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What exactly is the difference between key transport and key encapsulation? Either they seem to be used interchangeably or I'm mixing stuff up.

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Key encapsulation or key wrapping is the encryption of a key with another key. There may be a symmetric key or asymmetric key pair that encapsulates the key destined for transportation; this key can then be called a key transport key.

Key transportation is simply the secure transportation of a key. For public keys you'd expect integrity and authenticity - so that the receiver can trust the public key to have been sent by the right entity. Secret keys require confidentiality as well - which is why they are commonly encapsulated. Private keys would also require confidentiality of course, but generally you should not transport private keys at all - they're private: not to be shared.

Commonly I'd expect encapsulation / wrapping to be used for secret keys for secure transport. It is however perfectly possible to secure them otherwise (diplomatic post with a USB-thumbstick for instance).

Key encapsulation & transport is just one way of establishing keys between two or multiple parties. Another way would be (authenticated) key agreement, key sharing schemes and so on.

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