Beispiele und Tafelbilder 11.5.2023

20230511/rsa-genkey-01.c

+#include <stdio.h>
+
+int main (void)
+{
+  int p = 11117;
+  int q = 11171;
+  int n = (p - 1) * (q - 1);
+  int e = 137;
+  int d = 2;
+  while ((d * e) % n != 1)
+    d++;
+  printf ("d = %d\n", d);
+  return 0;
+}

20230511/rsa-genkey-02.c

+#include <stdio.h>
+
+void ext_eucl (int a, int b, int *ss, int *tt, int *ggt)
+{
+  int r0 = a;
+  int r1 = b;
+  int s0 = 1;
+  int s1 = 0;
+  int t0 = 0;
+  int t1 = 1;
+  loop: ;
+    int q = r0 / r1;
+    int r2 = r0 % r1;
+    int s2 = s0 - q * s1;
+    int t2 = t0 - q * t1;
+    if (r2 == 0)
+      {
+        *ggt = r2;
+        *ss = s2;
+        *tt = t2;
+        return;
+      }
+    r0 = r1;
+    s0 = s1;
+    r1 = r2;
+    s1 = s2;
+  goto loop;
+}
+
+int main (void)
+{
+  int p = 11117;
+  int q = 11171;
+  int n = (p - 1) * (q - 1);
+  int e = 137;
+  int d;
+  int t;
+  int ggt;
+  ext_eucl (e, n, &d, &t, &ggt);
+  printf ("d = %d\n", d);
+  return 0;
+}

20230511/rsa-genkey-03.c

+#include <stdio.h>
+
+void ext_eucl (int a, int b, int *ss, int *tt, int *ggt)
+{
+  int r0 = a;
+  int r1 = b;
+  int s0 = 1;
+  int s1 = 0;
+  int t0 = 0;
+  int t1 = 1;
+  loop: ;
+    int q = r0 / r1;
+    int r2 = r0 % r1;
+    int s2 = s0 - q * s1;
+    int t2 = t0 - q * t1;
+    if (r2 == 0)
+      {
+        *ggt = r2;
+        *ss = s2;
+        *tt = t2;
+        return;
+      }
+    r0 = r1;
+    s0 = s1;
+    r1 = r2;
+    s1 = s2;
+  goto loop;
+}
+
+int main (void)
+{
+  int p = 11117;
+  int q = 11171;
+  int n = (p - 1) * (q - 1);
+  int e = 137;
+  int d;
+  int t;
+  int ggt;
+  ext_eucl (e, n, &d, &t, &ggt);
+  while (d < 0)
+    d += n;
+  printf ("d = %d\n", d);
+  return 0;
+}

20230511/rsa-genkey-04.c

+#include <stdio.h>
+
+void ext_eucl (int a, int b, int *ss, int *tt, int *ggt)
+{
+  int r0 = a;
+  int r1 = b;
+  int s0 = 1;
+  int s1 = 0;
+  int t0 = 0;
+  int t1 = 1;
+  loop: ;
+    int q = r0 / r1;
+    int r2 = r0 % r1;
+    int s2 = s0 - q * s1;
+    int t2 = t0 - q * t1;
+    if (r2 == 0)
+      {
+        *ggt = r1;
+        *ss = s1;
+        *tt = t1;
+        return;
+      }
+    r0 = r1;
+    s0 = s1;
+    r1 = r2;
+    s1 = s2;
+  goto loop;
+}
+
+int main (void)
+{
+  int s, t, ggt;
+  ext_eucl (99, 78, &s, &t, &ggt);
+  printf ("s = %d, t = %d, ggT = %d\n", s, t, ggt);
+  return 0;
+}

