Changes the choice-code base from HashAndSquare(prime_i) to the encoding prime
itself (a G_q element). The card code becomes prime_i^{Σ_j k_j}, which is
algebraic and therefore recomputable by the CCs directly from the submitted
ciphertext at vote time — the prerequisite for a genuine cast-as-intended
return-code path. Setup and (upcoming) vote-time extraction use the same base,
keeping them consistent.
Co-Authored-By: Claude Fable 5 <noreply@anthropic.com>