Peculiarities of Applying Partial Convolutions to the Computation of Reduced Numerical Convolutions
Source abstract
Abstract
A method is proposed that reduces the computation of the reduced digital convolution operation to a set of independent convolutions computed in Galois fields. The reduced digital convolution is understood as a modified convolution operation whose result is a function taking discrete values in the same discrete scale as the original functions. The method is based on the use of partial convolutions, reduced to computing a modulo integer q0, which is the product of several prime numbers: q0=p1p2…pn. It is shown that it is appropriate to use the expansion of the number q0, to q=p0p1p2…pn, where p0 is an additional prime number, to compute the reduced digital convolution. This corresponds to the use of additional digits in the number system used to convert to partial convolutions. The inverse procedure, i.e., reducing the result of calculations modulo q to the result corresponding to calculations modulo q0, is provided by the formula that used only integers proved in this paper. The possibilities of practical application of the obtained results are discussed.
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Research context
OpenAlex topics: Cryptography and Residue Arithmetic · Mathematical Approximation and Integration · Coding theory and cryptography
SciVX discovery tags are terminology-based. OpenAlex topics are source-provided classifications.
Affiliations
National Engineering Academy of the Republic of Kazakhstan, Almaty 050010, Kazakhstan
Institute of Communication and Space Engineering, Almaty University of Power Engineering and Telecommunication Named Gumarbek Daukeev, Almaty 050013, Kazakhstan
National Scientific Laboratory for the Collective Use of Information and Space Technologies (NSLC IST), Satbayev University, Almaty 050013, Kazakhstan
Funding
Science Committee of the Ministry of Science and Higher Education of the Republic of Kazakhstan
References (59)
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