diff --git a/DAS/Arithmetic.md b/DAS/Arithmetic.md index 254a1c6..fa656c1 100644 --- a/DAS/Arithmetic.md +++ b/DAS/Arithmetic.md @@ -39,3 +39,12 @@ Only valid for GCD = 1 1. $A = q_1 * B + r_1$ 2. $B = q_2 * r_1 + r_2$ 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 \ No newline at end of file