Public Key Protocols over Twisted Dihedral Group Rings

Key management is a central problem in information security. The development of quantum computation could make the protocols we currently use unsecure. Because of that, new structures and hard problems are being proposed. In this work, we give a proposal for a key exchange in the context of NIST recommendations. Our protocol has a twisted group ring as setting, jointly with the so-called decomposition problem, and we provide a security and complexity analysis of the protocol. A computationally equivalent cryptosystem is also proposed

Post-Quantum Cryptography from Supersingular Isogenies (Theory and Applications of Supersingular Curves and Supersingular Abelian Varieties)

This paper is based on a presentation made at RIMS conference on “Theory and Applications of Supersingular Curves and Supersingular Abelian Varieties”, so-called “Supersingular 2020”. Post-quantum cryptography is a next-generation public-key cryptosystem that resistant to cryptoanalysis by both classical and quantum computers. Isogenies between supersingular elliptic curves present one promising candidate, which is called isogeny-based cryptography. In this paper, we give an introduction to two isogeny-based key exchange protocols, SIDH [17] and CSIDH [2], which are considered as a standard in the subject so far. Moreover, we explain briefly our recent result [24] about cycles in the isogeny graphs used in some parameters of SIKE, which is a key encapsulation mechanism based on SIDH

Biological Systems Workbook: Data modelling and simulations at molecular level

Nowadays, there are huge quantities of data surrounding the different fields of biology derived from experiments and theoretical simulations, where results are often stored in biological databases that are growing at a vertiginous rate every year. Therefore, there is an increasing research interest in the application of mathematical and physical models able to produce reliable predictions and explanations to understand and rationalize that information. All these investigations are helping to overcome biological questions pushing forward in the solution of problems faced by our society. In this Biological Systems Workbook, we aim to introduce the basic pieces allowing life to take place, from the 3D structural point of view. We will start learning how to look at the 3D structure of molecules from studying small organic molecules used as drugs. Meanwhile, we will learn some methods that help us to generate models of these structures. Then we will move to more complex natural organic molecules as lipid or carbohydrates, learning how to estimate and reproduce their dynamics. Later, we will revise the structure of more complex macromolecules as proteins or DNA. Along this process, we will refer to different computational tools and databases that will help us to search, analyze and model the different molecular systems studied in this course

A theoretical approach to the engineering of bioinspired systems: design, applications & information management

Premi extraordinari doctorat curs 2010-2011, àmbit d’Enginyeria Enginyeria IndustrialL’enginyeria de sistemes bioinspirats ha crescut en importància i nombre d’aplicacions en el últims anys, atraient l’atenció dels científics sobre els seus usos potencials en camps com ara la bionanotecnologia, la nanomedicina i la ciència de materials. En aquesta tesis, es presenta una aproximació mitjançant mètodes computacionals a l’enginyeria de sistemes biomimètics. Em posat la nostra èmfasi en l’estudi teòric basat en principis fonamentals de sistemes peptídics, això vol dir des de mètodes mecànic quàntics d’alt nivell per als elements més bàsics fins a la simulació de tot o part del sistema en un ambient més realista a partir de diferents aproximacions computacionals. Un altre objectiu del present treball és la recopilació exhaustiva de la informació derivada dels estudis fets així com dels potencials usos en un sistema informàtic orientat a l’usuari d’emmagatzemament de dades. S’han caracteritzat anàlegs conformacionalment restringits de l’arginina, prolina i fenilalanina a través de càlculs mecànic quàntics d’alt nivell. Aquest aminoàcids no codificats (és a dir que no estan entre els 20 aminoàcids naturals) han demostrat la seva capacitat de modulació del perfil conformacional dels pèptids a on són introduïts. A més a més, indueixen resistència a l’acció de les proteases a banda d’introduir noves propietats electròniques i espectroscòpiques útils en aplicacions tals com els sistemes de diagnòstic, alliberadors de fàrmacs i del camp de l’enginyeria de materials. Els aminoàcids obtinguts són emprats per a modificar pèptids de “homing”, blocs proteics autoagregants i superfícies actives recobertes de pèptids. La remarcable quantitat d’informació sobre aminoàcids no codificats accessible en publicacions científiques expressa la necessitat urgent de sistemes que, basant-se en ordinadors recopilin, organitzin i ofereixin aquesta informació de manera intel·ligible per a l’usuari final. Una base de dades ha estat dissenyada, creada i posada en funcionament per tal d’emmagatzemar dades conformacionals teòriques sobre aminoàcids no codificats. La base de dades també conté, en cas que la informació sigui accessible, dades experimentals referents a aplicacions, caracterització estructural i propietats espectroscòpiques. En resum, aquests treball ofereix un nou enfoc a l’enginyeria assistida per ordinador i la gestió de la informació de sistemes bioinspirats des de les seves unitats més elementals fins al disseny de les aplicacions de major complexitatThe engineering of systems inspired by biochemical molecules has grown in importance and number of applications in the recent years, focusing the researchers’ attention in its potential uses in fields such as nanotechnology, bionanotechnology, nanomedicine and material sciencie. A computational approach to engineering of biomimetic systems is presented in this work. Our emphasis is put on theoretical studies of some peptidic systems from scratch, this means from the use high level quantum mechanics studies of their primary building blocks to the simulation using different computational approaches of their behavior as part of an entire system in a more realistic environment. The thorough compilation of the derived information and its potential uses in a proper user-friendly data-storage support is also a question dealt in the thesis. Conformationaly restricted analogues of arginine, proline and phenylalanine amino acids are designed and fully characterized using high level quantum mechanics methods. These new non-coded amino acids (non-naturally occurring amino acids in proteins) demonstrate to modulate the conformational profile of peptides where they are inserted. Furthermore, they induce resistance to proteolysis altogether with new electronic and spectroscopic features useful in diagnostics, drug delivery and material engineering. The developed non-coded amino acids are used to engineer systems such as homing peptides, self-aggregating protein building blocks and peptide-coated active surfaces. The remarkable amount of information available about non-coded amino acids in scientific publications stressed out the dire need of computer-based systems to gather, to organize and to display in a user-friendly way the information about these compounds. A data base has been designed, implemented and run to store theoretically-obtained conformational information on non-coded amino acids. The data bases also contains, if available, experimentallyacquired knowledge such us structural and spectroscopic characterizations and reported applications. To conclude, this thesis offers a successful approach to the computer-aided engineering and information management of bioinspired systems from their basics to high complexity design.Award-winningPostprint (published version

