Mechanical properties of the composite constituents.
\r\n\tThe application of these equations and their solutions to solving boundary value problems are developed on the base of analytic mathematical methods.
\r\n\r\n\tThis book may be useful to specialists in the fields of mathematics, mathematical physics and mechanics.
",isbn:"978-1-83880-072-7",printIsbn:"978-1-83880-071-0",pdfIsbn:"978-1-83880-341-4",doi:null,price:0,priceEur:0,priceUsd:0,slug:null,numberOfPages:0,isOpenForSubmission:!0,hash:"38c88a4ec0ff6c0184a6694c21ddedc5",bookSignature:"Prof. Lyudmila Alexeyevna Alexeyeva",publishedDate:null,coverURL:"https://cdn.intechopen.com/books/images_new/9325.jpg",keywords:"mathematical theorem, fundamental solution, boundary value problem, hyperbolic equation, hyperbolic equations system, mathematical physics equation, generalized solution, green function, green tensor, mathematical physics",numberOfDownloads:null,numberOfWosCitations:0,numberOfCrossrefCitations:null,numberOfDimensionsCitations:null,numberOfTotalCitations:null,isAvailableForWebshopOrdering:!0,dateEndFirstStepPublish:"November 7th 2019",dateEndSecondStepPublish:"November 28th 2019",dateEndThirdStepPublish:"January 27th 2020",dateEndFourthStepPublish:"April 16th 2020",dateEndFifthStepPublish:"June 15th 2020",remainingDaysToSecondStep:"10 days",secondStepPassed:!0,currentStepOfPublishingProcess:3,editedByType:null,kuFlag:!1,editors:[{id:"232525",title:"Prof.",name:"Lyudmila",middleName:"Alexeyevna",surname:"Alexeyeva",slug:"lyudmila-alexeyeva",fullName:"Lyudmila Alexeyeva",profilePictureURL:"https://mts.intechopen.com/storage/users/232525/images/system/232525.jpg",biography:"The doctor of physical and mathematical sciences professor Alexeyeva Lyudmila Alexeyevna is the famous highly qualified specialist in the field of mathematical physics, mechanics, applied mathematics, dynamics of constructions. Now she is the chief researcher of Institute of Mathematics and mathematical modeling and professor of mechanics and Mathematics Faculty of Al Farabee University in Almaty in Kazakhstan. \r\n\r\nShe was born on January 12, 1947 in the city Kaliningrad (USSR, Russia Federation) in family of therapist doctors. The family had three daughters, Lyudmila - the eldest. Childhood was spent in frequent journeys in connection with the service of his father. In 1954 she entered the Soviet secondary school in the city of Yuterbog (DDR) at her father’s place of employment, in 1965 she graduated with a gold medal in the 11th grade of secondary school in the city Murom, Vladimir region. In the same year, Lyudmila entered the Faculty of Mechanics and Mathematics of M.V. Lomonosov Moscow State University (Moscow, USSR). She was Lenin scholarship for 4-5 courses. \r\n\r\nIn October 1970, she enrolled in the postgraduate program Mech-Mat. Faculty of Moscow State University, specialized in the Department of Theoretical Mechanics under the guidance of Corresponding Member of the USSR Academy of Sciences D.Ye. Okhotsimsky. PhD thesis on the topic “Modeling the dynamics and motion control of a walking apparatus” in the specialty 01.02.01. - theoretical mechanics - defended at Moscow State University in 1976.\r\n\r\nAfter graduating from postgraduate school in 1973, she with husband were assigned to work in Alma-Ata at the Institute of Mathematics and Mechanics of the Academy of Sciences of the Kazakh SSR. Here she worked in the laboratory of the theory of seismic stability of underground structures as junior researcher (1976-1977), senior researcher (1978-1987), general research associate (1988-1991). In 1991 she defended her doctoral thesis “Dynamics of Extended Underground Structures” at the Institute of Mathematics and Mechanics of the Academy of Sciences of the Kazakh SSR for the degree of Doctor of Physical and Mathematical Sciences in specialty 01.02.07 - soil mechanics, rocks and massive media . In 1992, also the USSR Higher Attestation Commission awarded her the title of professor of mechanics in the specialty 01.02.04 - mechanics of a deformable solid.\r\n\r\nIn 1992, the Institute of Theoretical and Applied Mathematics was organized. Since then she has been working at this institute. At first she worked as the head of the laboratory of wave dynamics (1992-2012), from 20012 to 2018 she was the head of the Department of Mathematical Physics and Modeling at this institute. Now she works as the chief researcher of this department, the head of a research project. Currently this institute is called the Institute of Mathematics and Mathematical Modeling\r\nConcurrently, she has been working for more than 20 years as a professor at the Faculty of Mechanics and Mathematics at the Al Farabi Kazakh National University. She teaches in graduate and doctoral studies.\r\n\r\nFor scientific activity she received the State Scientific Scholarship for scientists and specialists who made an outstanding contribution to the development of science and technology in 1997-2000, 2000-2002, 2004-2006, 2008-2010; awarded the Insignia for workers of science and education of the Republic of Kazakhstan. She is the member of European Mechanics Sosciety and the member of the International Academy of Sciences of Eurasia.",institutionString:"Institute of Mathematics and Mathematical Modeling",position:null,outsideEditionCount:0,totalCites:0,totalAuthoredChapters:"1",totalChapterViews:"0",totalEditedBooks:"0",institution:{name:"Institute of Mathematics and Mathematical Modeling",institutionURL:null,country:{name:"Kazakhstan"}}}],coeditorOne:null,coeditorTwo:null,coeditorThree:null,coeditorFour:null,coeditorFive:null,topics:[{id:"15",title:"Mathematics",slug:"mathematics"}],chapters:null,productType:{id:"1",title:"Edited Volume",chapterContentType:"chapter",authoredCaption:"Edited