I am new to infosec and am recently study cryptography. In AES, if i have 192-bit key to encrypt 128-bit block size, won't it only be using the first 128-bit of my 192-bit key?? So what's that extra 64-bit key used for and how does that increase security?
The key is first put through an algorithm called a key schedule, which splits it up and expands it into a number of 128-bit round keys. These round keys are always 128 bits in length, regardless of the size of the AES key itself. Each of these round keys are fed into the end of each single round of the block cipher using the XOR operation. AES128 expands a 128-bit key into 11 round keys, AES192 expands a 192-bit key into 13 round keys, and AES256 expands a 256-bit key into 15 round keys.
The internals of the AES algorithm are described excellently in A Stick Figure Guide to AES.