A simple alternative to Benaloh challenge for the cast-as-intended property in Helios/Belenios

Helios is a well-established online voting protocol which has been used for different real world elections, and which aims at ensuring-among other properties-verifiability. Belenios is a variant of Helios that brings eligibility verifiability and a threshold decryption à la Pedersen to distribute trust. In both protocols, the cast-as-intended property, part of verifiability, is obtained using a castor audit technique known as Benaloh challenge: each voter can choose to either audit her encrypted ballot, or to submit it. However, an audited ballot can never be submitted, as the audit breaks vote secrecy. This means that in particular none of the ballots which are actually submitted and counted have been audited. We propose a simple variant, that might be better suited in some situations. In our solution, each vote is partially audited before being submitted. The partial audit ensures that errors are detected with a certain probability, without breaking secrecy