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- - **Extended Euclidean Algorithm Explanation Help and Modular Multiplicative Inverse**
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Extended Euclidean Algorithm Explanation Help and Modular Multiplicative InverseHello to all, i have a hard time understand this these two topics.
I hope someone can clear my myth. I do check the EEA page and did quite amount of research regarding this topic. This is what i understand. 51x + 36y = gcd(a, b) Rewrite them in quotient remainder theorem Euclid Algorithm 51 = 1 x 36 + 15 52 / 36 = 3 r 6 36 = 2 x 15 + 6 36 / 15 = 2 r 6 15 = 2 x 6 + 3 15 / 6 = 2 r 3 6 = 2 x 3 + 0 6 / 2 = 3 r 0 Extended Euclidean Algorithm =Take the last second solution 15 = 2 x 6 + 3 Rewrite the remainder at LHS 3 = 15 - 2 x 6 = 15 - 2 x (36 - 2 * 15) = 5 * 15 - 2 * 36 (simplifying)(*) = 5 * (51 - 36) - 2 * 36 = 5 * 51 - 7 * 36 (simplifying)(*) Question 1. How modular multiplicative inverse related to EEA ? Please show example. 2. How to simplify the equation(*) ? 3. How human hand calculation differ to code implementation ? Thanks for your help. |

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