A Study of Cryptographic Algorithms on Special Linear Group Over Ring of Integers Modulo m

Despite the development of numerous cryptographic algorithms over the last decade to ensure greater security for the users, the cyberattack forms are still advancing, which creates a challenge for the research community to build more efficient infrastructure. It motivates us to design more advanced algorithms based on a set of matrices that form a group under matrix multiplication, meaning they satisfy the group axioms of closure, associativity, identity, and irreversibility. Specifically, this study explores the application of three cryptographic algorithms on a special linear group of matrices over a ring of integers modulo m. The first algorithm relies on the RSA key exchange algorithm, which we modify to a special linear group. The second is an asymmetric RSA variant of a cryptographic algorithm defined on the co-adjoint orbit of element K belonging to a special linear group. All matrices from the orbit of matrix K have the same order and can be easily encrypted and decrypted by a pair of secret asymmetric cryptographic keys. We apply the Kronecker product of non-Abelian groups to construct an energy-efficient cryptographic algorithm with possible application on sensor networks. Due to the multiplicative property of the Kronecker product, both the encryption and decryption can be performed in parallel over the matrices of low degree. The third one is another RSA variant of a symmetric cryptographic algorithm, which can be encoded with a special linear group to significantly increase its complexity at the stage of non-negative matrix factorization. To encrypt a given set of numbers, we write it in a matrix form with a secret sequence of generators. As a result, the decryption relies on solving a simple system of nonlinear equations. Security of the algorithm lies in its complexity, aimed at building a correct sequence of generators necessary for encryption

Suppression of insertions in the complex pdxJ operon of Escherichia coli K-12 by lon and other mutations.

Complementation analyses using minimal recombinant clones showed that all known pdx point mutations, which cause pyridoxine (vitamin B6) or pyridoxal auxotrophy, are located in the pdxA, pdxB, serC, pdxJ, and pdxH genes. Antibiotic enrichments for chromosomal transposon mutants that require pyridoxine (vitamin B6) or pyridoxal led to the isolation of insertions in pdxA, pdxB, and pdxH but not in pdxJ. This observation suggested that pdxJ, like pdxA, pdxB, and serC, might be in a complex operon. To test this hypothesis, we constructed stable insertion mutations in and around pdxJ in plasmids and forced them into the bacterial chromosome. Physiological properties of the resulting insertion mutants were characterized, and the DNA sequence of pdxJ and adjacent regions was determined. These combined approaches led to the following conclusions: (i) pdxJ is the first gene in a two-gene operon that contains a gene, temporarily designated dpj, essential for Escherichia coli growth; (ii) expression of the rnc-era-recO and pdxJ-dpj operons can occur independently, although the pdxJ-dpj promoter may lie within recO; (iii) pdxJ encodes a 26,384-Da polypeptide whose coding region is preceded by a PDX box, and dpj probably encodes a basic, 14,052-Da polypeptide; (iv) mini-Mud insertions in dpj and pdxJ, which are polar on dpj, severely limit E. coli growth; and (v) three classes of suppressors, including mutations in lon and suppressors of lon, that allow faster growth of pdxJ::mini-Mud mutants can be isolated. A model to account for the action of dpj suppressors is presented, and aspects of this genetic analysis are related to the pyridoxal 5'-phosphate biosynthetic pathway

Location and characterization of genes involved in binding of starch to the surface of Bacteroides thetaiotaomicron.

Previous studies of starch utilization by the gram-negative anaerobe Bacteroides thetaiotaomicron have demonstrated that the starch-degrading enzymes are cell associated rather than extracellular, indicating that the first step in starch utilization is binding of the polysaccharide to the bacterial surface. Five transposon-generated mutants of B. thetaiotaomicron which were defective in starch binding (Ms-1 through Ms-5) had been isolated, but initial attempts to identify membrane proteins missing in these mutants were not successful. We report here the use of an immunological approach to identify four maltose-inducible membrane proteins, which were missing in one or more of the starch-binding mutants of B. thetaiotaomicron. Three of the maltose-inducible proteins were outer membrane proteins (115, 65, and 43 kDa), and one was a cytoplasmic membrane protein (80 kDa). The genes encoding these proteins were shown to be clustered in an 8.5-kbp segment of the B. thetaiotaomicron chromosome. Two other loci defined by transposon insertions, which appeared to contain regulatory genes, were located within 7 kbp of the cluster of membrane protein genes. The 115-kDa outer membrane protein was essential for utilization of maltoheptaose (G7), whereas loss of the other proteins affected growth on starch but not on G7. Not all of the proteins missing in the mutants were maltose regulated. We also detected two constitutively produced proteins (32 and 50 kDa) that were less prominent in all of the mutants than in the wild type. Both of these were outer membrane proteins