There is an encryption scheme where the votes are encrypted with ElGamal and the decryption key is the secret that is shared among the authorities. After everybody voted they publish their part of the secret according to the Shamir tresholding scheme and everybody can calculate the tally.
Is it possible that every voter is also an authority and that a threshold scheme is implemented such that the secret is if and only if reveled when a relative majority publishes their parts of the secret?
The basic idea of the voting scheme is from Cramer, Genaro and Shoemaker
the requirements are:
- eligible voters can cast their votes
- only eligible voters are allowed to cast votes
- Privacy: the secrecy of an individual vote must be maintained
- Correctness: the votes must be counted correctly
- Robustness: the scheme must work correctly even in the presence of attackers and dishonestly involved parties