Randomness extraction algorithms play an essential role in Quantum Random Number Generators (QRNGs), where they are used to suppress unwanted classical noise and distill true randomness from their biased output. By employing the SHA-512 hash function and Toeplitz matrix multiplication, we analyse two suitable constructions based on different principles and reach postprocessing rates of 8.69 Mbps and 3.68 Mbps, respectively. Finally, we develop a length-compatible Toeplitz-hashing algorithm able to achieve rates of 143.29 Mbps in a parallelized GPU implementation.