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I took a brief look at the code, but I fail to see how this transformation could introduce any additional secrecy. If the randomness used to define the polynomial is good, then Shamir's secret sharing provides information theoretic secrecy (no matter how the secret actually looks like). What Ricky points out in his answer seems reasonable, i.e., to provide ...


Note that, despite your notation, the exponent does not need to be prime. "Why is that?" They probably do that to reduce the impact of malleability on the reconstruction process. "Which attack does it prevent?" It might prevent simple malleation when the secret is not easily guessable. "Does it help when the secret has a short bit length?" Yes.

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