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In the research paper Breaking the Bluetooth Pairing – The Fixed Coordinate Invalid Curve Attack? by Biham and Neumann, 2019, they talk about attacks in Bluetooth pairing, they state that in the pairing process which involves ECDH key exchange- "sending both the x-coordinate and the y-coordinate during the public key exchange is a design flaw as it is unnecessary and highly inadvisable, and it greatly increases the attack surface"

I'm aware that in other implementations only $x$-coordinate is sent in compressed form. I'm curious to know how sending both coordinates increases the attack surface, how important it is to know the information about the $y$-coordinate and what are the possible attacks related to this.

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The paper you reference mentions that although both coordinates are sent, the protocol only requires the x-coordinate to be authenticated and validated. This means that the y-coordinate is free to be manipulated in implementations that do the bare minimum. As mentioned in a comment, "poor programmers and bad quality testers will not consider [this vulnerability]".

Sending only one coordinate makes it less likely for an implementer to make a mistake. With only one coordinate, it's impossible for the second coordinate to be manipulated, and it's significantly harder to force someone to use a point not on the curve. It's easier to test that given a value, a function always generates a valid point or throws an error than it is to test that a protocol works correctly end-to-end for all possible inputs.

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  • $\begingroup$ I understand what you are trying to convey here, but I was thinking if there was anything else associated when it says "increased attack surface". Thanks. $\endgroup$
    – shijuza
    Aug 12 '20 at 20:57
  • $\begingroup$ During our research we discovered multiple design flaws in the Bluetooth specification. We then tested different Bluetooth implementations and found that a large majority of the Bluetooth devices are vulnerable. So, some has better team despite of the protocol flaw, or they just lucky. $\endgroup$
    – kelalaka
    Aug 12 '20 at 21:45

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