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According to wikipedia, if you are using shamir's secret sharing scheme with a field of order $p$, "High values of $p$ are risky because Eve knows that the chance for $f(x)\pmod{p}=f(x)$ increases with a higher $p$". Is this true? It seems wrong.

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  • $\begingroup$ what that means is f(x) is smaller than p, so mod p does not change the value $\endgroup$ Feb 13 '16 at 0:31
  • $\begingroup$ @RichieFrame Well, yeah. But why would $f(x) \pmod{p} = f(x)$ hurt security? $\endgroup$
    – PyRulez
    Feb 13 '16 at 0:50
  • $\begingroup$ when that is the case it is like you are not using the mod p at all, an attacker can skip that step completely, substantially reducing the effort to guess values if points are known $\endgroup$ Feb 13 '16 at 0:57
  • $\begingroup$ @RichieFrame Calculating moduluses wasn't that hard to begin with. Besides, Shamir's secret sharing is informationally secure, so it isn't a matter of effort anyway. $\endgroup$
    – PyRulez
    Feb 13 '16 at 1:05
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    $\begingroup$ "It seems wrong" -> it is wrong; there's no security issue with large $p$ values. $\endgroup$
    – poncho
    Feb 13 '16 at 4:11