by"},personalPublishingAssistant:{id:"286446",firstName:"Sara",lastName:"Bacvarova",middleName:null,title:"Ms.",imageUrl:"https://mts.intechopen.com/storage/users/286446/images/8491_n.jpg",email:"sara.b@intechopen.com",biography:"As an Author Service Manager my responsibilities include monitoring and facilitating all publishing activities for authors and editors. From chapter submission and review, to approval and revision, copyediting and design, until final publication, I work closely with authors and editors to ensure a simple and easy publishing process. I maintain constant and effective communication with authors, editors and reviewers, which allows for a level of personal support that enables contributors to fully commit and concentrate on the chapters they are writing, editing, or reviewing. I assist authors in the preparation of their full chapter submissions and track important deadlines and ensure they are met. I help to coordinate internal processes such as linguistic review, and monitor the technical aspects of the process. As an ASM I am also involved in the acquisition of editors. 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Venkateswarlu",coverURL:"https://cdn.intechopen.com/books/images_new/371.jpg",editedByType:"Edited by",editors:[{id:"58592",title:"Dr.",name:"Arun",surname:"Shanker",slug:"arun-shanker",fullName:"Arun Shanker"}],productType:{id:"1",chapterContentType:"chapter",authoredCaption:"Edited by"}}]},chapter:{item:{type:"chapter",id:"61089",title:"Optimization of Lay-Up Stacking for a Loaded-Carrying Slender Composite Beam",doi:"10.5772/intechopen.76566",slug:"optimization-of-lay-up-stacking-for-a-loaded-carrying-slender-composite-beam",body:'The glass/carbon fiber composites are widely used in the design of various aircraft and rotorcraft components such as stringers, the spars of the rotor blades, the stiffened panels of the wings and stabilizers, which have predominantly a thin-walled geometry and are made of composite laminates that most often are adopted as orthotropic. The main requirements for these parts are the specified dynamic and endurance properties to provide the aerodynamic quality and reliability of the aircraft assembly at the different flight conditions with limited part weight [1]. Most of these parts are manufactured by laying-up or winding of the unidirectional lamina and curing in closed molds or autoclaves where the parts are exposed to the controlled pressure and temperature according to the predetermined process.
The rapid growth of composite applications in aircraft and rotorcraft industries, the very complex mechanical behavior of anisotropic composite materials require new structural strength, rigidity, modeling, optimization and failure prediction methods using virtual testing analysis method, which is a concept with several attributes and is to be understood as the simulation of aircraft structure [2, 3]. In the survey paper [4] the main milestones of development of the optimization and its applications in aircraft systems design, especially in the context of the composite structures, are considered. According to the concept, which is present in the considered paper, a full workflow process of the composite structure optimization consists of the following three phases:
Free size or topology optimization
Detailed design: ply-bundle sizing with ply-based FE (finite element) modeling
Detailed design: ply stacking sequence optimization
During the second and third phases the composite plies with the different orientation are chosen and shuffled to determine the optimal stacking sequence for the given design optimization problem while satisfying some additional manufacturing constraints. As outlined in the article [5], such a composite structure optimization involved a large number of both the design variables and the objectives. As a result, designers must consider only a restricted set of parameters among the most influential. In the paper [5], the author uses the following parameters of optimized laminates: mass per unit area of an elementary plate, the compliance of elementary plate and the stiffness of a composite plate experienced by the uniform pressure. The stacking sequence, total number of plies and prepreg materials are accepted as the design variables, whereas the mass and the total number of layers are constrained. It was established that the ply orientation seems to have a significant influence on the most common mechanical criteria (mass, rigidity, etc.). Use of a more refined orientation set can improve the mechanical performance when accounting for inter-laminar stresses, or for laminates made of a few anisotropic plies. In most engineering applications, when there is a large number of plies, it is entirely warranted to restrict the layers’ orientations to a limited number of predefined values. Similar technologies and appropriate soft tools are being developed and improved by leaders of aircraft industry such as Altair Engineering GMBH [6].
Because the dynamic behavior of the aircraft structures at the operating conditions being within the structure strength limits is very important, many investigations are limited by the study of composites at the elastic conditions. Such elastic phenomena were the main assumptions used at the modeling and were formulated in the early fundamental work [7]. These assumptions include: (1) The results obtained assume that the composite material may be modeled as a single-phase anisotropic homogeneous continuum. This assumption is adequate for the elastic constants, provided the main consideration is the interface, but is unlikely to apply to the strength properties. (2) There is a representative volume element whose mechanical properties are equal to the average properties of the particular composite. (3) The constituent materials are linearly elastic and homogeneous, but in general anisotropic. (4) Linearity of the stress-strain relations is assumed to hold for the composite materials.
