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The '''Toeplitz Hash Algorithm''' describes [[hash function]]s that compute hash values through [[matrix multiplication]] of the key with a suitable [[Toeplitz matrix]].<ref name="Krawczyk1995">{{cite
As an example, with the Toeplitz matrix <math>T</math> the key <math>k</math> results in a hash <math>h</math> as follows:
<!-- in python: import scipy as sc; T=sc.linalg.toeplitz([1,0,1],[1,1,0,1]); k=[1,1,0,0]; h=T.dot(k)%2; print('h =',h) -->
:<math>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}</math>
where the entries are bits and all operations are modulo 2. In implementations the highly redundant matrix is not necessarily explicitly stored.
==References==
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