minirsa library functions

Author: robertjli

.metadata/.plugins/org.eclipse.core.resources/.root/.indexes/properties.index

@@ -1,4 +1,4 @@
-#Wed Apr 18 17:54:47 EDT 2012
+#Wed Apr 18 17:57:27 EDT 2012
 useQuickDiffPrefPage=true
 proposalOrderMigrated=true
 tabWidthPropagated=true
@@ -9,6 +9,7 @@ useAnnotationsPrefPage=true
 org.eclipse.jdt.ui.editor.tab.width=
 org.eclipse.jface.textfont=1|Consolas|11.25|0|WINDOWS|1|-15|0|0|0|400|0|0|0|0|3|2|1|49|Consolas;
 org.eclipse.jdt.ui.formatterprofiles.version=12
+content_assist_number_of_computers=16
 formatter_settings_version=12
 formatter_profile=_a
 spelling_locale_initialized=true

.metadata/.plugins/org.eclipse.core.runtime/.settings/org.eclipse.jdt.core.prefs

@@ -0,0 +1,15 @@
+<?xml version="1.0" encoding="UTF-8" standalone="no"?>
+<launchConfiguration type="org.eclipse.jdt.junit.launchconfig">
+<listAttribute key="org.eclipse.debug.core.MAPPED_RESOURCE_PATHS">
+<listEntry value="/MiniRSA Chat/src/minirsa/MiniRSATest.java"/>
+</listAttribute>
+<listAttribute key="org.eclipse.debug.core.MAPPED_RESOURCE_TYPES">
+<listEntry value="1"/>
+</listAttribute>
+<stringAttribute key="org.eclipse.jdt.junit.CONTAINER" value=""/>
+<booleanAttribute key="org.eclipse.jdt.junit.KEEPRUNNING_ATTR" value="false"/>
+<stringAttribute key="org.eclipse.jdt.junit.TEST_KIND" value="org.eclipse.jdt.junit.loader.junit4"/>
+<stringAttribute key="org.eclipse.jdt.launching.MAIN_TYPE" value="minirsa.MiniRSATest"/>
+<stringAttribute key="org.eclipse.jdt.launching.PROJECT_ATTR" value="MiniRSA Chat"/>
+<stringAttribute key="org.eclipse.jdt.launching.VM_ARGUMENTS" value=""/>
+</launchConfiguration>

.metadata/.plugins/org.eclipse.core.runtime/.settings/org.eclipse.jdt.ui.prefs

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+executed,command,org.eclipse.ui,3.7.0.I20110602-0100,"org.eclipse.ui.window.preferences",1334786087110
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.metadata/.plugins/org.eclipse.debug.core/.launches/MiniRSATest.launch

@@ -10,4 +10,3 @@ INDEX VERSION 1.126+D:\University of Pennsylvania\2011-2012 Spring Semester\CIT
 1115467115.index
 30765161.index
 3065916431.index
-3270485571.index

.metadata/.plugins/org.eclipse.epp.usagedata.recording/usagedata.csv

@@ -0,0 +1,12 @@
+<?xml version="1.0" encoding="UTF-8"?>
+<testrun name="MiniRSATest" project="MiniRSA Chat" tests="7" started="7" failures="0" errors="0" ignored="0">
+  <testsuite name="minirsa.MiniRSATest" time="0.045">
+    <testcase name="testEndecrypt" classname="minirsa.MiniRSATest" time="0.003"/>
+    <testcase name="testModInverse" classname="minirsa.MiniRSATest" time="0.001"/>
+    <testcase name="testTotientFromPrimes" classname="minirsa.MiniRSATest" time="0.0"/>
+    <testcase name="testGCD" classname="minirsa.MiniRSATest" time="0.008"/>
+    <testcase name="testCoprime" classname="minirsa.MiniRSATest" time="0.03"/>
+    <testcase name="testModulo" classname="minirsa.MiniRSATest" time="0.001"/>
+    <testcase name="testCrackKey" classname="minirsa.MiniRSATest" time="0.001"/>
+  </testsuite>
+</testrun>

