When they are authenticating, they derive a key known as the Pairwise Transient Key (PTK) using: The client and router MACs, client and router nonce values, and of course the PMK. The PMK (which you are trying to brute-force) is presumably held by both the client and the router. WPA-PSK iterates your SSID and Pre-shared key through a HMAC-SHA1 hash function into a "raw" 256 bit key called the Pairwise Master Key (PMK).
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