From 2ba0a03f03d730b1bbf0bacca3bb43f490fb1e65 Mon Sep 17 00:00:00 2001
From: Denis Monnerat <monnerat@u-pec.fr>
Date: Thu, 20 Feb 2025 11:41:41 +0100
Subject: [PATCH] tp1
---
README.md | 11 +-
td_tp/tp1/README.md | 193 ++++++
td_tp/tp1/aide.md | 41 ++
td_tp/tp1/img/TEA.png | Bin 0 -> 26625 bytes
td_tp/tp1/img/feistel.png | Bin 0 -> 64644 bytes
td_tp/tp1/img/feistel.svg | 1263 ++++++++++++++++++++++++++++++++++
td_tp/tp1/img/xtea.png | Bin 0 -> 4885 bytes
td_tp/tp1/src/ex1/file.crypt | Bin 0 -> 644 bytes
td_tp/tp1/src/ex1/lfsr.c | 42 ++
td_tp/tp1/src/ex2/key1.k | 1 +
td_tp/tp1/src/ex2/xtea.c | 11 +
11 files changed, 1561 insertions(+), 1 deletion(-)
create mode 100644 td_tp/tp1/README.md
create mode 100644 td_tp/tp1/aide.md
create mode 100644 td_tp/tp1/img/TEA.png
create mode 100644 td_tp/tp1/img/feistel.png
create mode 100644 td_tp/tp1/img/feistel.svg
create mode 100644 td_tp/tp1/img/xtea.png
create mode 100644 td_tp/tp1/src/ex1/file.crypt
create mode 100644 td_tp/tp1/src/ex1/lfsr.c
create mode 100644 td_tp/tp1/src/ex2/key1.k
create mode 100644 td_tp/tp1/src/ex2/xtea.c
diff --git a/README.md b/README.md
index e275134..3b491f7 100644
--- a/README.md
+++ b/README.md
@@ -1,3 +1,12 @@
# BUT2FI_R4.B.10
-Cryptographie - Outils et algorithmes
\ No newline at end of file
+Cryptographie - Outils et algorithmes
+
+[Cours crypto](cours/crypto.pdf)
+
+#### Semaine 1
+- cm : [Chiffrements par bloc, algorithmes à clefs symétriques](cours/crypto.pdf).
+- tp : [lfsr, tea, hachages](td_tp/tp1)
+
+
+
diff --git a/td_tp/tp1/README.md b/td_tp/tp1/README.md
new file mode 100644
index 0000000..0931fc3
--- /dev/null
+++ b/td_tp/tp1/README.md
@@ -0,0 +1,193 @@
+# TP1
+- Registre à décalage à rétroaction linéaire (lfsr),
+- Chiffrement par bloc symmétrique (TEA), fonction de hachage.
+
+## EX1
+Le but est d'implanter un registre à décalage linéaire, sur un octet.
+
+
+À chaque étape, le registre (un octet) $(b_7,b_6,b_5,b_4,b_3,b_2,b_1,b_0)$ est décalé à gauche, et
+le bit $b_0$ est remplacé par un bit, calculé par une fonction linéaire $f$.
+
+
+
+Vous disposez d'un [fichier](src/ex1/file.crypt) crypté avec un lfsr, en faisant
+un XOR de chacun des octets avec les valeurs successives du registre. L'état
+initial du registre était `0xa7`, et la fonction utilisée
+
+
+\[
+ f(b_7,b_6,b_5,b_4,b_3,b_2,b_1,b_0) = b_7\oplus b_6\oplus b_5\oplus b_4\oplus b_3\oplus b_1
+\]
+
+Retrouver le fichier initial.
+
+Vous pouvez utiliser la fonction interne `__builtin_parity` de `gcc`.
+
+## Ex2
+
+Tiny Encryption Algorithm est un algorithme de chiffrement symétrique par
+bloc. les algorithmes de chiffrement sysmétrique par bloc crypte/decrypte des
+**blocs** entiers, en utilisant la même clé secrète (symétrique). TEA est un
+exemple simple de tels algorithmes (DES, AES, Blowfish) facile à implanter. La
+plupart de ces algorithmes utilise ce que l\'on appelle un réseau de Feistel.
+
+##### Réseau de Feistel
+
+Désignons par $K$ la clé (un mot binaire). On décompose le bloc à
+crypter en 2 moitiés $(L_0,R_0)$ On lui applique une
+transformation de la forme :
+
+\[
+(L_0,R_0) \rightarrow (L_1,R_1)
+ \, où \,
+\left\{\begin{matrix} L_1 & = & R_0 \\
+R_1 & = & L_0 + f(R_0,K)
+\end{matrix}\right.
+\]
+
+
+- La loi $+$ doit simplement être "réversible" (une loi de
+ groupe). Dans la pratique, il s'agit souvent d'un xor, mais pour
+ TEA, il s\'agit de l'addition binaire.
+- La fonction $f$ n'a pas besoin d'être inversible pour que la
+ transformation précédente soit réversible.
+
+ Pourquoi ? Comment fait-on ?
