A cryptographic security scheme is proposed for a subsystem of the integrated computer-aided system that is intended for holding elections and counting the election returns. The main idea is to use two modern quantum cryptographic technologies: quantum bit commitment and quantum secret sharing. The scheme of information security of vote count procedure, and also the quantum bit commitment protocol and the quantum secret sharing protocol, are described. Using the protocols of quantum cryptography increases security of the computer-aided voting system on comparison with protocols of usual classical cryptography.