Most investigations that have been implemented in this area use the finite element modeling for solve the forward structural mechanics problem combined with some optimization algorithms based on the soft computing concepts, for example, genetic algorithm [8, 9, 10], shuffled Frog-Leaping (SFL) algorithm [11] for lay-up sequence optimization of laminate composite structures. However, there are no theorems to prove that a soft algorithm ensures the achievement of a unique global optimum. Therefore, some researchers use analytical approaches to optimize the simplest composite systems [12] or empirical methods for more complex ones [13, 14].
Some works are devoted to the optimization of composite structures subjected to aeroelastic or hydraulic dynamic loading. The common part of such works is the subtask of simulating aeroelastic actions on a composite structure. In particular, the paper [15] examined phenomenon of bending-torsional coupling rigidity for achieving an optimal design of a composite wing with a maximum flutter speed. In order to ensure an effective way to achieve an optimal lay-up, two optimization approaches have been investigated. In the first approach, the flutter speed was set in the objective function directly. In the second approach, optimization was carried out to minimize an objective function containing the torsional and coupling rigidities rather than flutter speed. Kalavalapally and co-workers [16] solving a multidisciplinary optimization problem for a lightweight torpedo model subjected to underwater explosions observed that the composite torpedo model is stronger and lighter than the metallic design when subjected to an underwater explosions at a given standoff distance. The paper [17] presented the numerical method and results of the structural optimization of the mounting zones of wind turbine blades to diminish and flatten the stress distribution at the action of the extremely stressed wind load on the blade, which had the stiff carbon/epoxy composite skin and less stiff lightweight core body.
When composite structure with complex shape is studied, its CAD model needs to be used for the virtual aerodynamic testing by the means of FE tools. The main objective of the paper [18] is the optimization of wall thickness and lay-up sequence of shell-like cowling made of the transversely isotropic multilayered composite. The used approach assumed: (1) conversion of the CAD model of the cowling surface to the FE representation, then (2) wind tunnel testing simulation at the different orientation of airflow to find the most stressed mode of flight that uses at the formulation of the loading pressure conditions for the forward problem of structural mechanics. The optimization problem used the global strain energy calculated within the optimized shell as the objective, whereas the total weight of the optimized part was considered as the design constraints.
The important conclusion that can be made taking into account the surveyed works is the multiobjective nature of most composite optimization problems. Such a conclusion can be made on the basis of the present chapter, which is broken into several parts. First, we present a brief description of the optimized composite structure, which is the tube-like cantilever slender beam experiencing distributed bending and torsion forces. Then we determine the elastic properties of laminates used in the modeled tube. We start from the mechanical properties of reinforcing fibers and epoxy resin, and then we determine the properties of the unidirectional lamina and, finally, the laminate properties. Our optimization approach contains three sequential stages. The preliminary stage is based on the consideration of the angular distribution of all engineering constants of laminates. This analysis allows us to choose the small enough set of “candidate” lay-ups, which should be used at the modeling of the mechanical response of the studied structure at three different load scenarios. The next “candidates”—higher level “candidates”—are appointed for the final dynamic test, which includes applying full load to the preferred structures and gives us the possibility to make the expert decision about final choice of quasi-optimal structure. Last, we discuss some considerations influencing the final choice of the best lay-up parameters that are the design variables.
The composite beam studied in this research is a slender tubular structure with optimizing prepreg lay-up sequence. Its cross-section is comprised of two straight stripes and two half-circles, each of them is made of eight laminating layers (see Figure 1), that is similar to those studied in [19]. The simulated structure is a greatly simplified design of D-like spar of the helicopter main rotor blade. Such spars are typically characterized by thickening of the cross section near the root, decreasing thickness of the airfoil and its twist as it approaches the end of the blade, without tapering of airfoil. The CAD model of the structure was built by using NX CAD (Siemens®) capabilities and converted into the Structural Mechanics Comsol Multiphysics environment.
Sketch of the beam cross-sections (a), 3D view of the CAD model and magnifying view on the cross-section of optimizing structure.
In order to define the structural anisotropy of the laminate and the distributed external loads, the curvilinear coordinate systems
Curvilinear local coordinate systems on the beam surface.
The root end face is fixed
In Eq. (1) the twisting load
The FE mesh has been constructed for the given geometry as swept mesh (see Figure 3) consisting of 128,893 domain elements, 37,959 boundary elements and 1350 edge elements. The number of degrees of freedom solved for is 625,409.
FE mesh used at the mechanics problem.
All numerical and experimental studies have been implemented for glass fiber reinforced epoxy based prepreg VPS-7. Initially, the properties of the fibers and resin, which was accepted as isotropic, have been studied experimentally using testing machines Galdabini. The samples of resin and bundles of the fibers were experienced by tensile forces with strains monitored by extensometers. During these experiments, the following elastic moduli have been obtained (see Table 1).
Components | Young module, GPa | Poisson ratio | Shear module, GPa |
---|---|---|---|
Glass fibers | 87.5 (longitudinal) | ||
Epoxy resin | 2.55 | 0.364 | 0.94 (calculated) |
Mechanical properties of the composite constituents.
The properties of unidirectional lamina, which has transversely isotropic symmetry, were determined both numerically and experimentally for the samples with volume fraction Vf = 0.534. In order to determine the parameters inaccessible through the experimental tests, we used the mixing rule and FE modeling in Abaqus environment according to the recommendation of [20, 21]. The values all found properties are shown in Table 2, where bold numbers denote the most reliable values, which have been used in the follow-up investigation. These values have been used for determination of elastic moduli of laminates of chosen structures.
