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UTC501/25-01-30/README.md

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+# UTC 501 31/01/2025
+
+## Exercice 7 
+
+```
+p = 17, q = 11
+
+n = pq = 187
+
+e = 7 premier avec (p - 1)(q - 1) = 160
+```
+
+### 1)
+
+```
+1 = u * 7 + v * 160
+    |
+    V
+    d
+
+160 = 22 * 7 + 6
+7 = 1 * 6 + 1
+6 = 6 * 1 + 0                   d    e
+                                |    |
+1 = 7 - 1 * 6                   V    V
+1 = 7 - 1(160 - 22 * 7) =-160 + 23 * 7
+```
+
+### 2)
+
+```
+12 00 13 01 20 08
+l  _  m  a  t  h
+
+séparer en groupe de 3
+
+120 013 012 008
+
+--------------------------
+
+120 = 
+
+(120²)³ * 120 Mod(187)
+120² = 14400 ≡ 1 Mod (187)
+1 * 120 ≡ 120 Mod (187)
+
+120
+
+--------------------------
+
+013 =
+
+(13³)² = 2197² ≡ 140² Mod(187)
+19600 ≡ 152 Mod (187)
+152*13 ≡ 103 Mod (187)
+
+106
+
+--------------------------
+
+012 = 
+
+(12³)² = 1728² ≡ 45² Mod (187)
+1764 ≡ 81 Mod (187)
+81 * 12 ≡ 37 Mod (187)
+
+
+
+
+---------------
+
+12⁷ (Mod 187) 
+
+35831808 modulo 187 = 177
+
+35831808 ≡ 177 (mod 187)
+177
+
+---------------
+
+00⁷ Mod(187)
+
+0 modulo 187 = 0
+
+0 ≡ 0 (mod 187)
+0
+
+---------------
+
+13⁷ (Mod 187)
+
+62748517 modulo 187 = 106
+
+62748517 ≡ 106 (mod 187)
+106
+
+---------------
+
+01⁷ (Mod 187)
+
+1 modulo 187 = 1
+
+1 ≡ 1 (mod 187)
+1
+
+---------------
+
+20⁷ (Mod 187)
+
+1280000000 modulo 187 = 147
+
+1280000000 ≡ 147 (mod 187)
+147
+
+---------------
+
+08⁷ Mod(187)
+
+2097152 modulo 187 = 134
+
+2097152 ≡ 134 (mod 187)
+134
+
+---------------
+
+Résultat Final 177-000-106-001-147-134
+
+---------------
+
+120
+
+
+```