  This paper presents the derivation of a new algorithm for multiplying of two
Kaluza numbers. Performing this operation directly requires 1024 real
multiplications and 992 real additions. The proposed algorithm can compute the
same result with only 512 real multiplications and 576 real additions. The
derivation of our algorithm is based on utilizing the fact that multiplication
of two Kaluza numbers can be expressed as a matrixvector product. The matrix
multiplicand that participates in the product calculating has unique structural
properties. Namely exploitation of these specific properties leads to
significant reducing of the complexity of Kaluza numbers multiplication.