Elastic module | Determination method | ||
---|---|---|---|
Experiment | Mixing rule | FE modeling | |
E1, MPa | 49,500 ± 2500 | 49,000 | 48,090 |
E2, MPa | 6000 ± 500 | 5500 | 8042 |
ν12 | 0.315 ± 0.015 | 0.31 | 0.299 |
ν23 | NA | NA | 0.459 |
G23, MPa | 2600 ± 200 | 2000 | 2758 |
G12, MPa | NA | NA | 2847 |
Mechanical properties of lamina.
Remark: Index 1 corresponds to the longitudinal ply orientation (along the fibers), whereas index 2 to the transversal ply orientation.
In order to diminish the formation of the residual stress and strains, which can arise during cure we use only 8-layers symmetric balanced laminates in our investigation. All used schemes of lamina stacking are shown in Figure 4 with their designations.
Used schemes of lamina stacking.
For each lay-up scheme the elastic moduli were determined independently by two methods: by the finite element method and on the base of the classical laminates theory. The last one proposes the following relationships for the elastic moduli of laminate.
where indices
Where,
The FE model for determining of elastic moduli simulated the experimental tests according to the standards ASTM D 3039–95 and ASTM D 5379–93 with the numerical methods for the accurate identification of the modules described in [24]. All modules to be determined in the numerical experiments are averaged by integration along the lines where the pure tensile or shear occurs (see Figure 5).
Geometry (a, c) and postprocessing results (b, d) of models simulating the mechanical tests ASTM D 3039–95 “Test Method for Tensile Properties of Polymer Matrix Composite Materials” (a, b) and ASTM D 5379–93 “Test Method for Shear Properties of Composite Materials by V-Notched Beam Method” (c, d).
Geometry of the FE models consists of eight separated layers, each of which is characterized by its orientation of lamina. Numerical calculation of elastic modules has been implemented for all lay-ups (see Figure 4) with the step
Some examples of longitudinal, transverse elastic moduli and Poisson ratios dependencies on the lay-up angles for the laminate stacking I, II, III, IV (see Figure 4).
In the next stage of investigation, the angular dependencies of the effective moduli were investigated. In order to avoid the significant reduction of the structural rigidity in some directions, these dependencies should not have sharp drops, corresponding to these directions. Some examples of such angular dependencies are shown in Figure 8. These dependencies have been used for the preliminary selections of the “candidates” lay-ups, which have been further used to test them in mechanical testing of the optimized slender structure.
The mechanical testing of the structure with different lay-ups and ply stacking angles has been implemented using FE model (see Figures 1–3) by using three abovementioned types of static bending and torsion loading. These loads were applied separately; for each load scenario the total strain energy
The in-plane shear module dependencies on the lay-up angles for the laminate stacking I, II, III, IV and V (see Figure 4).
The calculated dependencies of maximum deflections and torsion angles of the loaded beams on the lay-up parameters are present in Figure 9. These results together with the angular dependencies of elastic moduli that are partially presented in Figure 8 allowed to select eight “candidates” for further optimization. These candidates had to have acceptable values for the total strain energy and rigidity under all loading scenarios.
Angular dependencies of the longitudinal, shear modules and in-plane Poisson ratio for the lay-ups II (left) and IV (right) (see Figure 4).
In the final stage of investigation, the optimizing structure made of the preferred lay-ups “candidates” has been loaded simultaneously by the systems of three forces: bending by the distributed forces oriented along y and z axis and twisting torque applied to the external surface and given by Eqs. (1) and (2). The studied responses included total strain energy, the maximum bending deflections and objective, which was accepted in the normalized dimensionless form.
Where,
For the definiteness of the optimization problem statement the following constraints were imposed.
At the optimization workflow, the forward structural mechanics problem has been called by the built-in gradient-free Nelder-Mead optimizer. In order to start the iterative optimization procedures, we used such “candidates”: (I
Dependencies of maximum deflections and torsion angles of the loaded beams.
Figure 10 illustrates two examples of objective and other responses evolution during optimization process. These plots demonstrate very fast convergence to the quasi-optimal solutions for both optimized lay-up stacking. These solutions are not global optimum because they characterized by the different values of all responses.
Evolution of lay-up angle, objective and mechanical properties of structure during optimization for two “candidate” lay-ups: (I φin=300) and (V ψin=300;φin=150).
The final features of all optimized “candidate” structures are present in Figure 11. All optimized lay-ups were ranked according to calculated responses. The optimized lay-ups (I
Comparison among the best lay-ups of the optimized structure (stems with the filled symbols correspond to the preferred lay-ups).
This chapter studies a problem of lay-up optimization for a cantilevered long tube-like composite structure with varied cross-section that is manufactured by winding of glass fiber unidirectional tape. The optimized composite structure is the tube-like cantilever slender beam experiencing distributed bending and torsion forces. The multilayered composite material assumed and modeled as a single phase anisotropic elastic homogeneous continuum. We determine the elastic properties of laminates, which used in the modeled tube, taking as input data the mechanical properties of reinforcing fibers and epoxy resin to determine initially the elastic properties of the unidirectional lamina. For each accepted lay-up scheme and unidirectional prepreg orientation of the symmetric balanced laminate formation, the elastic moduli were determined independently by two methods: by the finite element method and on the base of the classical laminates theory.