.metadata/.plugins/org.eclipse.jdt.core/savedIndexNames.txt

@@ -0,0 +1,166 @@
+package minirsa;
+
+import java.util.Random;
+
+/**
+ * This class provides static library functions for the RSA algorithm.
+ * 
+ * @author Robert Li
+ * @version April 17, 2012
+ */
+public class MiniRSA {
+
+    /**
+     * Picks a random integer that is coprime to x, greater than 1, and less than x.
+     * 
+     * @param x The integer for which a coprime integer is selected.
+     * @return An integer that is coprime to x, greater than 1, and less than x.
+     */
+    public static long coprime(long x) {
+        Random rand = new Random();
+        long result = rand.nextLong() % x;
+        while (result <= 1 || GCD(x, result) != 1) {
+            result = rand.nextLong() % x;
+        }
+        return result;
+    }
+    
+    /**
+     * Encrypts the integer msg using the RSA key (key, c).
+     * 
+     * @param msg The message to be encrypted.
+     * @param key The exponent in the RSA key.
+     * @param c The modulus in the RSA key.
+     * @return The encrypted message.
+     */
+    public static long endecrypt(int msg, long key, long c) {
+        return modulo(msg, key, c);
+    }
+    
+    /**
+     * Calculates the greatest common divisor of a and b.
+     * 
+     * @param a
+     * @param b
+     * @return The greatest common divisor of a and b, or -1 if a and b are 
+     *         both 0.
+     */
+    public static long GCD(long a, long b) {
+        // Implemented using the Euclidean Algorithm. (Ugh CIS 160...)
+        if (a == 0 && b == 0) {
+            return 0;
+        }
+        long x = Math.abs(a);
+        long y = Math.abs(b);
+        long r;
+        while (y > 0) {
+            r = x % y;
+            x = y;
+            y = r;
+        }
+        return x;
+    }
+    
+    /**
+     * Calculates the modular inverse <code>base<super>-1</super> % m</code>.
+     * 
+     * @param base
+     * @param m
+     * @return The modular inverse of base (mod m).
+     */
+    public static long modInverse(long base, long m) {
+        long x = 0, y = 1, lastX = 1, lastY = 0, mod = m;
+        long quotient, temp;
+        while (mod != 0) {
+            quotient = base / mod;
+            
+            temp = base;
+            base = mod;
+            mod = temp % mod;
+            
+            temp = x;
+            x = lastX - quotient * x;
+            lastX = temp;
+            
+            temp = y;
+            y = lastY - quotient * y;
+            lastY = temp;
+        }
+        if (lastX < 0) {
+            lastX += m;
+        }
+        return lastX;
+    }
+    
+    /**
+     * Computes a<super>b</super> % c for large values of a, b, and c.
+     * 
+     * @param a
+     * @param b
+     * @param c
+     * @return a<super>b</super> % c.
+     */
+    public static long modulo(long a, long b, long c) {
+        // TODO is there a better algo?
+        long result = 1;
+        for (long i = 0; i < b; i++) {
+            result = (result * a) % c;
+        }
+        return result;
+    }
+    
+    /**
+     * Computes Euler's totient of the product of primes p and q.
+     * 
+     * @param p A prime number.
+     * @param q A prime number.
+     * @return Euler's totient of n = p * q.
+     */
+    public static long totient(long p, long q) {
+        return (p - 1) * (q - 1);
+    }
+    
+    /**
+     * Generates an RSA public/private key pair using primes p and q.
+     * 
+     * @param p A prime number.
+     * @param q A prime number.
+     * @return A 3-element array <code>a</code>, where <code>a[0]</code> is the 
+     * public exponent, <code>a[1]</code> is the private exponent, and 
+     * <code>a[2]</code> is the modulus.
+     */
+    public static long[] generateKey(long p, long q) {
+        long n = p * q;
+        long m = totient(p, q);
+        long e = coprime(m);
+        long d = modInverse(e, m);
+        System.out.println("Public: (" + e + ", " + n + "); Private: (" + 
+                           d + ", " + n + ").");
+        return new long[] {e, d, n};
+    }
+    
+    /**
+     * Given a public key (e, n), returns the private exponent d. Beware, this 
+     * can take a really <i>really</i> long time...
+     * 
+     * @param e The public exponent.
+     * @param n The modulus.
+     * @return The private exponent.
+     */
+    public static long crackKey(long e, long n) {
+        long q = -1;
+        long p;
+        for (p = 2; p < n / 2; p++) {
+            // find factors of n
+            q = n / p;
+            if (p * q == n) {
+                break;
+            }
+        }
+        if (q == -1) {
+            return -1;
+        }
+        long m = totient(p, q);
+        return modInverse(e, m);
+    }
+}

.metadata/.plugins/org.eclipse.jdt.junit.core/history/20120418-175733.424.xml

@@ -0,0 +1,63 @@
+package minirsa;
+
+import static org.junit.Assert.*;
+
+import org.junit.Test;
+
+public class MiniRSATest {
+
+    @Test
+    public void testCoprime() {
+        for (int i = 0; i < 1000; i++) {
+            long coprime1 = MiniRSA.coprime(1234);
+            assertTrue("Coprime: 1234 -> " + coprime1, 
+                       MiniRSA.GCD(1234, coprime1) == 1);
+            
+            long coprime2 = MiniRSA.coprime(8470);
+            assertTrue("Coprime: 1234 -> " + coprime2, 
+                       MiniRSA.GCD(8470, coprime2) == 1);
+        }
+    }
+
+    @Test
+    public void testEndecrypt() {
+        assertEquals(1148, MiniRSA.endecrypt(72, 451, 2623));
+        assertEquals(326, MiniRSA.endecrypt(101, 451, 2623));
+        assertEquals(2041, MiniRSA.endecrypt(33, 451, 2623));
+    }
+
+    @Test
+    public void testGCD() {
+        assertEquals(0, MiniRSA.GCD(0, 0));
+        assertEquals(1, MiniRSA.GCD(0, 1));
+        assertEquals(13, MiniRSA.GCD(169, 91));
+        assertEquals(14, MiniRSA.GCD(2842, 12698));
+        assertEquals(1, MiniRSA.GCD(451, 2520));
+    }
+
+    @Test
+    public void testModInverse() {
+        assertEquals(47, MiniRSA.modInverse(23, 120));
+        assertEquals(1531, MiniRSA.modInverse(451, 2520));
+        assertEquals(2753, MiniRSA.modInverse(17, 3120));
+    }
+
+    @Test
+    public void testModulo() {
+        assertEquals(1148, MiniRSA.modulo(72, 451, 2623));
+        assertEquals(326, MiniRSA.modulo(101, 451, 2623));
+        assertEquals(2041, MiniRSA.modulo(33, 451, 2623));
+    }
+
+    @Test
+    public void testTotientFromPrimes() {
+        assertEquals(2520, MiniRSA.totient(43, 61));
+        assertEquals(192, MiniRSA.totient(13, 17));
+    }
+    
+    @Test
+    public void testCrackKey() {
+        assertEquals(1531, MiniRSA.crackKey(451, 2623));
+    }
+
+}