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