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Well, we use finite fields to select shares. What happened if we use infinite fields.then will the scheme be vulnerable? Easy to break? Or share generation and reconstruction will be difficult? Please explain

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    $\begingroup$ You can't sample uniformly from an infinite set, for starters. $\endgroup$ – fkraiem Jun 21 '16 at 8:11
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https://en.wikipedia.org/wiki/Shamir%27s_Secret_Sharing

This will answer your question.

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