20230511/rsa-genkey-05.c

+#include <stdio.h>
+
+void ext_eucl (int a, int b, int *ss, int *tt, int *ggt)
+{
+  int r0 = a;
+  int r1 = b;
+  int s0 = 1;
+  int s1 = 0;
+  int t0 = 0;
+  int t1 = 1;
+  loop: ;
+    int q = r0 / r1;
+    int r2 = r0 % r1;
+    int s2 = s0 - q * s1;
+    int t2 = t0 - q * t1;
+    if (r2 == 0)
+      {
+        *ggt = r1;
+        *ss = s1;
+        *tt = t1;
+        return;
+      }
+    r0 = r1;
+    s0 = s1;
+    t0 = t1;
+    r1 = r2;
+    s1 = s2;
+    t1 = t2;
+  goto loop;
+}
+
+int main (void)
+{
+  int s, t, ggt;
+  ext_eucl (99, 78, &s, &t, &ggt);
+  printf ("s = %d, t = %d, ggT = %d\n", s, t, ggt);
+  return 0;
+}

20230511/rsa-genkey-06.c

+#include <stdio.h>
+
+void ext_eucl (int a, int b, int *ss, int *tt, int *ggt)
+{
+  int r0 = a;
+  int r1 = b;
+  int s0 = 1;
+  int s1 = 0;
+  int t0 = 0;
+  int t1 = 1;
+  loop: ;
+    int q = r0 / r1;
+    int r2 = r0 % r1;
+    int s2 = s0 - q * s1;
+    int t2 = t0 - q * t1;
+    if (r2 == 0)
+      {
+        *ggt = r1;
+        *ss = s1;
+        *tt = t1;
+        return;
+      }
+    r0 = r1;
+    s0 = s1;
+    t0 = t1;
+    r1 = r2;
+    s1 = s2;
+    t1 = t2;
+  goto loop;
+}
+
+int main (void)
+{
+  int p = 11117;
+  int q = 11171;
+  int n = (p - 1) * (q - 1);
+  int e = 137;
+  int d;
+  int t;
+  int ggt;
+  ext_eucl (e, n, &d, &t, &ggt);
+  printf ("d = %d\n", d);
+  return 0;
+}

20230511/rsa-genkey-07.c

+#include <stdio.h>
+
+void ext_eucl (int a, int b, int *ss, int *tt, int *ggt)
+{
+  int r0 = a;
+  int r1 = b;
+  int s0 = 1;
+  int s1 = 0;
+  int t0 = 0;
+  int t1 = 1;
+  int r2 = r0 % r1;
+  while (r2)
+    {
+      int q = r0 / r1;
+      int s2 = s0 - q * s1;
+      int t2 = t0 - q * t1;
+      r0 = r1;
+      s0 = s1;
+      t0 = t1;
+      r1 = r2;
+      s1 = s2;
+      t1 = t2;
+      r2 = r0 % r1;
+    }
+  *ggt = r1;
+  *ss = s1;
+  *tt = t1;
+}
+
+int main (void)
+{
+  int p = 11117;
+  int q = 11171;
+  int n = (p - 1) * (q - 1);
+  int e = 137;
+  int d;
+  int t;
+  int ggt;
+  ext_eucl (e, n, &d, &t, &ggt);
+  printf ("d = %d\n", d);
+  return 0;
+}

20230511/rsa-genkey-08.c

+#include <stdio.h>
+
+void ext_eucl (int a, int b, int *ss, int *tt, int *ggt)
+{
+  int r0 = a;
+  int r1 = b;
+  int s0 = 1;
+  int s1 = 0;
+  int t0 = 0;
+  int t1 = 1;
+  int r2 = r0 % r1;
+  while (r2)
+    {
+      int q = r0 / r1;
+      int s2 = s0 - q * s1;
+      int t2 = t0 - q * t1;
+      r0 = r1;
+      s0 = s1;
+      t0 = t1;
+      r1 = r2;
+      s1 = s2;
+      t1 = t2;
+      r2 = r0 % r1;
+    }
+  *ggt = r1;
+  *ss = s1;
+  *tt = t1;
+}
+
+int main (void)
+{
+  int p = 11117;
+  int q = 11171;
+  int n = (p - 1) * (q - 1);
+  int d;
+  int t;
+  int ggt;
+  printf ("        e          d\n");
+  for (int e = 137; e < 256; e++)
+    {
+      ext_eucl (e, n, &d, &t, &ggt);
+      printf ("%10d %10d\n", e, d);
+    }
+  return 0;
+}

