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There are many questions surrounding the differences between symmetric and asymmetric encryption keys. I think I've read them all at this point. But I'm still left wondering:

Why does a "secure" symmetric key only have to be (roughly) 256 bits, while asymmetric keys must be at least 2048 bits long to be considered "secure"?

Does the definition of "secure" change between the encryption types? Or is there something about specific implementations that necessitate much longer keys for asymmetric encryption schemes?

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