SHA3 HMAC key padding According to the pseudocode, keys longer than the block-size of the underlying hash function are shortened by hashing the key. Furthermore, keys shorter than the blocksize are zero-padded up the length of the block-size.

    if (length(key) &gt; blocksize) {
        key = hash(key) // keys longer than blocksize are shortened
    }
    if (length(key) &lt; blocksize) {
        // keys shorter than blocksize are zero-padded (where ∥ is concatenation)
        key = key ∥ [0x00 * (blocksize - length(key))] // Where * is repetition.
    }


Taking into account that the block-size of SHA3-512 is 72 bytes, and it's output is 64 bytes, does that mean the keys longer than 72 bytes should first be hashed and then the resulting 64 bytes should be zero-padded?
In lieu of any answers; I've compared my own implementation with the few test vectors I've been able to find (one of which can be found here) and it would appear that yes, keys longer than the block-size are hashed and zero-padded. It feels counter-intuitive to shorten a key and zero-pad it, but that's what the specification stipulates.