The first stage of used optimization approach is based on the analysis of the angular distribution of all engineering constants of laminates. This analysis allows us to choose the small enough set of “candidate” lay-ups, which should be used at the modeling of the mechanical response of the studied structure at three different load scenarios. The higher level “candidates” were appointed for the final dynamic test, which includes applying full load to the selected structures and gives us the possibility to make the expert decision about final choice of quasi-optimal structure. The short discussion of the obtained results confirms necessity of multiobjective approach to the studied optimization problem, taking into account many requirements and constraints that allows to make the final choice of the best lay-up parameters.
This work is implemented in the framework of the state mission for the South Scientific Center of Russian Academy of Science, project No. AAAA-A16-116012610052-3 and it was supported by the Russian Foundation for the Basic Research (Grant 15-08-99849 and Russian-Taiwanese project 16-58-52013 MNT_a).
Securing the digital world is essential as critical infrastructures are based on communicating with remote computers. The trust in the computer network is based on having a secure and authenticated communication. The change in social activity, where the big four companies Google, Amazon, Facebook, and Apple (GAFA) influence many aspects in modern society implies the need for secure computer and network infrastructures. The past interest in quantum cryptography has grown significantly in recent years. National Institute of Standards and Technology (NIST) authors wrote an overview on the subjects in 2009 [25], and the activity expanded dramatically, having dedicated conferences on the subject [27]. The most challenging component of Internet security that needs to be considered is the replacement of the existing asymmetric encryption scheme, namely, to replace an RSA [29]. For this there are several candidates: lattice-based cryptography (e.g., shortest vector problem, closest vector problem), code-based cryptography (e.g., McEliece, Niederreiter), and more (see, e.g., [24]). The second challenging task is a replacement for signature scheme; here hash-based Lamport’s one-time signature together with the Merkle tree is believed to address that need (see [39] for an overview). The integration of the post-quantum cryptographic ingredients into a complete infrastructure is also challenging (as we detail in the sequel).
\nWe present a design for quantum-safe communication over the existing Internet infrastructure. No hardware changes are required, only software updates over the heterogeneous Internet architecture. Different aspects of the solution are presented in the sequel.
\nThe emergence of quantum computers is a fact [12]; beyond the commercial non-universal commercial quantum computer of several thousand qubits (quantum bits) of D-Wave [10], IBM commercializes 50 qubits quantum computers [18]. The quantum computer race leads to exponential growth in the number of qubits, where in 2018 Intel presented 49 qubits quantum computer [19] and Google announced 72 qubits computers [16]. In addition, several startups including Rigetti announced a 36 qubits quantum computer [28] and a quantum processing unit (QPU) (see also Ion Q [20] and QCI [32]).
\nMany quantum computers restrict the qubits that participate as inputs for quantum gate operations and employ qubit teleportation to allow quantum gate operations over non-neighboring quantum bits, e.g., [36, 8]. The advance in techniques for producing entangled qubits and teleportation [37, 38] may assist in using several quantum computers to cooperate on a task by teleporting qubits from one to another, thus building a virtual quantum computer with the needed qubits for the task. In particular, for breaking the asymmetric encryption schemes in use almost immediately, much earlier than estimated.
\nShor’s algorithm [35], designed for quantum computers, changed the way modern cryptography and Internet security are captured. New algorithms for quantum computers are frequently invented [31, 4].
\nComputationally secure cryptography is based on the unproven assumption of the existence of one-way function, a function that can be computed easily but is hard to be inverted. The risk that an algorithm that breaks a considered one-way function will be found always exists, e.g., [1]. Even one-way functions proposed for post-quantum cryptosystems are at risk of the discovery of new efficient inverse algorithms. One famous example of an open problem for decades is the primality test that had no polynomial deterministic algorithm, until just such an algorithm was found [2].
\nThe asymmetric encryption schemes, proposed by Merkle [23], Diffie and Hellman [9], and Rivest et al. [29], revolutionized cryptography. The idea to use computational tasks in order to establish a symmetric key started with the suggestion of Merkle to use computation puzzles. Merkle’s puzzle scheme started with Alice choosing at random many computation puzzles, possibly hashed random numbers (with tuned lengths) each concatenated with a sequence number, such that Bob is able to randomly choose one of the puzzles and reverse this number in reasonable time. Then, Bob sends a few of the bits of the revealed random number back to Alice, identifying the puzzle Bob decided to solve. Both Alice and Bob will be using the unrevealed bits of the solved puzzle as their symmetric key. Eve on the other hand will not know which of the puzzles was chosen by Bob, will likely have to solve many puzzles before identifying the puzzle randomly chosen by Bob, and revealing the symmetric key they use. Later Diffie and Helman and then Rivest, Shamir and Adelman suggested more efficient schemes based on number theory assumptions.
\nAsymmetric encryption enabled the creation of a symmetric key among communicating parties over tapped communication links [23, 9] and is even able to identify the intervention of malicious parties in the communication [29]. The identification of such malicious parties was due to the capability of [29] to sign certificates that monolithically associated a public key with the entity identity description to which the public key belongs. The signature was issued by a trusted third party, the certificate authority. This public key infrastructure is the de facto security infrastructure today, securing Internet activity, including military, governmental, social, financial, and, in fact, all activities in the Internet.
