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The modified RSA provides high efficiency against attacks and, as a result, it is considered the ideal choice for many applications. In this paper, we introduce an alternative to the modified RSA key encryption system called TPRSA, based on Tri-Cartesian algebra and polynomials, by modifying the mathematical structure of text encryption and decryption keys to obtain a high level of security. [ABSTRACT FROM AUTHOR]

In 2022, Bantaojai et al. [3] introduced an algebra structure called Bd-algebras. In this paper, we define a new notion called fuzzy Bd-ideals of Bd-algebras and study some of its basic properties. Moreover, we characterize fuzzy Bd-ideals by the different types of their level subsets in Bd-algebras. [ABSTRACT FROM AUTHOR]

In this paper, we focus on terms with fixed variables count, terms under which the total numbers of occurrences of variables in each position are equal. Moreover, we determine conditions for which the set of terms with fixed variables count is closed under the generalized superposition. Furthermore, we form the partial algebras of such terms satisfying certain axioms as weak identities. [ABSTRACT FROM AUTHOR]

In this paper, we establish a new eight-dimensional algebra callked KAH-Octo. Moreover, we study subalgebras aand give some properties of the algebra such as division, isomorphism, simple, semi-simple, Jordan, Malcev, among others. Furthermore, we give some applications to some interesting areas of mathematics such as cryptography. [ABSTRACT FROM AUTHOR]

An endomorphism of a finite algebra is said to be highest if its pre-period is greater than or equal to the pre-period of all its endomorphisms. In this paper, we characterize all highest endomorphisms of a Boolean lattice. [ABSTRACT FROM AUTHOR]

In this paper, we present a new multidimensional public-key cryptosystem that is commutative and associative based on the subalgebra of Quintuple algebra called SQN which utilizes a novel mathematical structure of two public keys and four private keys. This new structure has made the public key system more secure. [ABSTRACT FROM AUTHOR]

With technological development, hackers are possible to access the transmitted data, so we need to constantly develop encryption methods to increase security. In this paper, we have introduced a new cryptosystem hexadecnion polynomial RSA (PH-RSA) by mixing NTRU and polynomial RSA based on a hexadecnion polynomial instead of polynomial RSA with a high level of security. [ABSTRACT FROM AUTHOR]

This paper's primary objective is to expand the connection between the presence of a symplectic form on a Mock-Lie algebra and the solution of the Yang-Baxter equation (YBE) into the realm of symplectic Jacobi-Jordan algebras. The study establishes an equivalence between the existence of an even symplectic form ѡ on a Mock-Lie algebra and the existence of an r-matrix of J, which is a solution r of the YBE. [ABSTRACT FROM AUTHOR]

Given the increase in the various types of transactions over the Internet and to ensure the confidentiality of the transmitted data, there is need for encryption with the continued development of cryptosystems. In this paper, we offer TRUFT, a multi-dimensional public key cryptosystem, as a replacement for the NTRU encryption with a new structure that increases complexity and security. [ABSTRACT FROM AUTHOR]

This paper focuses on finite-dimensional dual mock-Lie algebras. Let H be a dual mock-Lie algebra and V a vector space containing H as a subspace. All dual mock-Lie algebra structures on V containing H as a subalgebra are explicitly described and classified by non-abelian cohomological type objects: CH² (U,H) provides the classification up to an isomorphism that stabilizes H and will classify all such structures from the viewpoint of the extension problem. Here U is a complement of H in V. A general product, called the unified product, is introduced as a tool for our approach. The crossed (resp. bicrossed) products between two dual mock-Lie algebras are introduced as special cases of the unified product: crossed product is responsible for the extension problem while the bicrossed product is responsible for the factorization problem. The description and the classification of all complements of a given extension of dual mock-Lie algebras are given as a converse of the factorization problem. [ABSTRACT FROM AUTHOR]

NTRU is an alternative to those cryptosystems that were based on discrete logarithm problems or integer factorization. It delivers efficiency against many attacks and, as a result, is the perfect choice for many applications. In this paper, we introduce a new alternative to NTRU public key cryptosystem called HUDTRU which is built on Quintuple algebra, by changing the mathematical structure of keys to encrypt and decrypt the text to obtain a high level of security. [ABSTRACT FROM AUTHOR]

In this paper, we study algebraic structures called modified near algebras, normed modified algebras obtained from new near structures called modified near modules. [ABSTRACT FROM AUTHOR]

In this paper, we study some classes of terms, called trees, which play a key role in both universal algebra and theoretical computer science. We introduce the concept of terms defined by singular transformations and provide some concrete examples. We also prove that the set of such terms together with an operation of type (n + 1) for a fixed natural number n defined on that set forms an algebra of type (n + 1) satisfying the axiom of superassociativity. [ABSTRACT FROM AUTHOR]

In this paper, we introduce the new algebra structure which combines properties from B-algebras and d-algebras: An algebra X = (X, ◦, 0) is called a Bd-algebra if it satisfies the following axioms for all x, y ◦ X: x ◦ 0 = x, and if x ◦ y = 0 and y ◦ x = 0, then x = y. In addition, we give some properties of Bd-ideals and Bd-subalgebras of Bd-algebras and construction of quotient algebras. [ABSTRACT FROM AUTHOR]

In this paper, we analyze the links between congruences, ideals, and homomorphisms in pseudo-UP algebras. Moreover, we establish a theorem which can be viewed as the First Isomorphism Theorem for these algebras. Furthermore, our results may serve as a base to construct other isomorphism theorems for pseudo-UP algebras. [ABSTRACT FROM AUTHOR]

With the progress and development of life, cryptography became an indispensable science. As its usefulness is not limited to changing the form of information and making it in the form of symbols that are difficult to understand (even if it reaches unauthorized persons) but through it becomes known that the information is original and coming from its source and has not been modified during the sending or saving process. In this paper, we make an improvement and modification NTRU cryptosystem by using a new tripternion algebra and changing the mathematical structure for public and private keys, as well as for text encryption and decryption to obtain higher security. [ABSTRACT FROM AUTHOR]

In this work, we present an improvement to NTRU called ASTRU which is based on a new algebra called AS and a new mathematical structure. It was created in a way to increase the security of keys and it outperforms NTRU, QTRU, and QMNTR. [ABSTRACT FROM AUTHOR]

We introduce soft v-ideals, soft s-ideals and soft vs-ideals over a Menger algebra of rank n. Moreover, we investigate several properties of each of the types of soft ideals. Furthermore, we prove that the collection of all soft vs-ideals forms a distributive lattice. [ABSTRACT FROM AUTHOR]

Graph algebras establish a connection between directed graphs without multiple edges and special universal algebras of type (2,0). We say that a graph G satisfies a term equation s ≈ t if the corresponding graph algebra A(G) satisfies s ≈ t. The set of all graphs satisfying a set of term equations is called a graph variety. A term equation s ≈ t which is satisfied by all graphs in a graph variety is called an identity of that graph variety. An identity s ≈ t of a graph variety V is a hyperidentity of V if whenever the operation symbols occurring in s and t are replaced by any term operations of A(G) of the appropriate arity, the resulting identities hold in A(G) for all G in V. [ABSTRACT FROM AUTHOR]

One of natural measures of the complexity of a term is the length of term, the total number of both operation symbols and variables that occur in the term. Based on the usual superposition operation and the generalized superposition operation of terms, two significant formulas for counting the length of terms in these operations are established. We also define a novel class of terms which is called terms of a fixed length. The partial superposition for such terms is proposed under a suitable condition and the partial algebra of terms of a fixed length is constructed. [ABSTRACT FROM AUTHOR]