Abstract
In this chapter we introduce a novel scheme for constructing a class of parametric involutory transforms that are described by the computational lattice structure of fast cosine-Walsh type transform. Further on the practical effectiveness of the proposed class of transforms is evaluated experimentally in the task of data encryption. Finally, the selected aspects of mass-parallel realizations of the proposed class of involutory parametric transforms with usage of modern graphics processing units are considered and discussed.
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Notes
- 1.
It should be noted that adaptation of lattice structure presented in monograph [26] for fast calculations of Fourier transform to the field of cosine-Walsh transformation requires proper permutations of butterfly operators within consecutive stages. The required permutations can be described as follows: (I) in the first stage butterfly operators must be permuted in accordance to bit-reversal order, (II) the permutations in the following stages are calculated as even/odd order of operators taken from the directly preceding stage (c.f. Fig. 8).
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Puchala, D. (2018). Involutory Parametric Orthogonal Transforms of Cosine-Walsh Type with Application to Data Encryption. In: Shakhovska, N., Stepashko, V. (eds) Advances in Intelligent Systems and Computing II. CSIT 2017. Advances in Intelligent Systems and Computing, vol 689. Springer, Cham. https://doi.org/10.1007/978-3-319-70581-1_29
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