6.3

Uebung 6/Uebung6_3/Makefile

@@ -0,0 +1,52 @@
+
+# Name of the binary for Development
+BINARY = main
+# Name of the binary for Release
+FINAL = prototyp
+# Object files
+OBJS   = main.o
+# Compiler flags
+CFLAGS = -Werror -Wall -std=c++17 -g -fsanitize=address,undefined -g
+# Linker flags
+LFLAGS = -fsanitize=address,undefined
+#Which Compiler to use
+COMPILER = g++
+
+
+# all target: builds all important targets
+all: binary
+
+final : ${OBJS}
+	${COMPILER} ${LFLAGS} -o ${FINAL} ${OBJS}
+	rm ${OBJS}
+
+binary : ${OBJS}
+	${COMPILER} ${LFLAGS} -o ${BINARY} ${OBJS}
+
+# Links the binary
+${BINARY} : ${OBJS}
+	${COMPILER} ${LFLAGS} -o ${BINARY} ${OBJS}
+
+
+# Compiles a source-file (any file with file extension .c) into an object-file
+#
+# "%" is a wildcard which matches every file-name (similar to * in regular expressions)
+# Such a rule is called a pattern rule (because it matches a pattern, see https://www.gnu.org/software/make/manual/html_node/Pattern-Rules.html),
+# which are a form of so called implicit rules (see https://www.gnu.org/software/make/manual/html_node/Implicit-Rules.html)
+# "$@" and "$<" are so called automatic variables (see https://www.gnu.org/software/make/manual/html_node/Automatic-Variables.html)
+%.o : %.cpp
+	${COMPILER} -c ${CFLAGS} -o $@ $<
+
+
+# Rules can not only be used for compiling a program but also for executing a program
+run: ${BINARY}
+	./${BINARY}
+
+
+# Delete all build artifacts
+clean :
+	rm -rf ${BINARY} ${OBJS}
+
+
+# all  and clean are a "phony" targets, meaning they are no files
+.PHONY : all clean

Uebung 6/Uebung6_3/main.cpp

@@ -0,0 +1,88 @@
+#include <cmath>
+#include <iostream>
+
+// Konstanten aus der Angabe
+#define n 12
+#define k 6
+#define L 15
+
+// Liste der Primzahlen. Durch die oben angeführten Konstanten ist
+// sichergestellt dass diese eindeutig sind
+uint16_t listofPrimes[L];
+
+// Random n-bits Zahl generieren. MSB ist immer 1
+uint16_t createRandomNumber(uint8_t bits) {
+
+  uint16_t result = 1;
+  for (uint8_t i = 0; i < bits - 1; i++) {
+    result <<= 1;
+    result |= rand() % 2;
+  }
+  return result;
+}
+
+// Check ob eine Zahl Prim ist
+bool checkPrime(int number) {
+  for (int i = 2; i < sqrt(number); i++) {
+    if (number % i == 0) {
+
+      return false;
+    }
+  }
+  return true;
+}
+
+// Schreibe n primzahlen größer als start in array
+void findPrimesBiggerThan(uint16_t *array, int length, int start) {
+  for (int i = 0; i < length; i++) {
+    while (!checkPrime(start)) {
+      start++;
+    }
+    array[i] = start;
+    start++;
+  }
+}
+
+// die zwei Zahlen die Alice und Bob anfangs aussuchen
+int xAlice = createRandomNumber(n);
+int xBob = createRandomNumber(n);
+
+// Daten die an Bob übermittelt werden. j = x_A mod p_i. Bob antwortet mit Bool
+bool transmitToBob(int i, int j) {
+
+  if (j != (xBob % listofPrimes[i])) {
+    return false;
+  }
+  return true;
+}
+
+int main() {
+  // rand() mit timestamp seeden
+  srand(time(NULL));
+
+  // Primzahlen für Alice und Bob initialisieren
+  findPrimesBiggerThan(listofPrimes, L, pow(2, k));
+
+  // Alice sucht ein i zw. 1 und L aus
+  int iAlice = rand() % L - 1 + 1;
+
+  // Counter für false positives
+  int falseCounter = 0;
+
+  long long iterations = 1000000;
+  for (int i = 0; i < iterations; i++) {
+    // Frische Zahlen für Alice und Bob derinieren
+    xAlice = createRandomNumber(n);
+    xBob = createRandomNumber(n);
+
+    // false positive, wenn Bob behauptet die Zahlen wären gleich, sie es aber
+    // nicht sind
+    if (transmitToBob(iAlice, xAlice % listofPrimes[iAlice]) &&
+        xAlice != xBob) {
+      falseCounter++;
+    }
+  }
+
+  // false-positive rate in Prozent. Empirisch: ca. 1%
+  std::cout << 100 * (float)(falseCounter) / iterations << std::endl;
+}