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Security efficiency and hardware efficiency are equally important when designing a block cipher. In this paper, we propose a new block cipher that uses string transformations and requires less memory and fewer computational resources, making it suitable for highly constrained environments. We compare the performance of our design with AES-128 and quasigroup-based block cipher INRU in the cipher block chaining (CBC) mode of operation using the National Institute of Standards and Technology (NIST) test suite. We then analyze our design against the standard linear, differential, and algebraic attacks. Choosing suitable S-boxes and a quasigroup of a smaller order does not compromise the security of the cipher, but the storage space is reduced compared with AES-128 and INRU. [ABSTRACT FROM AUTHOR]

ElGamal cryptosystem has emerged as one of the most important construction in Public Key Cryptography (PKC) since Diffie-Hellman key exchange protocol was proposed. However, public key schemes which are based on number theoretic problems such as discrete logarithm problem (DLP) are at risk because of the evolution of quantum computers. As a result, other non-number theoretic alternatives are a dire need of entire cryptographic community.

The concept of the semigroup action problem (SAP) was first introduced by Monico in 2002. Monico explained in his paper that the discrete logarithm problem (DLP) can be generalized to SAP. After defining the action problem in a semigroup, the concept was extended using different mathematical structures. In this paper, we discuss the concept of SAP and present a detailed survey of the work which has been done using it in public-key cryptography.

A public-key cryptosystem is the undoubted spine of present-day communication systems. Many mathematical theories like number theory, group theory, and ring theory were utilized to design various cryptographic protocols. Similarly, quasigroups play a significant part in building both symmetric and public-key cryptosystems. Some famous cryptographic primitives like EdonX and NASHA are based on quasigroups. In this survey article, we will discuss some public-key cryptographic algorithms based on quasigroups and their structures. [ABSTRACT FROM AUTHOR]

In this paper, we investigate the properties of σ -A-nuclei of a quasigroup including relations between them and relations between their respective component sets, where σ ∈ S 3 . We also find connections between components of σ -A-nuclei of a quasigroup and components of σ -A-nuclei of the isostrophic images. Further, we investigate the properties of various inverse quasigroups using the derived connections. These properties will not only make the study of σ -A-nuclei of a quasigroup simple but also reduce the time required in the computation of σ -A-nuclei of a quasigroup for different values of σ. [ABSTRACT FROM AUTHOR]

In this paper, we investigate the properties of A-nuclei and σ -A-nuclei of a quasigroup including connections between components of σ -A-nuclei and local identity elements. To make the study easier, we give the explicit structure of σ -A-nuclei of a loop, a unipotent left loop and a unipotent right loop in terms of translation maps. We also find the left, right and middle A-nuclei of a quasigroup which is an isostrophic image of a loop in terms of translation maps. [ABSTRACT FROM AUTHOR]

The security of block ciphers solely depends on the S-boxes used in their design. Hence, for a secure block cipher, S-boxes should be chosen very thoughtfully. n-ary quasigroups of different orders and for different values of n are being used to design various cryptographic primitives. In the literature, many algorithms based on the quasigroups have been proposed for the generation of S-boxes of order 4. However, in this article, we propose a general method for the construction of symmetric S-boxes of even order using ternary quasigroups of order 4 with certain properties. These S-boxes give strong resistance against linear, differential, algebraic, and DPA attacks and hence provide good cryptographic properties. [ABSTRACT FROM AUTHOR]

Group Key Distribution (GKD) protocols are designed to distribute a group key to several users for establishing a secure communication over a public network. The central trusted authority, called the key distribution center (KDC) is in charge of distributing the group keys. For securing the communication, all the users share a common secret key in advance with KDC. In this paper, we propose a secure and efficient Group Authenticated Key Distribution (GAKD) protocol based on the simple idea of encryption in matrix rings. In this protocol, each user registers in private with the KDC, while all the other information can be transferred publicly. The scheme also supports authentication of group keys without assuming computational hard problems such as Integer Factorization Problem (IFP). The analysis of our GAKD protocol shows that the proposed protocol is resistant to reply, passive and impersonation attacks. Our construction leads to a secure, cost and computation- effective GAKD protocol. [ABSTRACT FROM AUTHOR]

The concept of undeniable signature scheme was put forward by D. Chaum and H. van Antwerpen in 1989. Such signature scheme requires the signer's co-operation at the verification step which defends the signer against the verification of his/her signature by an unwanted entity. In this paper, we propose a new undeniable signature scheme in a non-abelian group over group ring whose security relies on the difficulty of solving Factorization with Discrete Logarithm Problem (FDLP). [ABSTRACT FROM AUTHOR]

In this paper, we propose a new class of error-detecting codes based on quasigroups using automorphisms of the finite field 픽pn and the additive group (픽p, +). We demonstrate that these codes are effective in detecting burst errors caused by hardware damage or noisy transmission. We also explore the codes ability to detect various types of double errors, including transposition errors, twin errors, and phonetic errors. Our analysis extends beyond bit-level errors to include block-level errors. Finally, we provide a comparative analysis and demonstrate the real-world applications of our code. [ABSTRACT FROM AUTHOR]

Quasigroups have wide applications in coding theory and cryptography. We present a brief survey on quasigroups and discuss their applications in designing various cryptographic primitives including block cipher, stream cipher, hash function, public-key schemes, etc. [ABSTRACT FROM AUTHOR]

Let p be an odd prime, and δ be an arbitrary unit of the finite chain ring F p m + u F p m (u 2 = 0) . The Hamming distances of all δ -constacyclic codes of length 2 p s over F p m + u F p m are completely determined. We provide some examples from which some codes have better parameters than the existing ones. As applications, we determine all MDS repeated-root δ -constacyclic codes of length 2 p s over F p m + u F p m . [ABSTRACT FROM AUTHOR]