\nThus, the appearance of quantum computers and fitting quantum algorithms, which may break the basic mathematical foundations of [9, 29], has great implications. Post-quantum cryptosystems [26] are examined, e.g., [15], replacing the believed to be one-way functions that are currently used by other functions, which are also believed to be one-way functions. Provable perfect encryption does exist, namely, encryption based on the classical one-time pad [34], as long as the one-time pad is a true random sequence. True random sequences are possibly produced by the use of quantum effects, e.g., [17].
\nAnother difficulty in using one-time pad is the need to share the one-time pad prior to communication. The one-time pad can be shared prior to communication by physically delivering a copy of the one-time pad. Distribution of a one-time pad to many users may risk the loss or duplication of one copy of the one-time pad, nullifying the secrecy of the encryption.
\nQuantum key distribution [3] suggests using quantum bits superposition for detecting a tapper in the communication of random bits; however this scheme can only be used in direct links of at most 100 km. Recently, [22, 30] succeeded in using satellites and quantum bits entanglement to share a key over longer distances. This key can be viewed as a short one-time pad, as the rate of the received random bits is limited. One difficulty is the need to mobilize the symmetric key received from the satellite in one satellite receiver to the actual place the key should be used and the fact that the key authenticates the satellite receiver, but may not yield the identification of other users.
\nOccasionally, one needs to send a credit number electronically, sending one email with the first digits of the credit card and then another email with the rest. Still, the email servers and the Internet server providers may act as a man in the middle and tap in, capturing part or all of the digits of the credit card. It is possible to send a random string (one-time pad) via WhatsApp (owned by Facebook) and the bitwise x-or of the credit card with the random string via Gmail. On one hand, this resembles sending entangled bits in two channels. On the other hand, just like content distribution networks (CDN), e.g., Akamai, that uses overlay network of the Internet ISPs as their source for extra reliability and services, overlay security uses the accumulated secrecy, authenticity, and identification of the diverse capabilities of the communication channels, applications, and protocols.
\nThe maturity and evolvement of the Internet technology enabled the CDN company to use the Internet infrastructure as a playground for delivering contents at will. In the last decades, more and more communication channels identify, authenticate, and secure the communication between entities. Email, SMS, push notifications, and messengers (WhatsApp, Facebook Messenger, Skype, Snapchat, LINE, LinkedIn, Telegram, Weibo, Slack, etc.) form logical secured channels. Each of the channels, even if they use the same physical channel, implies already built trust in the identification and authentication of the entity communicated through the channel. Moreover, the maintenance and repair of the security of each channel are guaranteed by the channel supplier. Still, each channel may act as a man-in-the-middle accumulating the communications transmitted through the channel servers. The use of a random one-time pad over channels nullifies information accumulated by the server of each channel.
\nThis is the current playground suggested to be used by the overlay security concept, to create a symmetric key based on perfectly secure information-theoretical secure scheme, namely, quantum-safe replacements for asymmetric encryption. In addition, the security of new channels can be obtained inductively by the security of existing channels, employing them to create a random shared key for the new channel.
\nOverlay security uses several channels and random numbers to obtain a high level of confidence in identification, authentication, and secrecy, a level implied by all the used channels. However, if one of the channels, say Android push notification, is not available (possibly in China), then the communication is blocked. Secret sharing [33, 5] schemes imply a tunable threshold for the number of channels needed to reconstruct the secret. Shamir secret sharing is based on polynomials over a finite field, where each participant, in our case channel, receives one point of the polynomial and the secret is the free coefficient of the polynomial. For example, if the polynomial is a random linear function with the secret being the free coefficient, any two participants/channels can reveal the secret, but a single participant/channel has absolutely no information on the secret. Polynomials with greater degrees used over many channels may imply more trust in the aggregated identification, authentication, and secrecy while allowing several of the channels to be blocked or even to corrupt the information conveyed through them.
\nIdentifying and authenticating an entity in the physical world by the digital world are the biggest challenges in information security. Having secured robust and reliable identification and authentication of a person, an institute, a company, or a device are the first chain in securing digital representation and processing of information. For example, a bank client needs to be identified and authenticated for performing digital operations on their account. The linkage between the physical entity and the digital representation of an entity allows processing of digital and physical assets in the computers and the Internet.
\nThe need for identification and authentication of an entity started before computers exist. Certificates signed by trusted authorities were used by governments to monitor the activity of the society, to enable law and order. Certificates used to authenticate entities were and are part of business infrastructure. The procedures used to authenticate an entity were and are defined by societies. A newborn child does not need a certificate to be born, obviously when the child is born at home. Moreover, a newborn may not have a certificate with identifying details, including identifying number, without enforcing society’s regulations. Some societies pay parents of newborns when they register the child, an attractive payment that almost ensures that newborn will be registered.
\nIn the scope of people, biometric identifications, by using fingerprints, face recognition, iris, and palm, are becoming standard. The identification starts with the registration process in which there is a need to identify and link the person with the biometric information recorded during the registration process. This is an error-prone process that encapsulates the challenge in the authentication bay. There is a need for a trusted authority (e.g., government, banks) or trusted manufacturer (e.g., Apple, Samsung) to collect biometric samples while authenticating the person by other means (e.g., driving license, passport) and digitally link them in a digital record. The actual biometric sampling would be better stored in a form of one-way hash, just like passwords; otherwise, they can be copied and used without the actual involvement of the biometric identification device (e.g., fingerprint reader, camera). Keeping the biometric database private and secure is another challenging task, as once a biometric data is leaked to untrusted entities, the search for confusing biometric data to fake identification can be feasible.
