Toeplitz Hash Algorithm

Toeplitz Hash

General
Related to	Receive Side Scaling

The Toeplitz Hash Algorithm describes hash functions that compute hash values through matrix multiplication of the key with a suitable Toeplitz matrix. The Toeplitz Hash Algorithm is used in many network interface controllers for receive side scaling.

As an example, with the Toeplitz matrix $T$ the key $k$ results in a hash $h$ as follows:

$h=T\cdot k={\begin{pmatrix}1&1&0&1\\0&1&1&0\\1&0&1&1\\\end{pmatrix}}\cdot {\begin{pmatrix}1\\1\\0\\0\\\end{pmatrix}}={\begin{pmatrix}0\\1\\1\\\end{pmatrix}}$

where the entries are bits and all operations are modulo 2. In implementations the highly redundant matrix is not necessarily explicitly stored.