20230511/rsa-genkey-09.c

+#include <stdio.h>
+
+void ext_eucl (int a, int b, int *ss, int *tt, int *ggt)
+{
+  int r0 = a;
+  int r1 = b;
+  int s0 = 1;
+  int s1 = 0;
+  int t0 = 0;
+  int t1 = 1;
+  int r2 = r0 % r1;
+  while (r2)
+    {
+      int q = r0 / r1;
+      int s2 = s0 - q * s1;
+      int t2 = t0 - q * t1;
+      r0 = r1;
+      s0 = s1;
+      t0 = t1;
+      r1 = r2;
+      s1 = s2;
+      t1 = t2;
+      r2 = r0 % r1;
+    }
+  *ggt = r1;
+  *ss = s1;
+  *tt = t1;
+}
+
+int main (void)
+{
+  int p = 11117;
+  int q = 11171;
+  int n = (p - 1) * (q - 1);
+  int d;
+  int t;
+  int ggt;
+  printf ("        e          d        db\n");
+  for (int e = 137; e < 256; e++)
+    {
+      int db = 2;
+      while (db < n && (e * db) % n != 1)
+        db++;
+      ext_eucl (e, n, &d, &t, &ggt);
+      printf ("%10d %10d %10d\n", e, d, db);
+    }
+  return 0;
+}

20230511/rsa-genkey-10.c

+#include <stdio.h>
+
+void ext_eucl (int a, int b, int *ss, int *tt, int *ggt)
+{
+  int r0 = a;
+  int r1 = b;
+  int s0 = 1;
+  int s1 = 0;
+  int t0 = 0;
+  int t1 = 1;
+  int r2 = r0 % r1;
+  while (r2)
+    {
+      int q = r0 / r1;
+      int s2 = s0 - q * s1;
+      int t2 = t0 - q * t1;
+      r0 = r1;
+      s0 = s1;
+      t0 = t1;
+      r1 = r2;
+      s1 = s2;
+      t1 = t2;
+      r2 = r0 % r1;
+    }
+  *ggt = r1;
+  *ss = s1;
+  *tt = t1;
+}
+
+int main (void)
+{
+  int p = 11117;
+  int q = 11171;
+  int n = (p - 1) * (q - 1);
+  int d;
+  int t;
+  int ggt;
+  printf ("        e          d        db\n");
+  for (int e = 137; e < 256; e++)
+    {
+      int db = 2;
+      while (db < n && (e * db) % n != 1)
+        db++;
+      ext_eucl (e, n, &d, &t, &ggt);
+      while (d < 0)
+        d += n;
+      printf ("%10d %10d %10d\n", e, d, db);
+    }
+  return 0;
+}

20230511/rsa-genkey-11.c

+#include <stdio.h>
+
+void ext_eucl (int a, int b, int *ss, int *tt, int *ggt)
+{
+  int r0 = a;
+  int r1 = b;
+  int s0 = 1;
+  int s1 = 0;
+  int t0 = 0;
+  int t1 = 1;
+  int r2 = r0 % r1;
+  while (r2)
+    {
+      int q = r0 / r1;
+      int s2 = s0 - q * s1;
+      int t2 = t0 - q * t1;
+      r0 = r1;
+      s0 = s1;
+      t0 = t1;
+      r1 = r2;
+      s1 = s2;
+      t1 = t2;
+      r2 = r0 % r1;
+    }
+  *ggt = r1;
+  *ss = s1;
+  *tt = t1;
+}
+
+int main (void)
+{
+  int p = 11117;
+  int q = 11171;
+  int n = (p - 1) * (q - 1);
+  int d;
+  int t;
+  int ggt;
+  printf ("        e         ggT         d        db\n");
+  for (int e = 137; e < 256; e += 2)
+    {
+      int db = 2;
+      while (db < n && (e * db) % n != 1)
+        db++;
+      ext_eucl (e, n, &d, &t, &ggt);
+      while (d < 0)
+        d += n;
+      printf ("%10d %10d %10d %10d\n", e, ggt, d, db);
+    }
+  return 0;
+}