The current state of affairs in the field of using polymer hydrogels for the creation of innovative systems for signal and image processing, of which computing is a special case, is analyzed. Both of these specific examples of systems capable of forming an alternative to the existing semiconductor-based computing technology, but assuming preservation of the used algorithmic basis, and non-trivial signal converters, the nature of which requires transition to fundamentally different algorithms of data processing, are considered. It is shown that the variability of currently developed information processing systems based on the use of polymers, including polymer hydrogels, leads to the need to search for complementary algorithms. Moreover, the well-known thesis that modern polymer science allows for the realization of functional materials with predetermined properties, at the present stage, receives a new sounding: it is acceptable to raise the question of creating systems built on a quasi-biological basis and realizing predetermined algorithms of information or image processing. Specific examples that meet this thesis are considered, in particular, promising information protection systems for UAV groups, as well as systems based on the coupling of neural networks with holograms that solve various applied problems. These and other case studies demonstrate the importance of interdisciplinary cooperation for solving problems arising from the need for further modernization of signal processing systems.

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 $q_0$, which is the product of several prime numbers: $q_0=p_1{p}_2\dots p_n$. It is shown that it is appropriate to use the expansion of the number $q_0$, to $q=p_0{p}_1{p}_2\dots p_n$, where $p_0$ 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 $q_0$, is provided by the formula that used only integers proved in this paper. The possibilities of practical application of the obtained results are discussed.

It is shown that it is reasonable to use Galois fields, including those obtained by algebraic extensions, to describe the position of a point in a discrete Cartesian coordinate system in many cases. This approach is applicable to any problem in which the number of elements (e.g., pixels) into which the considered fragment of the plane is dissected is finite. In particular, it is obviously applicable to the processing of the vast majority of digital images actually encountered in practice. The representation of coordinates using Galois fields of the form GF(p²) is a discrete analog of the representation of coordinates in the plane through a complex variable. It is shown that two different types of algebraic extensions can be used simultaneously to represent transformations of discrete Cartesian coordinates described through Galois fields. One corresponds to the classical scheme, which uses irreducible algebraic equations. The second type proposed in this report involves the use of a formal additional solution of some equation, which has a usual solution. The correctness of this approach is justified through the representation of the elements obtained by the algebraic expansion of the second type by matrices defined over the basic Galois field. It is shown that the proposed approach is the basis for the development of new methods of information protection, designed to control groups of UAVs in the zone of direct radio visibility. The algebraic basis of such methods is the solution of systems of equations written in terms of finite algebraic structures.

It is shown that focusing systems built on the basis of a system of radio receivers spaced apart in space and simulating the operation of a lens can be used to ensure the protection of information during data transmission in the direct radio visibility zone. The synthesis of the lens equivalent in this case is carried out by using a system of phase shifters that change the phase of the oscillations arriving at each of the receivers, so that the receiving system is tuned to a radio wave source located at a specific point in space. In this case, information protection is provided according to the “friend or foe” principle, and any commands coming from other areas of space, except for the point where the authorized operator is located, are ignored. The advantage of this approach is the ability to partially or completely abandon the use of cryptographic methods. It is shown that the proposed approach is of considerable interest for ensuring the stable operation of groups of unmanned aerial vehicles from the point of view of the possibility of intercepting control using electronic warfare methods.

It is shown that a serial-parallel processor, comparable in bit capacity to a 16-bit binary processor, can be implemented based on an algorithm built on the residue number system, a distinctive feature of which is the use of the first four quasi-Mersenne numbers, i.e., prime numbers representable as $p_k=2^k+1, k=1,2,3,4$. Such a set of prime numbers satisfies the criterion $2p_1{p}_2{p}_3{p}_4+1=P$, where $P$ is also a prime number. Fulfillment of this criterion ensures the possibility of convenient use of the considered RNS for calculating partial convolutions developed for the convenience of using convolutional neural networks. It is shown that the processor of the proposed type can be based on the use of a set of adders modulo a quasi-Mersenne number, each of which operates independently. A circuit of a modulo $2^k+1$ adder is proposed, which can be called a trigger circuit, since its peculiarity is the existence (at certain values of the summed quantities) of two stable states. The advantage of such a circuit, compared to known analogs, is the simplicity of the design. Possibilities for further development of the proposed approach related to the use of the digital logarithm operation, which allows reducing the operations of multiplication modulo $2^k+1$ to addition operations, are discussed.