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We then design the decomposition/recomposition algorithm by means of downsampling/upsampling and convolution products.
In Sect. 2 we define convolution products and prove a convolution theorem.
The convolution, Kronecker convolution and Hadamard convolution products are matrix functions defined for as follows (whenever the integral is defined).
We are concerned with Kronecker and Hadamard convolution products and present some important connections between these two products.
Then by applying the single and double convolution products, we produce some new equations having polynomials coefficients.
It is also proved that the results can be extended to the finite number of matrices, and some basic properties of matrix convolution products are also derived.
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NTRU's technology differs from other encryption processes, Mr. Crenshaw said, because it relies on a mathematical system called a "convolution product" to make it faster and more efficient.
(ii Kronecker convolution product.
(2.2). (iii)Hadamard convolution product.
The notations,, and are convolution product, Kronecker convolution product and Hadamard convolution product of matrix functions and, respectively.
The operator ∗ indicates the convolution product.
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