With these products, we show how practically feasible attacks on PKES systems are prevented.
With PKES, the car owner is passively authenticated based on the proximity of a car to its corresponding key, which belongs to the car owner.
demonstrated that relay attacks could be used against PKES in modern cars .
In this section, we explain the PKES system and the metrics used for similarity measurements.
With PKES, a car communicates with its corresponding key using magnetically coupled RF signals.
In contrast to existing PKES, our method needs both entities to have a microphone by which they record sounds; accordingly, it seems that our method might have a limitation to be directly applied into current cars.
 presented a KDM-CPA secure PKE for the set of Boolean circuits whose sizes are a priori bounded, which is a very large function set.
 proposed the first efficient KDM[[F.sup.d.sub.poly]]-CPA secure PKE. The ciphertext of their PKE construction is almost compact and consists of only O(d) group elements.
The CCS approach follows the Naor-Yung paradigm , and the building blocks are a PKE scheme with CCA security, a PKE scheme with KDM-CPA security, and a noninteractive zero-knowledge (NIZK) proof system which proves that the two PKE schemes encrypt the same message.
To obtain efficient KDM-CCA secure PKE, we have to employ an efficient PKE scheme with KDM-CPA security and the Groth-Sahai proofs if we follow the CCS approach .
 proposed a KDM-CCA secure PKE scheme from the Matrix Decisional Diffie-Hellman assumption.
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