introductioncurrently, bitcoin, cryptocurrency, adoption, compared, traditional, currencies, total, underlying, blockchain, contains, transactions, gib, additionally, currency, per, fairly, manageable, personal, computers, entire, validity, incoming, transaction, easier, system, recent, exponential, growth, increasing, circulation, volume, comparable, larger, processed, billion, non, trillion, corresponds, average, greater, validation, infeasible, global, economy, constantly, growing, faster, successful, network, incomprehensible, individual, compute, nodes, keeping, decentralized, trustworthy, various, attempts, scalability, example, suggested, coding, sharing, propose, microblocks, generation, secure, decreasing, latency, proposed, alleviate, solve, aspects, scaling, issue, biggest, higher, thesis, analyze, degree, exibility, interact, utilize, node, behavior, facilitates, currently, lightweight, validate, existence, workload, dissuade, resulting, centralized, distribute, contribute, overwhelmed, unmanageable, relies, detects, invalid, conict, spending, easily, inform, sending, information, involved, verify, ino, using, merkle, error, analyzing, verifying, reported, errors, combing, nd, creates, type, called, validator, specializes, binary, pseudorandom, generators, outsource, validators, permits, mining, retain, barrier, entry, practical, considerations, scenarios, increased, complexity, providing, solutions, countermeasures, section, necessary, knowledge, model, operates, describing, types, cooperate, nally, summary, results, backgroundin, presenting, preliminary, dealing, preliminaries, main, concepts, hash, functions, function, simply, functionh, hfrom, messagesmto, valuesh, generally, properties, computational, ease, pre, image, resistance, practically, collision, pairx, mandx, analysis, specic, beyond, scope, cryptography, encryption, characterized, functione, decryption, functiond, heremis, cis, encrypted, andkis, generate, keysk, encrypt, cwith, decrypt, cto, mwith, designed, deducek, vice, versa, alice, conrm, conversely, makesk, specics, systems, educational, treea, merkele, objects, hashed, hashing, dened, thus, hashh, ofy, calculate, calculated, decent, pass, corresponding, perfect, relax, structure, constraints, variants, consider, unnecessary, trading, units, bitcoins, simplied, inputs, outputs, generated, fee, provided, output, basically, owned, ensure, publish, private, input, elegant, protecting, create, determine, valid, prevent, repeatedly, resolves, serves, ledger, consists, connected, contain, previous, shown, lighter, contents, header, hashes, completely, malicious, entities, spamming, satisfy, difculty, criteria, leading, zeroes, nonce, arbitrary, attached, purpose, required, process, connections, nding, appropriate, generates, roughly, adjusted, provides, chronological, ordering, considered, ignored, represented, longest, collecting, computing, adding, result, orphaned, incentive, namely, xed, awarded, mined, plus, fees, collect, contained, security, based, assumption, dishonest, accepted, reversing, starting, trying, longer, effectively, succeed, attackers, extending, honestly, nonexistent, convenient, aspect, less, users, scenario, surge, popularity, allowing, removing, limit, assume, latter, approach, former, produce, similar, incomprehensibility, risk, modelin, assumes, aforementioned, limits, lifted, internet, communicate, parameters, happened, looking, thatnis, thanr, wont, noticeable, efciently, thenstored, processing, rnew, specialization, systemthe, solution, decentralization, trustworthiness, divided, observers, spreading, across, detected, existing, addition, specialized, added, signicantly, subtypes, detail, effort, benet, propagate, critical, observer, headers, current, considering, storage, modern, computer, witho, consistent, whether, later, trivially, validating, presence, procedure, informed, erroneous, checking, possibly, smaller, chunks, functiong, whereuis, whichgis, distribution, assigns, tto, determinism, random, inputx, functiongcan, naturally, extended, tuples, denote, asg, instrumental, distributing, withklevels, assigned, recursive, algorithm, assign, ifg, hereh, tis, andlthe, responsible, accomplish, randomly, discretion, associated, primary, us, mechanism, accomplishes, variablexand, levellthe, satises, gwhereu, rgis, integers, letybe, index, toxwith, haveni, hashesx, fraction, igets, wherey, nare, indices, eachp, expected, according, kasn, reasonably, approximation, reality, evidence, evenly, introduced, assigning, directly, increasekwhile, consistency, increasekby, responsibility, discarding, belonging, retaining, acting, minimizes, communication, shufing, data, discard, recall, potentially, future, facilitate, secondary, bytes, stored, consist, byte, depth, iso, realistic, correspond, tracked, role, difcult, perform, assembled, assembling, tricky, obvious, resources, collaboratively, independent, lower, coordination, disjoint, constructed, provide, themselves, occurred, declare, individually, compresses, perfectly, balanced, hleaves, construct, intoo, constructing, takeso, theo, communicated, method, acquire, combine, containing, attach, combining, rst, situations, constructs, vertices, vertex, duplicated, construction, lowest, duplicate, append, consecutive, obtain, constructon, duplicates, illustrated, introduce, partial, received, acquired, array, hashesh, letl, icovers, obvouslyl, merge, elements, haccording, ifjh, jh, jto, eraseh, jfrom, ifjt, jis, tjj, jt, appends, element, fori, toj, appendh, hkt, pairwise, merging, duplicating, costsfirst, focus, expense, acquiring, transmitted, heightk, herek, fortunately, probably, collaborating, multiple, rely, handling, doing, requirements, metadata, cheaper, assurance, validated, latest, shared, checked, agreement, resolve, discrepancies, observed, untrustworthy, candidate, orphaning, interest, worked, relevant, properly, concern, complication, deduced, subtract, within, occurs, slightly, complicated, assemble, consequently, actually, wasted, recieve, conicting, resolved, exclude, conicts, include, consideration, reduce, problematic, pretend, toll, reputation, proof, invalidity, therefore, colluding, intenioned, corrupted, claim, ne, actual, barring, signicant, complain, complaints, legitimate, unless, disagreement, complaining, investigating, disagreements, forcing, investigators, entity, stake, honesty, motive, decieve, reputable, majority, recieving, dishonestly, effectiveness, ooding, especially, exceedingly, unlikely, possibility, falsely, claiming, access, available, hopefully, extremely, problem, signed, originator, veriable, hamper, ow, visible, heavily, scrutinized, comparison, closesly, resembles, original, proposal, functionalities, exist, exactly, ensuring, thorough, reliance, capabilities, theory, principles, conclusionin, analyzed, wider, class, greatly, potential, efcient, proved, combatable, common, core, demanded, research, solved, relying, reduced