Bio-Nano Robo-Mofos : Design and Synthesis of DNA Origami Nanostructures and Assembly of Nanobot Superstructures

In the field of bio-nanotechnology, molecules like DNA are repurposed as building materials for the construction of self-assembling nanostructures. The DNA origami method involves rationally coding many short synthetic DNA strands which ‘fold’ longer scaffold strands into precise, addressable structures for applications in areas like medicine, structural biology and molecular biophysics. DNA origami subunits are also used to explore fundamental principles of self-assembly, revealing insights into biology and expanding our control of matter at the nanoscale. But despite the usefulness of the method, DNA origami designs are limited in size by the length of scaffold strands, and in scope by the available tools needed to navigate the complex geometries of DNA nanostructures. My thesis addresses this in two ways: First, I present a set of principles for the design of DNA origami nanotubes, a class of strained structure with many applications. I parametrised variables related to nanotube design and created a computational tool to convert desired geometries into DNA strand layouts. I validated this via synthesis of various designs, including novel nanotubes with pleated walls, reconfigurable twist and varying diameter, characterising them with TEM, SAXS and MD simulations. This revealed insights into how design variables affect properties such as diameter and rigidity, and how global strain affects DNA nanostructures. Next, I present two schemes for assembling DNA origami subunits into self-limiting, open superstructures, exploring fundamental principles to control self-assembly while also overcoming DNA origami’s size limitations. The first is a strain accumulation scheme, which was explored theoretically and then embodied in a modular subunit with allosteric binding domains. With simulation and synthesis, I demonstrated that the subunit could structurally encode the extent of its own polymerisation. The second scheme is Vernier assembly, in which I showed that the combined geometries of two DNA origami subunits could determine the size of a superstructure and explored parameters important to maximise yield. Both studies provide guidance for future studies and applications which may require finite superstructures made from small numbers of unique components. Combined, the works in this thesis expand the design space for DNA-nanotechnology and fields beyond, enabling a range of biologically-inspired nanoscale autonomous modular formations, or ‘Bio-Nano Robo-Mofos’

Quantum algorithms for algebraic problems

Quantum computers can execute algorithms that dramatically outperform classical computation. As the best-known example, Shor discovered an efficient quantum algorithm for factoring integers, whereas factoring appears to be difficult for classical computers. Understanding what other computational problems can be solved significantly faster using quantum algorithms is one of the major challenges in the theory of quantum computation, and such algorithms motivate the formidable task of building a large-scale quantum computer. This article reviews the current state of quantum algorithms, focusing on algorithms with superpolynomial speedup over classical computation, and in particular, on problems with an algebraic flavor.Comment: 52 pages, 3 figures, to appear in Reviews of Modern Physic

