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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]

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]

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]

Due to the importance of the NTRU public key cryptosystem, many improvements have been made to it by increasing security or speed to keep pace with the process of technological development in exchanging various data. In this paper, we construct a public key cryptosystem called HAQTR using non-commutative quaternion algebra with the change of the mathematical structure. [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]

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]

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]

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]

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]

With the need to store a huge amount of personal information, Computer hardware has become extremely vital nowadays. However, some challenges follow this expansion; for instance, solving the problem of maintaining security challenges by using high-security algorithms. As a result, a high-security cryptosystem with low computation power is needed. One of the lattice-based cryptosystems that meet these requirements is NTRU. Since the NTRU cryptosystem proposal, many variants were proposed by researchers using different algebraic structures. In this paper, we design a new cryptosystem variant of NTRU, called BOTRU, which is a high-performing system based on bi-octonion subalgebra and it has good resistance to some well-known attacks, such as a brute force attack. The creation of two public keys in the system proposed has differentiated it from NTRU and NTRU like cryptosystems. Some arithmetic operations are used for comparing the efficiency of BOTRU with the OTRU cryptosystem. Based on arithmetic assessment, the comparison reveals that the BOTRU has a higher speed than the OTRU. [ABSTRACT FROM AUTHOR]