With the advent of Internet Communications Technologies (ICT), the use of cryptographic protocols is a technical response to the loss of all traditional means that were used so far to establish security in democratic elections. We employ simple cryptographic techniques to address the “abstaining voters” problem in electronic elections with central administration. In such elections, voting authorities can cast a bogus vote on behalf of an authorized voter who decides to abstain. Our system is equitably fair: while a voter who registers for the election is allowed to abstain form voting (legal abstention), all registered voters who cast an encrypted vote must acknowledge, at some time later, the fact that they have voted. If not (illegal abstention), a cryptographic time capsule will be broken and their identity will be disclosed. Our system satisfies most requirements of a secure election and could be used in similar frameworks such as electronic polling and/or surveys over the Web.