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Jan Meyer
2026-03-09 23:19:23 +01:00
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DAS/Arithmetic.md
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@@ -39,3 +39,12 @@ Only valid for GCD = 1
1. $A = q_1 * B + r_1$ 1. $A = q_1 * B + r_1$
2. $B = q_2 * r_1 + r_2$ 2. $B = q_2 * r_1 + r_2$
3. $r_1 = q_3 * r_2 + 1$ 3. $r_1 = q_3 * r_2 + 1$
2. **Unwrap**
1. $1 = r_1 - (q_3 * r_2)$ mit $r_2 = B - q_2 * r_1$
2. $1 = r_1 - (q_3 * (B - q_2 * r_1))$ mit $q_3$ ausmultiplizieren
3. $1 = (1 + q_3 * q_2) * r_1 - q_3 * B$ mit $r_1 = A - q_1 * B$
4. $1 = (1 + q_3 * q_2) * (A - q_1 * B) - q_3 * B$
3. **Simplify to** $x * A + y * B$
4. Coefficient of $A$ is the modular inverse