UNDERSTANDING CARBOHYDRATE RECOGNITION MECHANISMS IN NON-CATALYTIC PROTEINS THROUGH MOLECULAR SIMULATIONS

Non-catalytic protein-carbohydrate interactions are an essential element of various biological events. This dissertation presents the work on understanding carbohydrate recognition mechanisms and their physical significance in two groups of non-catalytic proteins, also called lectins, which play key roles in major applications such as cellulosic biofuel production and drug delivery pathways. A computational approach using molecular modeling, molecular dynamic simulations and free energy calculations was used to study molecular-level protein-carbohydrate and protein-protein interactions. Various microorganisms like bacteria and fungi secret multi-modular enzymes to deconstruct cellulosic biomass into fermentable sugars. The carbohydrate binding modules (CBM) are non-catalytic domains of such enzymes that assist the catalytic domains to recognize the target substrate and keep it in proximity. Understanding the protein-carbohydrate recognition mechanisms by which CBMs selectively bind substrate is critical to development of enhanced biomass conversion technology. We focus on CBMs that target both oligomeric and non-crystalline cellulose while exhibiting various similarities and differences in binding specificity and structural properties; such CBMs are classified as Type B CBMs. We show that all six cellulose-specific Type B CBMs studied in this dissertation can recognize the cello-oligomeric ligands in bi-directional fashion, meaning there was no preference towards reducing or non-reducing end of ligand for the cleft/groove like binding sites. Out of the two sandwich and twisted forms of binding site architectures, twisted platform turned out to facilitate tighter binding also exhibiting longer binding sites. The exterior loops of such binding sites were specifically identified by modeling the CBMs with non-crystalline cellulose showing that high- and low-affinity binding site may arise based on orientation of CBM while interacting with non-crystalline substrate. These findings provide various insights that can be used for further understanding of tandem CBMs and for various CBM based biotechnological applications. The later part of this dissertation reports the identification of a physiological ligand for a mammalian glycoprotein YKL-40 that has been only known as a biomarker in various inflammatory diseases and cancers. It has been shown to bind to oligomers of chitin, but there is no known function of YKL-40, as chitin production in the human body has never been reported. Possible alternative ligands include proteoglycans, polysaccharides, and fibers such as collagen, all of which make up the mesh comprising the extracellular matrix. It is likely that YKL-40 is interacting with these alternative polysaccharides or proteins within the body, extending its function to cell biological roles such as mediating cellular receptors and cell adhesion and migration. We considered the feasibility of polysaccharides, including cello-oligosaccharides, hyaluronan, heparan sulfate, heparin, and chondroitin sulfate, and collagen-like peptides as physiological ligands for YKL-40. Our simulation results suggest that chitohexaose and hyaluronan preferentially bind to YKL-40 over collagen, and hyaluronan is likely the preferred physiological ligand, as the negatively charged hyaluronan shows enhanced affinity for YKL-40 over neutral chitohexaose. Collagen binds in two locations at the YKL-40 surface, potentially related to a role in fibrillar formation. Finally, heparin non- specifically binds at the YKL-40 surface, as predicted from structural studies. Overall, YKL-40 likely binds many natural ligands in vivo, but its concurrence with physical maladies may be related to the associated increases in hyaluronan

Synthesis and Performance Characterization of Polymer Semiconductors for Organic Thin Film Transistors

As the most promising semiconductor candidates for organic thin film transistors (OTFTs), donor-acceptor (D-A) type π-conjugated polymers have received much attention in the recent years. Their excellent printability, light weight, mechanical robustness and flexibility are desirable characteristics for low cost and portable electronics. Some issues of polymer semiconductors as such relatively low charge carrier mobility compared to that of silicon as well as the poor stability during manufacturing and device operation in an ambient environment still remain. Although extensive efforts have been made to develop electron acceptor building blocks, which are considered to be critical for achieving high mobility, very few electron acceptors for constructing novel high performance D-A polymers are available. Nowadays most D-A polymers were synthesized using traditional Suzuki or Stille coupling, which use boron- or tin-containing monomers that require extra synthetic steps and are highly toxic in some cases (such as organotin monomers). As an alternative method, the direct (hetero)arylation polymerization (DHAP), provides a new approach to constructing D-A polymers in a cost-effective and environment friendly manner. Certain polymers synthesized by DHAP have demonstrated similar or even better performance compared to the polymers made by other methods. However side reactions and limitations on the types of monomers for DHAP have been reported. To bring the OTFT performance of polymer semiconductors to the next level, new acceptor building blocks and a further study of DHAP need to be exploded. In the first part of this thesis (Chapters 2-4), a novel electron acceptor building block, indigo is chosen, considering its electron deficiency property, highly coplanar geometry and ease of synthesis. Furthermore, indigo and its small molecule derivatives have been demonstrated to be promising semiconductors in OTFTs. However, indigo-containing polymer semiconductors have not been reported yet. In this study, we used 6,6’-indigo as an electron acceptor to successfully develop several n-type electron transport semiconductors. Surprisingly, when 5,5’-indigo was used, the opposite p-type hole transport performance was observed. To the best of our knowledge, this is the first observation that the charge transport polarity could be controlled or switched through different regiochemical connections of a building block. The second part of this thesis (Chapters 5 and 6) focuses on the optimization and development of dipyrrolopyrrole (DPP) based polymers. In Chapter 5, DHAP is used to construct a novel high performance pyrrolo[3,4-c]pyrrole-1,4(2H,5H)-dione (1,4-DPP)-thiazole based polymer. Two synthetic routes are compared and discussed, and the polymer synthesized under optimized DHAP conditions showed better performance than that of a similar polymer obtained by Stille coupling. In Chapter 6, pyrrolo[3,4-c]pyrrole-1,3(2H,5H)-dione (1,3-DPP), an isomer of 1,4-DPP, is developed for constructing polymer semiconductors with promising performance in OTFTs. Systematic studies on the synthesis of these new acceptor building blocks as well as the exploration of DHAP have provided insights into the structure-property relationships of novel D-A polymers and may lead to the discovery of the next generation high mobility polymer semiconductors