Toeplitz Hash Algorithm

The Toeplitz Hash Algorithm describes hash functions that compute hash values through matrix multiplication of the key with a suitable Toeplitz matrix.^[1] The Toeplitz Hash Algorithm is used in many network interface controllers for receive side scaling.^[2][3]

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

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

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