\nMoreover, current technologies for identifying a person biometrically are not perfect. Biometric identifications have false positives, when a non-authorized person is identified as another authorized person and performs an action they are not allowed to perform. Biometric identifications also have false negatives, when a person is not correctly identified as the person registered and cannot perform actions they are authorized to take. DNA identification will also be possible in the near future; still identical twins share the same DNA.
\nHaving unique attributes is only one facet of the identification and authentication process, as there should be trust in the digital identification and authorization process. For example, consider a program identifying a person having DNA linked to the registered digital record of a person with a certain identity number, and then send an approval on the check. There are several questions to ask on the program actions. Does the program have the means to verify that the input device (e.g., fingerprint, camera) observed the person, or is it a mock-up? Were the input device compromised and a replay attack performed? Another question is whether the program verified the collected data from the input device against the right registration record or was maybe hacked to output approval with no actual checking. This chain of trust is yielded from the trust in the biometric device producer.
\nIn the framework of the Internet of Things (IoT), the identification of things is even more challenging, as devices and items tend to be produced identically. Vehicle networking is now emerging, and the means to identify a car (by another car) is one of the basic ingredients that the trust vehicles have in inter-vehicle communication. Recent works suggested to monolithically sign the car description (e.g., driving license, color, and brand) and the public key associated with the car description in one monolithically signed certificate. The signing authority can be the governmental vehicle registration [10]. The car description should allow for a unique identification by means of an out-of-band channel such as a camera. Note that the identity of a device can be challenging; for example, consider two cars of the same model; if one exchanges the doors of these cars, does that alter the identity of the car? What about changing the engine? And so on.
\nAnother possibility for identifying IoT devices requires trust in the producer, which embeds a unique serial identification number, A unique identifying numbers in unaltered barcode, QR code, RFID, and ROM that can be used as part of the identification and authentication process.
\nThe cloud and blockchain infrastructures enable a new opportunity for representing each person, entity, and organization by a digital avatar. The avatar, being a digital historical record of events, digital assets, and procedures/functions defined to be executed upon given events. The identity linkage between the avatar and the physical entity accumulates trust over time, letting the physical entity monitor the possibility of identity theft, as recorded actions for the avatar can be examined by the actual entity represented by the avatar.
\nFake avatars already exist, and they are represented by profiles in social networks, Facebook, LinkedIn, etc., and may interact with persons as bots do. This is one light form of identity theft where there may be no real entity linked to the avatar. Identity theft has been a trust problem in societies from the years of the bible where Jacob represented himself as Esav to Itzhak. Nowadays, the remote actions enabled in the digital interaction make the identity theft phenomena a major concern.
\nIn some cases, e.g., cryptocurrency, anonymity is an important aspect, as cash money, or digital money, appearing in an account had better not carry its history. Thus every coin or bill having an identical value. Blockchain associates an account with a public key, where the matching private key is held by the owner of a wallet. This somewhat anonymous linkage between an entity and digital assets is only by the means of the private key. The vulnerability of such a solution erases the famous cases of lost/stolen private keys.
\nPrivate keys are also a means to sign transactions binding the holder (even in court) to the transaction; thus, the way to secure the private key, possibly in enclaved memory, is very important. Moreover, having a quantum-safe signature is a must, as the bidding is a very important aspect of the trust infrastructure, and if the bidding is broken, deniability of actions is possible. A client that transferred a million dollars from their account may rightly claim that someone else preformed the transfer to this account on their behalf, with no permission.
\nAnother aspect of the authentication bay is the usage of passwords. The illusion that passwords can contribute to the security of the communication is misleading. Many of the passwords are subject to dictionary attacks. Users tend to forget and manage passwords in vulnerable storage, leading to many password lists being sold on the black net. The typical password renewal procedure involves password reset invocation and a temporal password sent through email. Such single channel security is another weak chain in the security infrastructure, a weak chain that may dramatically benefit using the multichannel security and authenticity yielded from the overlay security concept.
\nCertificate authorities are a major source of trust for the public key infrastructure. The certificate authority identifies an entity and signs a certificate that associates a public key with the entity description. The history of the Internet testifies to examples of the vulnerability of the trust associated with certificate authorities. For example, private keys that were used to sign certificates were stolen, and significant percentage of the Internet were not secure [7, 37]. Recently, Estonia, Canada, and other countries started to use distributed trust among several trusted and heterogeneous entities as a source for identification. Such distributed trust is enabled by blockchain technology [14]. Identity, verified by several trusted entities, possibly including governmental, financial, and notary entities, among others, is logged in a distributed fashion.
\nTo communicate with an entity, a search of several participants in the distributed ledger returns contact information for the entity. Using the communication channels in the contact information and secret sharing enables the creation of a symmetric key. The newly created random symmetric key may, in turn, be used in employing efficient advanced encryption standard (AES) over a single communication link. Unlike the functions used in asymmetric encryption, AES is crafted, rather than relying on number theory challenge, and believed to imply quantum-safe encryption. The key length should still be carefully selected to accommodate the quadratic speedup of search of Grover’s algorithm [13]. Note that secure hash algorithms (SHA) are crafted, similarly to AES, and are also believed to be quantum safe, reducing the risk of finding an efficient number theory solution for a natural problem, such as discrete logarithm.
