An analysis of the RC4 family of stream ciphers against algebraic attacks

To date, most applications of algebraic analysis and attacks on stream ciphers are on those based on lin- ear feedback shift registers (LFSRs). In this paper, we extend algebraic analysis to non-LFSR based stream ciphers. Specifically, we perform an algebraic analysis on the RC4 family of stream ciphers, an example of stream ciphers based on dynamic tables, and inves- tigate its implications to potential algebraic attacks on the cipher. This is, to our knowledge, the first pa- per that evaluates the security of RC4 against alge- braic attacks through providing a full set of equations that describe the complex word manipulations in the system. For an arbitrary word size, we derive alge- braic representations for the three main operations used in RC4, namely state extraction, word addition and state permutation. Equations relating the inter- nal states and keystream of RC4 are then obtained from each component of the cipher based on these al- gebraic representations, and analysed in terms of their contributions to the security of RC4 against algebraic attacks. Interestingly, it is shown that each of the three main operations contained in the components has its own unique algebraic properties, and when their respective equations are combined, the resulting system becomes infeasible to solve. This results in a high level of security being achieved by RC4 against algebraic attacks. On the other hand, the removal of an operation from the cipher could compromise this security. Experiments on reduced versions of RC4 have been performed, which confirms the validity of our algebraic analysis and the conclusion that the full RC4 stream cipher seems to be immune to algebraic attacks at present.

Human preadipocyte proliferation and differentiation

Obesity represents a major health, social and economic burden to many developing and Westernized communities, with the prevalence increasing at a rate exceeding almost all other medical conditions. Despite major recent advances in our understanding of adipose tissue metabolism and dynamics, we still have limited insight into the regulation of adipose tissue mass in humans. Any significant increase in adipose tissue mass requires proliferation and differentiation of precursor cells (preadipocytes) present in the stromo-vascular compartment of adipose tissue. These processes are very complex and an increasing number of growth factors and hormones have been shown to modulate the expression of genes involved in preadipocyte proliferation and differentiation. A number of transcription factors, including the C/EBP family and PP ARy, have been identified as integral to adipose tissue development and preadipocyte differentiation. Together PP ARy and C/EBPa regulate important events in the activation and maintenance of the terminally differentiated phenotype. The ability of PP ARy to increase transcription through its DNA recognition site is dependent on the binding of ligands. This suggests that an endogenous PP ARy ligand may be an important regulator of adipogenesis. Adipose tissue functions as both the major site of energy storage in the body and as an endocrine organ synthesizing and secreting a number of important molecules involved in regulation of energy balance. For optimum functioning therefore, adipose tissue requires extensive vascularization and previous studies have shown that growth of adipose tissue is preceded by development of a microvascular network. This suggests that paracrine interactions between constituent cells in adipose tissue may be involved in both new capillary formation and fat cell growth. To address this hypothesis the work in this project was aimed at (a) further development of a method for inducing preadipocyte differentiation in subcultured human cells; (b) establishing a method for simultaneous isolation and separate culture of both preadipocytes and microvascular endothelial cells from the same adipose tissue biopsies; (c) to determine, using conditioned medium and co-culture techniques, if endothelial cell-derived factors influence the proliferation and/or differentiation of human preadipocytes; and (d) commence characterization of factors that may be responsible for any observed paracrine effects on aspects of human adipogenesis. Major findings of these studies were as follows: (A) Inclusion of either linoleic acid (a long-chain fatty acid reported to be a naturally occurring ligand for PP ARy) or Rosiglitazone (a member of the thiazolidinedione class of insulin-sensitizing drugs and a synthetic PPARy ligand) in differentiation medium had markedly different effects on preadipocyte differentiation. These studies showed that human preadipocytes have the potential to accumulate triacylglycerol irrespective of their stage of biochemical differentiation, and that thiazolidinediones and fatty acids may exert their adipogenic and lipogenic effects via different biochemical pathways. It was concluded that Rosiglitazone is a more potent inducer of human preadipocyte differentiation than linoleic acid. (B) A method for isolation and culture of both endothelial cells and preadipocytes from the same adipose tissue biopsy was developed. Adipose-derived microvascular endothelial cells were found to produce factor/s, which enhance both proliferation and differentiation of human preadipocytes. (C) The adipogenic effects of microvascular endothelial cells can be mimicked by exposure of preadipocytes to members of the Fibroblast Growth Factor family, specifically ~-ECGF and FGF-1. (D) Co-culture of human preadipocytes with endothelial cells or exposure of preadipocytes to either ~-ECGF or FGF-1 were found to 'prime' human preadipocytes, during their proliferative phase of growth, for thiazolidinedione-induced differentiation. (E) FGF -1 was not found to be acting as a ligand for PP ARy in this system. Findings from this project represent a significant step forward in our understanding of factors involved in growth of human adipose tissue and may lead to the development of therapeutic strategies aimed at modifying the process. Such strategies would have potential clinical utility in the treatment of obesity and obesity related disorders such as Type II Diabetes.