In this paper, we present an electronic voting (namely e-voting) system based on cryptographic techniques. Recently, some countries have used e-voting systems using an electronic voting device instead of a voting sheet. These e-voting systems are the early stage which is not online voting. Many cryptographers have studied on-line e-voting systems based on cryptographic techniques. For a secure on-line e-voting system, it is required some requirements like privacy, unreusability, verifiability, receipt-freeness, and so on. In this paper, we point out that it can be happened a vote-selling and a vote-coercion in the conventional voting (i.e., the paper voting) by a cellular phone with camera and a mini digital camera. To prevent the vote-selling and a vote-coercion, a few receipt-free schemes have been proposed in the e-voting system area. The existing 1-out-of-L e-voting systems are based on ElGamal cryptosystem. We compare the computational complexity of the proposed 1-out-of-L e-voting system with that of the 1-out-of-L e-voting system based on ElGamal cryptosystem. Moreover, we extend the proposed 1-out-of-L e-voting system to ballot-cancellation property. The existing e-voting systems had been overlooked the ballot-cancellation property. There is the reason that the ballot is cancelled according to an election law. For our e-voting system with ballot-cancellation property, we extend the homomorphic property based on r-th residue encryption. The extended homomorphic property is used to cancel votes with guaranteeing anonymity and privacy. When the ballot is cancelled, the ballot-cancellation scheme should satisfy privacy and verifiability.
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