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Fast modular exponentiation — `PowerMod[b, e, m] == Mod[b^e, m]`.
`PowerMod[a, b, m]` computes `a^b mod m`. Modular inverses - the `b = -1` form - are the exception: above roughly 61-bit moduli the call returns unevaluated while smaller moduli work, which is exactly the field size cryptographic work uses. Until that is fixed, compute the inverse with `ExtendedGCD[a, m][[2, 1]]`, which is reliable at any size and returns the same value (reduce it with `Mod[..., m]` if you need the canonical representative).