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Group polynomials over rings
A. V. Akishin MIREA — Russian Technological University, Moscow
Abstract:
We consider polynomials over rings such that the polynomials represent Latin squares and define a group operation over the ring. We introduce the notion of a group polynomial, describe a number of properties of these polynomials and the groups generated. For the case of residue rings $\mathbb{Z}_{r^n}$, where $r$ is a prime number, we give a description of groups specified by polynomials and identify a class of group polynomials that can be used to construct controlled cryptographic transformations.
Keywords:
cryptography, groups, residue rings, polynomial groups.
Received: 05.02.2019
Citation:
A. V. Akishin, “Group polynomials over rings”, Diskr. Mat., 31:2 (2019), 3–13; Discrete Math. Appl., 30:6 (2020), 357–364
Linking options:
https://www.mathnet.ru/eng/dm1565https://doi.org/10.4213/dm1565 https://www.mathnet.ru/eng/dm/v31/i2/p3
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Abstract page: | 372 | Full-text PDF : | 58 | References: | 36 | First page: | 37 |
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