From 3a0026d68e6fbbef5662060e00b1ff50955c35fa Mon Sep 17 00:00:00 2001 From: Peter Gerwinski <peter.gerwinski@hs-bochum.de> Date: Sun, 14 May 2023 21:12:00 +0200 Subject: [PATCH] Beispiele und Tafelbilder 11.5.2023 --- 20230511/rsa-03.png | Bin 0 -> 108958 bytes 20230511/rsa-genkey-01.c | 14 +++++++++++ 20230511/rsa-genkey-02.c | 42 ++++++++++++++++++++++++++++++++ 20230511/rsa-genkey-03.c | 44 ++++++++++++++++++++++++++++++++++ 20230511/rsa-genkey-04.c | 36 ++++++++++++++++++++++++++++ 20230511/rsa-genkey-05.c | 38 +++++++++++++++++++++++++++++ 20230511/rsa-genkey-06.c | 44 ++++++++++++++++++++++++++++++++++ 20230511/rsa-genkey-07.c | 42 ++++++++++++++++++++++++++++++++ 20230511/rsa-genkey-08.c | 45 +++++++++++++++++++++++++++++++++++ 20230511/rsa-genkey-09.c | 48 +++++++++++++++++++++++++++++++++++++ 20230511/rsa-genkey-10.c | 50 +++++++++++++++++++++++++++++++++++++++ 20230511/rsa-genkey-11.c | 50 +++++++++++++++++++++++++++++++++++++++ 20230511/rsa.xcf.gz | Bin 379922 -> 418309 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1); + int e = 137; + int d = 2; + while ((d * e) % n != 1) + d++; + printf ("d = %d\n", d); + return 0; +} diff --git a/20230511/rsa-genkey-02.c b/20230511/rsa-genkey-02.c new file mode 100644 index 0000000..32da9f4 --- /dev/null +++ b/20230511/rsa-genkey-02.c @@ -0,0 +1,42 @@ +#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; +} diff --git a/20230511/rsa-genkey-03.c b/20230511/rsa-genkey-03.c new file mode 100644 index 0000000..5286e8b --- /dev/null +++ b/20230511/rsa-genkey-03.c @@ -0,0 +1,44 @@ +#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; +} diff --git a/20230511/rsa-genkey-04.c b/20230511/rsa-genkey-04.c new file mode 100644 index 0000000..149c293 --- /dev/null +++ b/20230511/rsa-genkey-04.c @@ -0,0 +1,36 @@ +#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; +} diff --git a/20230511/rsa-genkey-05.c b/20230511/rsa-genkey-05.c new file mode 100644 index 0000000..36d9850 --- /dev/null +++ b/20230511/rsa-genkey-05.c @@ -0,0 +1,38 @@ +#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; +} diff --git a/20230511/rsa-genkey-06.c b/20230511/rsa-genkey-06.c new file mode 100644 index 0000000..652d45f --- /dev/null +++ b/20230511/rsa-genkey-06.c @@ -0,0 +1,44 @@ +#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; +} diff --git a/20230511/rsa-genkey-07.c b/20230511/rsa-genkey-07.c new file mode 100644 index 0000000..740d45e --- /dev/null +++ b/20230511/rsa-genkey-07.c @@ -0,0 +1,42 @@ +#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; +} diff --git a/20230511/rsa-genkey-08.c b/20230511/rsa-genkey-08.c new file mode 100644 index 0000000..b8d0d63 --- /dev/null +++ b/20230511/rsa-genkey-08.c @@ -0,0 +1,45 @@ +#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; +} diff --git a/20230511/rsa-genkey-09.c b/20230511/rsa-genkey-09.c new file mode 100644 index 0000000..50e5a9f --- /dev/null +++ b/20230511/rsa-genkey-09.c @@ -0,0 +1,48 @@ +#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; +} diff --git a/20230511/rsa-genkey-10.c b/20230511/rsa-genkey-10.c new file mode 100644 index 0000000..55f7eee --- /dev/null +++ b/20230511/rsa-genkey-10.c @@ -0,0 +1,50 @@ +#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; +} diff --git a/20230511/rsa-genkey-11.c b/20230511/rsa-genkey-11.c new file mode 100644 index 0000000..5c33814 --- /dev/null +++ b/20230511/rsa-genkey-11.c @@ -0,0 +1,50 @@ +#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; +} diff --git a/20230511/rsa.xcf.gz b/20230511/rsa.xcf.gz index 99c800d647e8970e3a2576fe290d777464913638..43b1808cba4258247e056c6f9f465e1b86d5926b 100644 GIT binary patch literal 418309 zcmb2|=3oE=<~MseOJbjw%2hR3$Dd(nKYf^Uj`~C)RliB?b4*Tl9afp9yv*52ZC$b? zlc|%+($y#Vzwb>i_sH4qcwt%9B<a$v1(VFSXdm-^vuoj#uuH*L#1fUvnN(X9Qe2mC zcx*d$!^rc&obCJb>z^};FIr|*8~b|g@uS^;=l|#VJ*WQ0|9Sss^W8JMP<>wgch&oS zS--z2aB!La|9IbiYy9-Tvu3^V@BiCnpBDP#=6=?1r*FM4{H+@#d0p4!!(_JGd7Iqx z|2~o3e)rqT+x;w7H~%KL+kNd+p1*73_Nosa_3!=vT{&OJlWtY{^5AW|!pqCI-79(V zpm*0U%^MXzPVC)Yx9a-`+3j+B3WF<?@B7Z*^Z1%I-`6~q8&xls#s749A9{P;qy48v zwyoZ9GVkxy(|2~&{%g(GeQ>RskH6;8WcK|1E6b~YrL5lby=dyH+f~=!viE<H+w*tw z-}zQOzu&)jZT)AZ^4{Y2b=gy|o7|H!`Ir5xn0@{~*+Y-Ma&z2{|NHiV?*CVRJHq0> 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