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127ae61d11 Cast-as-intended return codes: CC extraction + voter check
The return code the voter checks is now genuinely computed by the CCs from the
submitted ciphertext, not looked up from the card:

- returncode_extract.go: after a ballot is accepted, the server asks each CC to
  exponentiate E2 by its return-code key (product over CCs = Enc(vote^Σk)), then
  each CC contributes a partial-decryption factor; the server recovers vote^Σk,
  which equals the card base prime_sel^Σk, and looks up the short code.
- The server returns that code to the voter, who checks it against the card for
  the chosen option; a mismatch aborts with a clear error.

Soundness test: a malicious client that encrypts option A for the tally (E1) but
option B in the return-code channel (E2) is REJECTED by the plaintext-equality
proof — so the code shown always reflects the tallied vote. This closes the
cast-as-intended gap (the old return codes were decorative, finding F16).

Card lCC now uses a fixed tau so extraction can recompute it without learning
the option up front.

Co-Authored-By: Claude Fable 5 <noreply@anthropic.com>
2026-07-06 15:52:30 +02:00