expanded example

ctnt2018/CTNT ECM Example.ipynb

@@ -0,0 +1,112 @@
+{
+ "cells": [
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "metadata": {},
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "Factor of F_7 is 59649589127497217\n"
+     ]
+    }
+   ],
+   "source": [
+    "# %load ECM.py\n",
+    "# %load ec3.py\n",
+    "from math import log\n",
+    "import pickle\n",
+    "import gmpy2\n",
+    "\n",
+    "with open('primes10000.pickle','rb') as f:\n",
+    "    Primes10000=pickle.load(f)\n",
+    "                                                                                                                                                                                                             \n",
+    "def ecm(N,arange=100,krange=10000):\n",
+    "    for a in range(-arange,arange):\n",
+    "        x,y=0,1\n",
+    "        for B in Primes10000:\n",
+    "            k=B**(int(log(10000)/log(B)))\n",
+    "            sx,sy,t=x,y,k\n",
+    "            first=True\n",
+    "            while t>0:\n",
+    "                if t%2==1:\n",
+    "                    if first:\n",
+    "                        xm,ym=sx,sy\n",
+    "                        first=False\n",
+    "                    else:\n",
+    "                        # x1=xm,y1=ym, x2=sx,y2=sy,a=a,b=1,N=N\n",
+    "                        d,u,v=gmpy2.gcdext(sx-xm,N)\n",
+    "                        if d>1:\n",
+    "                            if d==N:\n",
+    "                                break\n",
+    "                            else:\n",
+    "                                return d\n",
+    "                        L=(u*(sy-ym)) % N\n",
+    "                        x_sum=(L*L-xm-sx) % N\n",
+    "                        ym=(L*(xm-x_sum)-ym) % N\n",
+    "                        xm=x_sum\n",
+    "                # sx=x,sy=y,a=a,b=1,N\n",
+    "                d,u,v=gmpy2.gcdext(2*sy,N)\n",
+    "                if d>1:\n",
+    "                    if d==N:\n",
+    "                        break\n",
+    "                    else:\n",
+    "                        return d\n",
+    "                L=(u*(3*sx*sx+a)) % N\n",
+    "                x2=(L*L-2*sx) % N\n",
+    "                sy=(L*(sx-x2)-sy) %N\n",
+    "                sx=x2\n",
+    "                t=t//2\n",
+    "            x,y=xm,ym\n",
+    "    print('Failed')\n",
+    "\n",
+    "\n",
+    "\n",
+    "N=2**(128)+1\n",
+    "print('Factor of F_7 is',ecm(N))\n",
+    "N=2**(256)+1\n",
+    "print('Factor of F_8 is',ecm(N))\n",
+    "N=2**(512)+1\n",
+    "print('Factor of F_9 is',ecm(N))\n",
+    "\n"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "metadata": {},
+   "outputs": [],
+   "source": []
+  },
+  {
+   "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": "3.6.4"
+  }
+ },
+ "nbformat": 4,
+ "nbformat_minor": 2
+}

ctnt2018/ECM.py

@@ -20,7 +20,6 @@ def ecm(N,arange=100,krange=10000):
                         xm,ym=sx,sy
                         first=False
                     else:
-                        # x1=xm,y1=ym, x2=sx,y2=sy,a=a,b=1,N=N
                         d,u,v=gmpy2.gcdext(sx-xm,N)
                         if d>1:
                             if d==N:
@@ -31,7 +30,6 @@ def ecm(N,arange=100,krange=10000):
                         x_sum=(L*L-xm-sx) % N
                         ym=(L*(xm-x_sum)-ym) % N
                         xm=x_sum
-                # sx=x,sy=y,a=a,b=1,N
                 d,u,v=gmpy2.gcdext(2*sy,N)
                 if d>1:
                     if d==N: