In the paper we propose a new algorithm of data encryption, exploiting maps, also chaotic, of the unit interval. We consider the finite-state implementation of the systems, e.g. in computers. The characteristic feature of the algorithm is the possibility of adjusting security of data to be transmitted by means of the security index and the usage of chaos-based pseudorandom number generators as the source of running encryption keys. The algorithm enables fast encryption of those parts of data, which do not require high security. The change in encryption speed is achieved without any change of the length of encryption key, which can be fixed and constant during transmission. It is a distinguishing feature of the proposed system as compared to existing schemes.