Partitioning Multivariate Polynomial Equations via Vertex Separators for Algebraic Cryptanalysis and Mathematical Applications

We present a novel approach for solving systems of polynomial equations via graph partitioning. The concept of a variable-sharing graph of a system of polynomial equations is defined. If such graph is disconnected, then the system of equations is actually two separate systems that can be solved individually. This can provide a significant speed-up in computing the solution to the system, but is unlikely to occur either randomly or in applications. However, by deleting a small number of vertices on the graph, the variable-sharing graph could be disconnected in a balanced fashion, and in turn the system of polynomial equations are separated into smaller ones of similar sizes. In graph theory terms, this process is equivalent to finding balanced vertex partitions with minimum-weight vertex separators. The techniques of finding these vertex partitions are discussed, and experiments are performed to evaluate its practicality for general graphs and systems of polynomial equations. Applications of this approach to the QUAD family of stream ciphers, algebraic cryptanalysis of the stream cipher Trivium and its variants, as well as some mathematical problems in game theory and computational algebraic geometry are presented. In each of these cases, the systems of polynomial equations involved are well-suited to our graph partitioning method, and constructive results are discussed

Differential Random Fault Attacks on certain CAESAR Stream Ciphers (Supplementary Material)

This document contains supplementary material to the paper with the same title available from the proceedings of the International Conference on Information Security and Cryptology (ICISC) 2019. In this supplementary material, we demonstrate that the random fault attack strategy described in the full paper can be applied to ciphers in the MORUS family, resulting in partial state recovery for these ciphers

State convergence and keyspace reduction of the Mixer stream cipher

This paper presents an analysis of the stream cipher Mixer, a bit-based cipher with structural components similar to the well-known Grain cipher and the LILI family of keystream generators. Mixer uses a 128-bit key and 64-bit IV to initialise a 217-bit internal state. The analysis is focused on the initialisation function of Mixer and shows that there exist multiple key-IV pairs which, after initialisation, produce the same initial state, and consequently will generate the same keystream. Furthermore, if the number of iterations of the state update function performed during initialisation is increased, then the number of distinct initial states that can be obtained decreases. It is also shown that there exist some distinct initial states which produce the same keystream, resulting in a further reduction of the effective key space

Algebraic analysis of Trivium-like ciphers

Trivium is a bit-based stream cipher in the final portfolio of the eSTREAM project. In this paper, we apply the approach of Berbain et al. to Trivium-like ciphers and perform new algebraic analyses on them, namely Trivium and its reduced versions: Trivium-N, Bivium-A and Bivium-B. In doing so, we answer an open question in the literature. We demonstrate a new algebraic attack on Bivium-A. This attack requires less time and memory than previous techniques which use the F4 algorithm to recover Bivium-A\u27s initial state. Though our attacks on Bivium-B, Trivium and Trivium-N are worse than exhaustive keysearch, the systems of equations which are constructed are smaller and less complex compared to previous algebraic analysis. Factors which can affect the complexity of our attack on Trivium-like ciphers are discussed in detail

Tweaking Generic OTR to Avoid Forgery Attacks

This paper considers the security of the Offset Two-Round (OTR) authenticated encryption mode \cite{cryptoeprint:2013:628} with respect to forgery attacks. The current version of OTR gives a security proof for specific choices of the block size $(n)$ and the primitive polynomial used to construct the finite field $\mathbb{F}_{2^n}$. Although the OTR construction is generic, the security proof is not. For every choice of finite field the distinctness of masking coefficients must be verified to ensure security. In this paper, we show that some primitive polynomials result in collisions among the masking coefficients used in the current instantiation, from which forgeries can be constructed. We propose a new way to instantiate OTR so that the masking coefficients are distinct in every finite field $\mathbb{F}_{2^n}$, thus generalising OTR without reducing the security of OTR

Prognostic implications of surrogate markers of atherosclerosis in low to intermediate risk patients with type 2 diabetes.

