Car-sharing is currently a very popular and rapidly expanding service. On the one hand, it helps users to use their vehicles efficiently and reduce the cost of car ownership. On the other hand, it allows users who do not own a car to have a car on demand if they need it. In this paper, we present a novel car-sharing system where users can use and share their cars without the need for physical keys. The system design targets smaller fleets and car-sharing solutions that require simplicity, high security, user privacy, and low computational power. The system is based on secure cryptographic algorithms. We also provide several experimental results that demonstrate the effectiveness of the system on different devices including computationally constrained devices such as microcontrollers and smart cards.