\nThe ability to perform a transaction in an undeniable fashion over the Internet is important, especially when financial transactions are executed. Lamport’s one-time signature [21] is not tied to a particular one-way function. Thus, Lamport’s signature can employ secure hash function, such as SHA. The use of Merkle trees with multiple private keys in the leaves (leaves that can also be produced by several nested hash functions) and the root of the tree serving as the public key yields an efficient, quantum-safe signature scheme.
\nIn greater detail, the private key is an array of pairs of random numbers. The first random number pair is used to sign the first bit of the message; the second random number pair is used to sign the second bit of the message and so on. Note that, for reasons of efficiency, typically, the hash of the message is signed instead of signing the longer original message. Each random number in each pair is hashed (in fact, any other one-way functions can be used instead of hash), and the resulting array of hashed values serve as the public key. Once the public key is published in a way that links the signing entity to the public key, the construction can serve in signing any single binary string, a string that may be the hash of the original message to be signed. The actual signature is a sequence of random numbers from the private key, one from each pair, attached to the message to be signed. The first random number in the signature is the first (second) random number in the first pair if the first bit to be signed is zero (one, respectively). Similarly, the second random number in the signature is the first (second) random number in the second pair if the first bit to be signed is zero (one, respectively) and so on. Since the array of numbers in the public key are results of one-way hash function, no one but the producer of the public key is able (under standard computation assumptions) to know and expose the right portions of the private key. Hence, the signature is binding.
\nStill, the need to identify an entity and associate the entity to the public key is the most challenging stage in authentication. Lamport’s signature essentially requires such an identification process for each signature. Fortunately, many of Lamport’s signatures may share a single public key, which consists of the roots of Merkle tree, one tree for each position of a random number in each pair of the private keys. The first positions, representing the private keys used to sign a zero value of the strings, consist of random numbers, such that such numbers belonging to the first two private keys are concatenated and hashed to yield the value of their common parent in the first Merkle tree. Similarly, for the second positions, the two random numbers are concatenated and hashed to yield the value of their parent in a second Merkle tree and so on. The parent of any such two leaves is concatenated to the hash obtained from the next two random numbers that reside in the same positions in the next two private keys and hashed yielding the value of the grandparent of these four values and so on.
\nA signature will use one of the leaves, where each leaf is connected by a path to the roots of Merkle trees, one tree for each random number in the leaf. When using a leaf to sign, the appropriate random number in each pair of the leaf is exposed together with the missing hash values that are concatenated in each level of the tree. Thus allowing the verifier to check that indeed any revealed random number leads to the corresponding value of the Merkle tree root public value.
\nThe root value may be stored with the contact information that resides in the blockchain. The contact information with the public value of the root will be added to the distributed ledger after the blockchain participants verify and approve the identity of the contact information and root value owner.
\nOverlay security combined with distributed trust forms an immediate quantum-safe alternative to the public key infrastructure. The existing technologies enable (1) the use of multi-logical/multi-physical channels to create a random secret at will, (2) use of the blockchain distributed ledger as a replacement for single point of failure trusted authority, and to (3) produce quantum-safe signatures.
\nThe suggested changes can gradually, seamlessly, and smoothly emerge over the existing infrastructure without the need to restructure any component of the Internet.
\nWe pride ourselves on our belief that scientific progress is generated by collaboration, that the playing field for scientific research should be leveled globally, and that research conducted in a democratic environment, with the use of innovative technologies, should be made available to anyone.
\n\nWe look forward to hearing from individuals and organizations who are interested in new discoveries and sharing their research.
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I am also a member of the team in charge for the supervision of Ph.D. students in the fields of development of silicon based planar waveguide sensor devices, study of inelastic electron tunnelling in planar tunnelling nanostructures for sensing applications and development of organotellurium(IV) compounds for semiconductor applications. I am a specialist in data analysis techniques and nanosurface structure. 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Focus of his research activity is drug delivery, physico-chemical characterization and biological evaluation of biopolymers micro and nanoparticles as modified drug delivery system, and colloidal drug carriers (liposomes, nanoparticles etc.).",institutionString:null,institution:{name:"Marmara University",country:{name:"Turkey"}}},{id:"61051",title:"Prof.",name:"Andrea",middleName:null,surname:"Natale",slug:"andrea-natale",fullName:"Andrea Natale",position:null,profilePictureURL:"//cdnintech.com/web/frontend/www/assets/author.svg",biography:null,institutionString:null,institution:null},{id:"100762",title:"Prof.",name:"Andrea",middleName:null,surname:"Natale",slug:"andrea-natale",fullName:"Andrea Natale",position:null,profilePictureURL:"//cdnintech.com/web/frontend/www/assets/author.svg",biography:null,institutionString:null,institution:{name:"St David's Medical Center",country:{name:"United States of America"}}},{id:"107416",title:"Dr.",name:"Andrea",middleName:null,surname:"Natale",slug:"andrea-natale",fullName:"Andrea Natale",position:null,profilePictureURL:"//cdnintech.com/web/frontend/www/assets/author.svg",biography:null,institutionString:null,institution:{name:"Texas Cardiac Arrhythmia",country:{name:"United States of America"}}},{id:"64434",title:"Dr.",name:"Angkoon",middleName:null,surname:"Phinyomark",slug:"angkoon-phinyomark",fullName:"Angkoon Phinyomark",position:null,profilePictureURL:"https://mts.intechopen.com/storage/users/64434/images/2619_n.jpg",biography:"My name is Angkoon Phinyomark. 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