introductioncurrently, bitcoin, cryptocurrency, adoption, compared, traditional, currencies, total, underlying, blockchain, contains, transactions, gib, additionally, peak, per, fairly, manageable, personal, computers, entire, check, validity, single, incoming, everyone, going, easier, trust, system, recent, however, exponential, growth, increasing, beginning, circulation, volume, comparable, larger, processed, billion, non, cash, trillion, corresponds, given, average, greater, rate, quickly, validation, infeasible, global, economy, constantly, growing, amount, faster, successful, network, incomprehensible, individual, compute, nodes, question, possible, deal, keeping, decentralized, trustworthy, various, attempts, improve, scalability, example, suggested, coding, sharing, authors, propose, microblocks, speed, generation, secure, decreasing, latency, proposed, alleviate, solve, aspects, scaling, issue, remains, biggest, facing, higher, thesis, analyze, itself, allows, degree, exibility, interact, utilize, behavior, facilitates, currently, lightweight, validate, existence, workload, dissuade, running, resulting, centralized, distribute, contribute, being, overwhelmed, unmanageable, relies, detects, invalid, conict, double, spending, easily, inform, sending, information, involved, verify, ino, log, using, merkle, error, analyzing, verifying, reported, combing, nd, creates, type, called, validator, specializes, binary, pseudorandom, generators, divides, miners, outsource, permits, mining, retain, barrier, entry, finally, practical, considerations, attack, scenarios, arise, increased, complexity, providing, solutions, countermeasures, section, necessary, background, knowledge, model, operates, describing, cooperate, nally, summary, results, backgroundin, setting, presenting, preliminary, dealing, main, concepts, used, hash, functions, simply, functionh, hfrom, set, messagesmto, valuesh, generally, following, properties, computational, ease, pre, image, resistance, practically, collision, pairx, mandx, analysis, specic, beyond, scope, public, cryptography, encryption, characterized, functione, decryption, functiond, heremis, messages, cis, encrypted, andkis, generate, keysk, encrypt, cwith, decrypt, cto, mwith, designed, deducek, vice, versa, alice, conrm, conversely, makesk, educational, treea, merkele, leaves, objects, useful, root, hashed, hashing, dened, thus, bob, hashh, prove, ofy, calculate, calculated, matches, decent, impossible, pass, corresponding, relax, structure, constraints, variants, consider, unnecessary, trading, units, simplied, inputs, outputs, generated, difference, fee, level, provided, basically, owned, ensure, owner, publish, spent, private, elegant, protecting, determine, valid, prevent, repeatedly, resolves, serves, ledger, consists, connected, chain, having, previous, shown, lighter, contents, header, completely, share, malicious, entities, spamming, satisfy, difculty, criteria, leading, zeroes, nonce, arbitrary, string, attached, sole, purpose, required, process, connections, nding, appropriate, roughly, adjusted, provides, chronological, ordering, considered, ignored, represented, longest, collecting, computing, adding, becoming, orphaned, incentive, namely, xed, awarded, mined, plus, collect, form, contained, security, based, assumption, power, honest, dishonest, cannot, accepted, reversing, starting, trying, longer, effectively, succeed, attackers, extending, honestly, built, nonexistent, convenient, rather, less, users, surge, popularity, allowing, removing, limit, assume, latter, approach, former, produce, similar, incomprehensibility, risk, modelin, aforementioned, lifted, internet, communicate, parameters, happened, looking, thatnis, thanr, wont, noticeable, efciently, thenstored, processing, rnew, specialization, systemthe, describe, decentralization, trustworthiness, divided, observers, task, spreading, across, report, detected, existing, interesting, addition, simple, specialized, added, signicantly, subtypes, detail, effort, state, benet, propagate, critical, current, considering, storage, cost, modern, witho, consistent, whether, later, trivially, correct, validating, presence, procedure, informed, erroneous, someone, checking, possibly, smaller, chunks, functiong, whereuis, whichgis, distribution, assigns, tto, determinism, uniform, random, inputx, functiongcan, naturally, extended, tuples, denote, asg, instrumental, distributing, withklevels, assigned, recursive, algorithm, ifg, otherwise, hereh, tis, andlthe, repeat, responsible, accomplish, randomly, discretion, associated, primary, mechanism, variablexand, levellthe, satises, gwhereu, rgis, integers, letybe, index, toxwith, haveni, hashesx, fraction, igets, wherey, nare, eachp, expected, according, law, kasn, reasonably, approximation, reality, evidence, evenly, reason, introduced, assigning, directly, increasekwhile, consistency, increasekby, choices, responsibility, discarding, belonging, choose, retaining, acting, minimizes, communication, shufing, data, discard, recall, potentially, future, secondary, bytes, stored, depth, iso, realistic, tracked, role, difcult, perform, assembled, assembling, tricky, obvious, pool, resources, collaboratively, independent, lower, coordination, disjoint, constructed, themselves, occurred, declare, broadcast, individually, compresses, perfectly, balanced, hleaves, construct, receive, intoo, constructing, takeso, theo, communicated, method, acquire, somehow, combine, containing, attach, combining, rst, situations, odd, vertices, duplicated, construction, behaves, fashion, lowest, duplicate, append, consecutive, obtain, constructon, connects, illustrated, introduce, partial, received, acquired, array, hashesh, letl, icovers, obvouslyl, merge, sort, elements, haccording, ifjh, jh, jto, eraseh, jfrom, ifjt, jis, tjj, jt, fori, toj, appendh, hkt, sweeps, pairwise, merging, length, duplicating, costsfirst, focus, terms, expense, acquiring, transmitted, daily, heightk, herek, fortunately, collaborating, powerful, multiple, nor, handling, doing, requirements, metadata, cheaper, assurance, validated, latest, shared, checked, agreement, values, resolve, discrepancies, sum, observed, equal, hidden, untrustworthy, candidate, orphaning, interest, worked, relevant, willing, properly, concern, complication, deduced, subtract, within, occurs, slightly, complicated, assemble, consequently, actually, wasted, fault, recieve, conicting, resolved, exclude, include, accept, reduce, problematic, toll, reputation, proof, invalidity, therefore, colluding, intenioned, corrupted, claim, ne, actual, barring, signicant, complain, really, complaints, legitimate, unless, disagreement, complaining, investigating, forcing, investigators, known, stake, record, honesty, motive, decieve, reputable, majority, recieving, likely, dishonestly, effectiveness, ooding, especially, drain, exceedingly, unlikely, possibility, falsely, claiming, access, vote, available, lose, hopefully, extremely, false, signed, originator, veriable, hamper, ow, visible, heavily, scrutinized, comparison, closesly, resembles, original, proposal, scale, functionalities, exist, exactly, ensuring, thorough, reliance, capabilities, theory, tried, principles, conclusionin, analyzed, wider, class, greatly, potential, efcient, weak, proved, combatable, weaknesses, common, stack, truly, core, demanded, avenue, research, solved, relying, overhead, reduced