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Документ Відкритий доступ Extremal graph theory and generation of quadratic multivariate transformations of Algebraic Post-Quantum Cryptography(Igor Sikorsky Kyiv Polytechnic Institute, 2023) Ustymenko, Vasyl; Wróblewska, Aneta; Pustovit, OleksandrWe introduce large groups of quadratic transformations of a vector space over the finite fields defined via symbolic computations with the usage of algebraic constructions of Extremal Graph Theory. They can serve as platforms for the protocols of Noncommutative Cryptography. The modifications of these symbolic computations in the case of large fields of characteristic two allow us to define quadratic bijective multivariate public keys such that the inverses of public maps has a large polynomial degree. We suggest the usage of constructed protocols for the private delivery of quadratic encryption maps instead of the public usage of these transformations.Документ Відкритий доступ On Inverse Protocols of Post Quantum Cryptography Based on Pairs of Noncommutative Multivariate Platforms Used in Tandem(Igor Sikorsky Kyiv Polytechnic Institute, 2023) Ustymenko, VasylNon-commutative cryptography studies cryptographic primitives and systems which are based on algebraic structures like groups, semigroups and noncommutative rings. We continue to investigate inverse protocols of Non-commutative cryptography defined in terms of subsemigroups of Affine Cremona Semigroups over finite fields or arithmetic rings Zm and homomorphic images of these semigroups as possible instruments of Post Quantum Cryptography. This approach allows to construct cryptosystem which are not public keys, when protocol finish correspondents have mutually inverse transformations on affine space K n or variety (K*)n where K is the field or arithmetic ring. The security of such inverse protocol rests on the complexity of word problem to decompose element of Affine Cremona Semigroup given in its standard form into composition of given generators. We discuss the idea of usage combinations of two cryptosystems with cipherspaces(K*)n and K n to form a new cryptosystem with the plainspace(K*)n , ciphertextK n and nonbijective highly nonlinear encryption map.