
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 2,
+ "metadata": {},
+ "outputs": [
+ {
+ "ename": "MemoryError",
+ "evalue": "",
+ "output_type": "error",
+ "traceback": [
+ "\u001b[1;31m---------------------------------------------------------------------------\u001b[0m",
+ "\u001b[1;31mMemoryError\u001b[0m Traceback (most recent call last)",
+ "\u001b[1;32m<ipython-input-2-e09ae1952765>\u001b[0m in \u001b[0;36m<module>\u001b[1;34m\u001b[0m\n\u001b[0;32m 53\u001b[0m \u001b[0mb\u001b[0m \u001b[1;33m=\u001b[0m \u001b[1;36m12542369\u001b[0m\u001b[1;33m;\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m 54\u001b[0m \u001b[0mm\u001b[0m \u001b[1;33m=\u001b[0m \u001b[1;36m610292520201644\u001b[0m\u001b[1;33m;\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[1;32m---> 55\u001b[1;33m \u001b[0mprint\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mdiscreteLogarithm\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0ma\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0mb\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0mm\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m;\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0m\u001b[0;32m 56\u001b[0m \u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m 57\u001b[0m \u001b[0ma\u001b[0m \u001b[1;33m=\u001b[0m \u001b[1;36m610292520201647\u001b[0m\u001b[1;33m;\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n",
+ "\u001b[1;32m<ipython-input-2-e09ae1952765>\u001b[0m in \u001b[0;36mdiscreteLogarithm\u001b[1;34m(a, b, m)\u001b[0m\n\u001b[0;32m 27\u001b[0m \u001b[0mn\u001b[0m \u001b[1;33m=\u001b[0m \u001b[0mint\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mmath\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0msqrt\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mm\u001b[0m\u001b[1;33m)\u001b[0m \u001b[1;33m+\u001b[0m \u001b[1;36m1\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m;\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m 28\u001b[0m \u001b[1;33m\u001b[0m\u001b[0m\n\u001b[1;32m---> 29\u001b[1;33m \u001b[0mvalue\u001b[0m \u001b[1;33m=\u001b[0m \u001b[1;33m[\u001b[0m\u001b[1;36m0\u001b[0m\u001b[1;33m]\u001b[0m \u001b[1;33m*\u001b[0m \u001b[0mm\u001b[0m\u001b[1;33m;\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0m\u001b[0;32m 30\u001b[0m \u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m 31\u001b[0m \u001b[1;31m# Store all values of a^(n*i) of LHS\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n",
+ "\u001b[1;31mMemoryError\u001b[0m: "
+ ]
+ }
+ ],
+ "source": [
+ "# Python3 program to calculate \n",
+ "# discrete logarithm \n",
+ "import math; \n",
+ "\n",
+ "# Iterative Function to calculate \n",
+ "# (x ^ y)%p in O(log y) \n",
+ "def powmod(x, y, p): \n",
+ "\n",
+ "\tres = 1; # Initialize result \n",
+ "\n",
+ "\tx = x % p; # Update x if it is more \n",
+ "\t\t\t# than or equal to p \n",
+ "\n",
+ "\twhile (y > 0): \n",
+ "\t\t\n",
+ "\t\t# If y is odd, multiply x with result \n",
+ "\t\tif (y & 1): \n",
+ "\t\t\tres = (res * x) % p; \n",
+ "\n",
+ "\t\t# y must be even now \n",
+ "\t\ty = y >> 1; # y = y/2 \n",
+ "\t\tx = (x * x) % p; \n",
+ "\treturn res; \n",
+ "\n",
+ "# Function to calculate k for given a, b, m \n",
+ "def discreteLogarithm(a, b, m): \n",
+ "\tn = int(math.sqrt(m) + 1); \n",
+ "\n",
+ "\tvalue = [0] * m; \n",
+ "\n",
+ "\t# Store all values of a^(n*i) of LHS \n",
+ "\tfor i in range(n, 0, -1): \n",
+ "\t\tvalue[ powmod (a, i * n, m) ] = i; \n",
+ "\n",
+ "\tfor j in range(n): \n",
+ "\t\t\n",
+ "\t\t# Calculate (a ^ j) * b and check \n",
+ "\t\t# for collision \n",
+ "\t\tcur = (powmod (a, j, m) * b) % m; \n",
+ "\n",
+ "\t\t# If collision occurs i.e., LHS = RHS \n",
+ "\t\tif (value[cur]): \n",
+ "\t\t\tans = value[cur] * n - j; \n",
+ "\t\t\t\n",
+ "\t\t\t# Check whether ans lies below m or not \n",
+ "\t\t\tif (ans < m): \n",
+ "\t\t\t\treturn ans; \n",
+ "\t\n",
+ "\treturn -1; \n",
+ "\n",
+ "# Driver code \n",
+ "a = 610292520201647; \n",
+ "b = 12542369; \n",
+ "m = 610292520201644; \n",
+ "print(discreteLogarithm(a, b, m)); \n",
+ "\n",
+ "a = 610292520201647; \n",
+ "b = 1852642; \n",
+ "m = 610292520201644; \n",
+ "print(discreteLogarithm(a, b, m)); \n",
+ "\n",
+ "# This code is contributed by mits "
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "metadata": {},
+ "outputs": [],
+ "source": []
+ }
+ ],
+ "metadata": {
+ "kernelspec": {
+ "display_name": "Python 3",
+ "language": "python",
+ "name": "python3"
+ },
+ "language_info": {
+ "codemirror_mode": {
+ "name": "ipython",
+ "version": 3
+ },
+ "file_extension": ".py",
+ "mimetype": "text/x-python",
+ "name": "python",
+ "nbconvert_exporter": "python",
+ "pygments_lexer": "ipython3",
+ "version": "3.7.3"
+ }
+ },
+ "nbformat": 4,
+ "nbformat_minor": 2
+}
--
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