Abstract
We study sequences \(\left\{A_n\right\}_{n=-\infty}^{+\infty}\) of elements of an arbitrary field \(\mathbb{F}\) that satisfy decompositions of the form
where \(a_1,a_2,b_1,b_2\colon \mathbb{Z}\to\mathbb{F}\). We prove some results concerning the existence and uniqueness of such sequences. The results are used to construct analogs of the Diffie–Hellman and ElGamal cryptographic algorithms. The discrete logarithm problem is considered in the group \((S,+)\), where the set \(S\) consists of quadruples \(S(n)=(A_{n-1},A_n, A_{n+1}, A_{n+2})\), \(n\in\mathbb{Z}\), and \(S(n)+S(m)=S(n+m)\).
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Translated from Problemy Peredachi Informatsii, 2023, Vol. 59, No. 2, pp. 102–119. https://doi.org/10.31857/S0555292323020079
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Illarionov, A.A. Existence of Sequences Satisfying Bilinear Type Recurrence Relations. Probl Inf Transm 59, 163–180 (2023). https://doi.org/10.1134/S0032946023020072
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DOI: https://doi.org/10.1134/S0032946023020072