This is such a cool technique, and you could even teach it in secondary schools as a neat thing computer scientists can do with polynomials.
I am a secondary math teacher and I do exactly this with my students.
When working on retrieving the expression of an affine function, I tell them about Shamir'..., they choose a secret pin as the slope, generate two points, give them to two other students who have to pair together to find the pin again. The students are always very engaged.
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