Applications and Reality Checks

Modular Lock Lab

When the Key Exists, Extended Euclid Finds It

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gcd(a, m)

Inverse

Locked?

13 * (-13) + 34 * (5) = 1

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Rigour stays visible

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Extended Euclid produces coefficients x and y with a*x + b*y = gcd(a, b).
If gcd(a, b) = 1, the x coefficient from extended Euclid gives the inverse of a modulo b.

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