Applications of VANET (Vehicular ad hoc Networks) networks is focused on monitoring of the safety states of vehicles or roadway by exchanging messages between vehicles and infrastructure so that the applications will be able to help a driver to handle insecure situations. They are able to warn before possible risks which can occur during the process of transportation. Essential tool for assuring of safety communications within developed applications of intelligent transportations systems are cryptography constructions on the basis of digital signature schemes. In order to assuring safety and anonymity within vehicular communications are used pseudorandom authentications methods. The authors in the paper are focused on realization of mathematical model and description of modified cryptographic constructions which are suitable for sensor networks and applications orientated to memory and performance. In these systems it is very important to use signature scheme which do not have only computational safety but must also be effective from the view of performance and must generate short digital signatures in order to communications in real time conditions.
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