A graph theoretic method for securing key fobs
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ORIGINAL RESEARCH
A graph theoretic method for securing key fobs Farideh Heydari1 · Alireza Ghahremanian2 Received: 17 July 2020 / Accepted: 7 November 2020 © Islamic Azad University 2020
Abstract Key fobs are small security hardware devices that are used for controlling access to doors, cars and etc. There are many types of these devices, more secure types of them are rolling code. They often use a light weight cryptographic schemas to protect them against the replay attack. In this paper, by the mean of constructing a Hamiltonian graph, we propose a simple to implement and secure method which overrides some drawbacks of traditional ones. Let m, n > 1 be two integers, and ℤn be a ℤm-module. Here, we determine the values of m and n for which the ℤn-intersection graph of ideals of ℤm is Hamiltonian. Then a suitable sequence will be produced which by some criteria can be used as the authenticator. Keywords Security · Access control key fob · Intersection graph · Hamiltonian cycle Mathematics Subject Classification 05C25 · 05C45 · 13M05 · 68R10
Introduction In the context of RKE (remote keyless entry), Key fobs are electronic devices which are used for controlling and granting access to buildings or automobiles by the mean of radio frequency (or infrared beams in older variants). Key fobs are part of a system which consists of two main parts, one part is key fob which has less memory and computing power and the other is receiver which is richer in both items. Most of these devices use simple protocols which are based on one way authentication schemes and light weight cryptographic algorithms such as Hitag or keeloq.
Contribution Often in RKE’s protocols every device has a unique serial number (sometimes as UID), a counter, a factory key and an encryption key. Some devices use factory key as encryption
key and some do not use factory key directly. They derive a new key from factory key by a vendor defined mechanism and then use this new key as encryption key. Each time a user push one of key fob’s button, counter increases one, then the new counter encrypted using encryption key to generate KS. The obtained KS beside some plain parts such as a portion of counter, serial number and pressed button are sent over the air as a bit sequence (Fig. 1). The key point in these type of protocols is to guarantee no one can predict neither the next KS nor the keys. But since the serial number and partial part of counter are sent plain, adversaries can gain them to attack the algorithm and break it in acceptable time [1, 2]. It is clear that eliminating plain items from sent frame or removing the relation between authenticator (KS) and plain items will improve the security. In this paper, by gaining Hamiltonian cycles a new and non-cryptographic successor for traditional approaches is given. We introduce a Hamiltonian cycle by a constructive method which also generates KS independent of plain parts.
* Farideh Heydari f‑[email protected]
Organization
Alireza Ghahremanian [email protected]
The rest of this paper is f
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