+- Le chiffrement consiste alors à itérer la transformation (appelée
+ round) un certain nombre de fois.
+
+<div align="center">
+<img src="./img/feistel.png">
+</div>
+
+##### XTEA
+
+XTEA (cf cours) crypte des blocs de 8 octets, en utilisant une clé de 16 octets.
+
+Un cycle (2 rounds, itéré 32 fois) de XTEA est donné par le réseau
+suivant :
+<div align="center">
+
+<img src="./img/xtea.png">
+</div>
+
+En vert, il s'agit de l'addition binaire sur 32 bits, en rouge le xor.
+
+- la clé est décomposée 4 sous-clés $K[0],K[1],K[2],K[3]$.
+- chaque round utilise un multiple de $\delta = ( \sqrt{5} - 1 ) * 2^{31}$ pour rendre les rounds non symétriques.
+
+Voici un exemple de code correspondant :
+```c
+void encrypt(uint32_t v[2], uint32_t const key[4])
+{
+ unsigned int i;
+ uint32_t v0=v[0], v1=v[1], sum=0, delta=0x9E3779B9;
+ for (i=0; i < 32; i++) {
+ v0 += (((v1 << 4) ^ (v1 >> 5)) + v1) ^ (sum + key[sum & 3]);
+ sum += delta;
+ v1 += (((v0 << 4) ^ (v0 >> 5)) + v0) ^ (sum + key[(sum>>11) & 3]);
+ }
+ v[0]=v0; v[1]=v1;
+}
+```
+
+
+##### Padding (bourrage)
+
+Lorsque l'on cherche à crypter un fichier, sa taille n'est pas
+toujours un multiple de la longueur des blocs chiffrés par
+l'algortihme. Il existe différentes techniques dites de padding. Nous
+utiliserons celle-ci :
+
+- Si le dernier bloc à chiffer du fichier n'est pas entier, on écrit
+ dans son dernier octet le nombre d'octets manquants. Les octets
+ précédents peuvent être zéroifiés, ou remplis aléatoirement.
+- Si le dernier bloc est entier, on rajoute tout un bloc pour qu'il
+ n'y est pas d'ambiguité.
+
+Voici un exemple avec des blocs de taille 8 octets. Le fichier en entrée
+est
+```
+ascii : hello word!
+hex : 68 65 6c 6c 6f 20 77 6f 72 6c 64 21
+```
+
+Le dernier bloc est
+```
+ascii : ord!
+hex : 72 6c 64 21 00 00 00 04
+```
+
+On ajoute des zéros (ou des octets aléatoires), et le dernier est le
+nombre d'octets ajoutés (ici, 4). Si le dernier bloc est complet, on
+rajoute tout un bloc.
+
+```
+hex : 00 00 00 00 00 00 00 00 08
+```
+
+##### Votre travail
+
+1. Ecrire une fonction qui decrypte un bloc.
+2. Ecrire une commande **xtea** qui permet de (dé)chiffrer un fichier.
+
+ ```bash
+ xtea -e|-d filekey file1 file2
+ ```
+
+ - `filekey` est le fichier ou est stocké la clé. Vous pouvez en
+ générer en utilisant le pseudo fichier `/dev/urandom`, et la
+ commande `dd`.
+ - l'option `-e` crypte. `file1` est alors le fichier à crypter,
+ `file2` le fichier crypté.
+ - l'option `-d` decrypte. `file1` est alors le fichier crypté, `file2`
+ le fichier decrypté.
+3. Testez avec cette [clé](./src/ex2/key1.k), et ce [fichier
+ crypté](./src/ex2/fichier.crypt) sur une architecture little-endian.
+
+4. Écrire une version de tea en mode CBC :
+
+ ```bash
+ xtea_cbc -e|-d iv filekey file1 file2
+ ```
+
+ `iv` est le vecteur d'initialisation (8 octets) donné sur la ligne de commande.
+
+ **Rappel** : en mode CBC, le bloc à chiffrer subit un XOR avec le chiffré du bloc précédent. Le vecteur d'initialisation sert
+ pour le premier bloc.
+
+### Ex3: une fonction de hachage cryptographique avec XTEA
+
+Une fonction de hachage cryptographique permet de "résumer" un
+fichier, message en calculant une empreinte. Une telle fonction,
+mathématiquement, peut-être formalisée par
+
+\[
+ \begin{matrix}
+\{0,1\}^{*} & \rightarrow & \{0,1\}^n \\
+m &\rightarrow & f(m) \end{matrix}
+
+\]
+
+$n$ est la taille de l'empreinte. Elle vaut 128 par exemple pour MD5 et SHA-1.
+
+Grâce à XTEA, on va construire une telle fonction pour avec $n=64$.
+
+Voici le principe.
+
+- Le message ou fichier est décomposé en bloc de 24 octets (on bourrera
+ le dernier bloc suivant le pricincipe déjà vu en ajoutant des octets
+ avec la valeur du nombre d'octets ajoutés).
