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Background

I read an article about how car keys that remotely open one's car are not secure. This answer also talks about different encryption methods being insecure.

The article mentions that common encryption keys were used across many different vehicles.

Unique end-to-end encryption

Now, I am wondering: why do manufacturers not just assign unique keys for every single car-key combination?

A simple implementation I would imagine is the vehicle and key using a unique mathematic formula to build a code based on time. Now, only keeping the time accurate would need to be assured and I cannot imagine a way of a third party cracking this scheme. See: the code would never be the same for any second in time and with a formula complex enough no correlation visible.

Why are remote keys insecure?

Car keys still being insecure today leads me to the conclusion that there must be some loophole in my idea.

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