The basis of a significant amount of cryptographic systems for information protection are different computationally hard problems. One of these problems is finding the discrete logarithm value in a certain finite group. The problem is to obtain for any two given elements of this group such natural number that the first element to the power of the number equals the second element.
In order to implement the cryptosystem, they have to choose an appropriate finite group and an element of high multiplicative order in it, so that computing the discrete logarithm is a hard problem. Powerful quantum computers will solve in polynomial time the discrete logarithm problem in the most common finite groups (multiplicative group of prime or extended finite field, group of points of elliptic curve over a finite field). That is why, as one of directions, they study groups consisting of invertible elements of group rings specified by various rings and groups. In the paper, the issue of finding high order units for special group rings, defined by finite field and dihedral group, is explore
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