+- Chaque bloc est vu comme un bloc suivi d'une clé de XTEA $x,k$
+ (bloc $x$ de 8 octets, clé $k$ de 16 octets). On calcule
+ $hash = xtea(x,k) \oplus x$.
+- On combine le hash du bloc courant avec le hash du bloc précédent à
+ l'aide d'un xor. Le hash finale est l'empreinte.
+
+##### Votre travail
+
+1. Implantez le fonction prédente. Testez-là. Vérifiez que pour un message
+"assez proche", l'empreinte est "vraiment" différente.
+
+
diff --git a/td_tp/tp1/aide.md b/td_tp/tp1/aide.md
new file mode 100644
index 0000000..422bef6
--- /dev/null
+++ b/td_tp/tp1/aide.md
@@ -0,0 +1,41 @@
+### Setting a bit
+
+Use the bitwise OR operator (|) to set a bit.
+
+`number |= 1 << x;`
+
+That will set bit x.
+
+### Clearing a bit
+
+Use the bitwise AND operator (&) to clear a bit.
+
+`number &= ~(1 << x);`
+
+That will clear bit x. You must invert the bit string with the bitwise NOT operator (~), then AND it.
+
+### Toggling a bit
+
+The XOR operator (^) can be used to toggle a bit.
+
+`number ^= 1 << x;`
+
+That will toggle bit x.
+
+### Checking a bit
+
+You didn't ask for this but I might as well add it.
+
+To check a bit, shift the number x to the right, then bitwise AND it:
+
+`bit = (number >> x) & 1;`
+
+That will put the value of bit x into the variable bit.
+
+### Changing the nth bit to x
+
+Setting the nth bit to either 1 or 0 can be achieved with the following:
+
+`number ^= (-x ^ number) & (1 << n);`
+
+Bit n will be set if x is 1, and cleared if x is 0.
diff --git a/td_tp/tp1/img/TEA.png b/td_tp/tp1/img/TEA.png
new file mode 100644
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diff --git a/td_tp/tp1/src/ex1/file.crypt b/td_tp/tp1/src/ex1/file.crypt
new file mode 100644
index 0000000000000000000000000000000000000000..1f1e6c254d0fa5ffb3b54687f074421b66eacbf8
GIT binary patch
literal 644
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literal 0
HcmV?d00001
diff --git a/td_tp/tp1/src/ex1/lfsr.c b/td_tp/tp1/src/ex1/lfsr.c
new file mode 100644
index 0000000..ffa713d
--- /dev/null
+++ b/td_tp/tp1/src/ex1/lfsr.c
@@ -0,0 +1,42 @@
+#include <stdio.h>
+#include <assert.h>
+#include <stdlib.h>
+#include <unistd.h>
+#include <fcntl.h>
+
+#define MASK_BIT_7 0x80
+#define MASK_BIT_6 0x40
+#define MASK_BIT_5 0x20
+#define MASK_BIT_4 0x10
+#define MASK_BIT_3 0x08
+#define MASK_BIT_2 0x04
+#define MASK_BIT_1 0x02
+#define MASK_BIT_0 0x01
+
+
+unsigned char next(unsigned char lfsr)
+{
+ // TODO
+}
+
+int main(int argc, char *argv[])
+{
+ int fd_in,fd_out;
+ unsigned char w,buf;;
+
+
+ assert(argc >= 4);
+ fd_in = open(argv[1],O_RDONLY);
+ fd_out = open(argv[2],O_WRONLY|O_TRUNC|O_CREAT,0600);
+ w = (unsigned char)strtol(argv[3],NULL,0);
+
+ while(1){
+ ssize_t nb = read(fd_in,&buf,1);
+ if (nb <=0)
+ break;
+ buf ^= w;
+ write(fd_out,&buf,1);
+ w=next(w);
+ }
+ return 0;
+}
diff --git a/td_tp/tp1/src/ex2/key1.k b/td_tp/tp1/src/ex2/key1.k
new file mode 100644
index 0000000..7fc6ef4
--- /dev/null
+++ b/td_tp/tp1/src/ex2/key1.k
@@ -0,0 +1 @@
+ �N� {q2�*:����mfU#� `���?&Q3
\ No newline at end of file
diff --git a/td_tp/tp1/src/ex2/xtea.c b/td_tp/tp1/src/ex2/xtea.c
new file mode 100644
index 0000000..549caf6
--- /dev/null
+++ b/td_tp/tp1/src/ex2/xtea.c
@@ -0,0 +1,11 @@
+void encrypt(uint32_t v[2], uint32_t const key[4])
+{
+ unsigned int i;
+ uint32_t v0=v[0], v1=v[1], sum=0, delta=0x9E3779B9;
+ for (i=0; i < 32; i++) {
+ v0 += (((v1 << 4) ^ (v1 >> 5)) + v1) ^ (sum + key[sum & 3]);
+ sum += delta;
+ v1 += (((v0 << 4) ^ (v0 >> 5)) + v0) ^ (sum + key[(sum>>11) & 3]);
+ }
+ v[0]=v0; v[1]=v1;
+}