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Hsf1 and Hsp90 orchestrate temperature-dependent global transcriptional remodelling and chromatin architecture in Candida albicans

We thank Karim Gharbi and Urmi Trivedi for their assistance with RNA sequencing, carried out in the GenePool genomics facility (University of Edinburgh). We also thank Susan Fairley and Eduardo De Paiva Alves (Centre for Genome Enabled Biology and Medicine, University of Aberdeen) for help with the initial bioinformatics analysis. We thank Aaron Mitchell for kindly providing the ALS3 mutant, Julian Naglik for the gift of TR146 cells, and Jon Richardson for technical assistance. We thank the Genomics and Bioinformatics core of the Faculty of Health Sciences for Next Generation Sequencing and Bioinformatics support, the Information and Communication Technology Office at the University of Macau for providing access to a High Performance Computer and Jacky Chan and William Pang for their expert support on the High Performance Computer. Finally, we thank Amanda Veri for generating CaLC2928. M.D.L. is supported by a Sir Henry Wellcome Postdoctoral Fellowship (Wellcome Trust 096072), R.A.F. by a Wellcome Trust-Massachusetts Institute of Technology (MIT) Postdoctoral Fellowship, L.E.C. by a Canada Research Chair in Microbial Genomics and Infectious Disease and by Canadian Institutes of Health Research Grants MOP-119520 and MOP-86452, A.J. P.B. was supported by the UK Biotechnology and Biological Sciences Research Council (BB/F00513X/1) and by the European Research Council (ERC-2009-AdG-249793-STRIFE), KHW is supported by the Science and Technology Development Fund of Macau S.A.R (FDCT) (085/2014/A2) and the Research and Development Administrative Office of the University of Macau (SRG2014-00003-FHS) and R.T.W. by the Burroughs Wellcome fund and NIH R15AO094406. Data availability RNA-sequencing data sets are available at ArrayExpress (www.ebi.ac.uk) under accession code E-MTAB-4075. ChIP-seq data sets are available at the NCBI SRA database (http://www.ncbi.nlm.nih.gov) under accession code SRP071687. The authors declare that all other data supporting the findings of this study are available within the article and its supplementary information files, or from the corresponding author upon request.Peer reviewedPublisher PD

The Candida albicans transcription factor Cas5 couples stress responses, drug resistance and cell cycle regulation

We thank Cowen lab members for helpful discussions. We also thank David Rogers (University of Tennessee) for sharing microarray analysis of the CAS5 homozygous mutant, and Li Ang (University of Macau) for assistance in optimizing the ChIP-Seq experiments. J.L.X. is supported by a Canadian Institutes of Health Research Doctoral award and M.D.L. is supported by a Sir Henry Wellcome Postdoctoral Fellowship (Wellcome Trust 096072). B.T.G. holds an Ontario Graduate Scholarship. C.B. and B.J.A. are supported by the Canadian Institutes of Health Research Foundation Grants (FDN-143264 and -143265). D.J.K. is supported by a National Institute of Allergy and Infectious Diseases grant (1R01AI098450) and J.D.L.C.D. is supported by the University of Rochester School of Dentistry and Medicine PREP program (R25 GM064133). A.S. is supported by the Creighton University and the Nebraska Department of Health and Human Services (LB506-2017-55). K.H.W. is supported by the Science and Technology Development Fund of Macau S.A.R. (FDCT; 085/2014/A2). L.E.C. is supported by the Canadian Institutes of Health Research Operating Grants (MOP-86452 and MOP-119520), the Natural Sciences and Engineering Council (NSERC) of Canada Discovery Grants (06261 and 462167), and an NSERC E.W.R. Steacie Memorial Fellowship (477598).Peer reviewedPublisher PD

Novel Variants Identified in Multiple Sclerosis Patients From Southern China

Background: Multiple sclerosis (MS) is an autoimmune and demyelinating disease. Genome-wide association studies have shown that MS is associated with many genetic variants in some human leucocyte antigen genes and other immune-related genes, however, those studies were mostly specific to Caucasian populations. We attempt to address whether the same associations are also true for Asian populations by conducting whole-exome sequencing on MS patients from southern China.Methods: Genomic DNA was extracted from the peripheral blood mononucleocytes of 8 MS patients and 26 healthy controls and followed by exome sequencing.Results: In total, 41,227 variants were found to have moderate to high impact on their protein products. After filtering per allele frequencies according to known database, 17 variants with the allele frequency <1% or variants with undetermined frequency were identified to be unreported and have significantly different frequencies between the MS patients and healthy controls. After validation via Sanger sequencing, one rare variant located in exon 7 of TRIOBP (Chr22: 37723520G>T, Ala322Ser, rs201693690) was found to be a novel missense variant.Conclusion: MS in southern China may have association with unique genetic variants, our data suggest TRIOBP as a potential novel risk gene