introductioncryptographically, secure, stamping, mostly, deals, security, hash, based, timestamping, protocols, quantum, computers, achieved, attacks, functions, seemingly, concern, setting, recently, buldaset, al, noted, differences, classical, results, carried, however, notion, scheme, postquantum, currently, undened, shown, commitments, subtleties, dealing, states, adversaries, denitions, longer, capture, intended, meaning, appropriate, explore, outcomes, overview, current, cryptographical, section, dene, post, unpredictable, differ, signicantly, brief, contemporary, rewinding, techniques, aim, prove, collapsing, sufcient, polynomially, bounded, keyless, theorem, proof, standard, model, cryptographic, backgroundwe, expect, reader, knowledge, cryptography, computing, reference, guide, across, term, recognize, additionally, lemmata, index, appendix, quoted, shaded, proper, accompanying, citation, exception, lemma, cite, original, article, source, notation, base, buldas, laur, following, probabilistic, letfpbe, class, computable, polynomial, turing, collision, cdenote, hif, resistance, functionh, fis, resistant, byu, nwe, denote, uniform, distribution, familyfd, kg, ispoly, sampleableif, exists, ad, pwith, output, distributiond, equal, tod, preimage, pr[x, pr[, adopted, dominique, unruhs, cryptology, dimensionalquantum, stateis, represented, vector, cn, jjjijj, hilbert, space, abbreviatex, components, asx, nwhere, tensor, product, kronecker, unitary, matrices, matrixm, nis, ifm, iis, identity, hadamard, usually, denoted, dened, equivalently, transformation, cnis, matrixu, uj, measurement, projective, measurementon, spacehis, specied, familyf, ig, iof, orthogonal, projections, onhlabelled, possible, outcomesi, pairwise, ip, sum, measuring, ioccurs, probability, jj, ij, ijj, pij, introductiona, timestamp, used, data, existed, specic, life, applications, consider, simplied, scenario, someone, timestamped, media, predates, public, release, claim, author, convincing, difcult, forge, operating, systems, le, creation, copyright, dispute, easily, forged, changing, local, trusted, stamps, establish, relative, temporal, authenticity, absolute, incredibly, complicated, impossible, allows, verier, correctly, identify, stamped, documents, signed, earlier, outline, types, properties, optional, previous, publish, relies, completely, service, distributes, digital, signature, benets, approach, simplicity, verication, links, existing, primitives, requires, unconditional, trust, continuous, secrecy, private, client, timestampsof, documentxprovides, withx, wherehis, server, generates, timestamptusing, creates, combined, hashc, jjt, signscusing, signing, ign, sk, lient, device, similar, process, locally, hashed, using, generated, extracted, issued, concatenated, resulting, inc, procedure, called, ensure, verify, pk, commercial, conrming, studied, clupeket, focuses, chain, referred, ashash, publishschemes, linked, sort, structure, root, published, widely, available, newspaper, certicate, necessary, required, node, contrast, existence, contain, needed, dependent, achieve, subtle, rst, proposed, haber, stornetta, includes, known, advance, thus, including, formally, receives, request, stringyfor, unique, identier, th, query, nto, swheret, actual, measured, thet, andl, internal, memory, previously, linking, information, requested, hassandi, check, whethersis, valid, whethert, correct, challenger, legitimacy, colluding, sby, producing, actually, legitimate, contact, personi, fori, thati, alternatively, access, toi, nand, backwards, publishing, fool, fake, exhaust, involved, recent, periodically, publicly, accessible, timetn, within, frame, instances, periodic, publishingl, mif, constantly, veried, publishedl, mis, tol, values, anchor, numerous, drawbacks, pedagogic, purposes, checking, linear, stored, indenitely, future, proven, efcient, optimal, constructs, regular, intervals, submit, constructed, hashing, inner, single, merkle, given, causes, logarithmic, respect, rather, string, strengthen, alternative, offered, benaloh, de, mare, leaf, letdenote, ifx, kandx, kthen, xwe, leth, kbe, anh, fromx, ktor, kwe, possibly, sequence, conditions, byf, rthe, proposition, thatcis, fromxtor, xfor, binary, asymptotically, scope, securityin, related, familiar, itself, outlined, briey, mention, protection, againstbackdatingattacks, produces, invention, released, potentially, ownership, providing, manufacture, unpredictability, interesting, considered, provably, saarepera, sampled, y], later, closely, inuence, importantly, altering, whitespace, symbols, basis, letfpube, staged, polytime, predictor, poly, x], advice, stringa, allowing, individual, negligible, outputsr, anda, fora, thatrneed, created, usingh, valuex, certicatecsuch, fc, fs, r], thathdoes, requirement, thathisschain, hisupreand, samplable, effectively, strongly, r[h, preserves, inputs, preservation, kgisunpredictability, preservingif, fd, addition, dening, relationships, notably, separation, betweenupreand, thatupreis, equivalent, xed, familyh, fh, kgis, weak, everywhere, un, predictable, familya, max, eld, preserving, rgenson, reductions, oracle, imply, amount, allowed, laaneoja, bound, pre, image, aware, insecure, random, awareness, assumptions, ifh, corresponding, unbounded, independent, regards, specically, nding, initialization, likely, iterative, assumingcomputational, uniformityfrom, compression, average, worst, complexities, greatly, alternate, view, bindingn, doubles, extractor, ksuch, adv, pr, gen, ver, coins, ofa, working, ofk, execute, treat, write, iffx, [loc, ]], commitmentccant, unknown, algorithmkwhich, efciently, extract, unsuitable, arbitrary, algorithms, cant, securitysince, highly, regarded, immune, study, ofhash, publishtime, stating, restrictions, placed, offpuinvolves, copying, interestingly, direct, lifting, offpuleads, less, generalizable, clear, designed, groundwork, realizable, remove, runtime, unnecessary, perform, analysis, whether, critical, lose, convey, hastily, replaces, normal, bitstrings, perfectly, satises, computationally, binding, extremely, directly, translated, obstacles, doing, variables, reason, modeled, sense, ais, supposed, represent, possibility, proposes, stated, cannot, copied, according, cloning, explicit, stringato, bothanda, therefore, eliminated, intuitive, solution, requireto, disturb, stateaduring, computation, demonstrate, generalize, wherercan, stage, useful, subelds, prefer, allowrto, invokingdoes, undisturbing, predictoris, detectordthe, valuej, jgame, jis, qfpu, letqfpube, whereaanda, natural, question, satisable, performed, collapses, somewhat, surprisingly, unlimited, statea, tor, spectral, decomposition, measure, disturbing, operatormon, spacevis, diagonal, orthonormal, forv, conversely, diagonaliazable, operator, outer, representation, thatmcan, written, asm, ih, ijwhere, iare, eigenvalues, ofm, eachji, ian, eigenvector, ofmwith, projectors, whereiare, andp, onto, ieigenspace, satisfy, completeness, relationp, orthonormality, relation, composition, whyinqfpuis, additional, allowto, strict, modelling, letcp, fpurefer, version, whereis, letcu, trivial, ascu, fpuonly, givesmore, computational, power, forcu, letube, predictorin, ofcu, uhas, non, advantage, predictorpfor, incp, fpuand, succeeds, gamesg, fpuwith, extra, topwhich, consequence, thusg, allpdoes, calla, applies, topand, reorder, y^, due, transitivity, ofx, removing, uthen, nal, ofcp, predictorpin, considering, statistical, predicted, decreases, accurate, simulating, making, ideal, being, multiple, ofpand, radically, apwhich, plug, meaningful, negative, raised, asqfpuxed, lifted, fairly, formality, display, qupre, sampleable, kgand, wesec, kgsatisesq, wesecif, kon, qschain, kgstrongly, preliminary, review, argumentation, thepost, qupreproof, forupre, resistanceholds, uprerequires, versed, theory, analyzed, kin, superposition, impact, forpost, wayholds, forcr, schaindoes, showingcr, qschainand, reviewed, constraints, rewindingrewinding, common, refers, saving, separate, developed, watrous, applicable, classically, via, crucial, role, showcr, schain, limited, hinges, turning, attempts, solve, simulator, repeatedly, operation, qwith, success, probabilitypa, overwhelming, keeping, executions, gain, letqbe, fromh, anctohout, succwithhsucc, thatdim, anc, dim, succsince, square, assume, valuep, anyj, applyingqtoj, measuringh, succin, probabilityp, letj, succ, idenote, depending, parameter, initialize, exit, successfully, qy, fliptoh, jx, jxi, qtimes, suitable, rexits, difculties, applying, preciselyprather, pand, auxiliary, fullled, theflipoperation, slightly, disrupt, otherwise, applyingqright, applyingqy, sinceqis, denitionqq, cancel, rewind, successful, context, sigma, com, vc, example, succeeding, provides, requiresstrict, bindingorstrict, soundness, messages, uniquely, splits, prover, pinto, multiplea, indexed, msent, informally, circuit, indicate, essence, rewinda, mby, runninga, msincec, andmuniquely, determine, whatucan, negligibly, functionhand, algorithmsa, comp, registers, ofmin, ifpr[, c], min, functionhis, iff, differenceadv, jpr[, advthe, qschainwe, focus, namely, thatcr, requiring, provecollapse, provingcr, schainfor, analyze, sequencec, valuesc, cis, ifcis, thenx, andh, everyi, r[, general, sketch, fromfpuit, thatpr[, ]is, nd, toa, witnesses, dont, predict, statements, againstschain, witness, fm, jg, rconsider, thisas, thatsucceeds, predicting, jwhich, thatjm, jmust, infpu, contradicts, lethbe, thathis, bsuch, wheregis, recursive, pattern, matching, syntax, ifc, length, sobis, thenh, lthen, search, recursively, eventually, ifcends, thenc, happening, quantify, bas, r^, [x, makesba, nder, forh, hsatises, liftingtheorem, challenges, wording, performing, stateswill, changed, ofu, contained, nomwhich, thata, exponentially, forx, xwill, catastrophically, fixed, guarantee, fully, overlap, fortunately, havinga, adversarybthat, longest, degree, openings, wherea, cbefore, thenpr[, viewing, ofi, conforms, proving, subproblemthatpr[, minimal, showing, disturbance, deningqfpu, neatly, generalizeable, candidate, notwas, thereforealso, ona, otherwisedcould, distinguish, qfpudenition, benecial, pictured, wherevdoes, measurecuntil, received, whichpr[b, qfpubut, clearly, commitmentrand, form, zeroes, runsh, hj, vi, described, atp, xing, uniformly, chosenias, vhas, ifwho, stateaand, identical, uniformiwhich, whata, rejectsa, predictorwhich, similarly, noticeable, repeated, conjecture, showingcollapse, recall, transcripts, guaranteed, analogue, exponential, ascollapse, inqfpu, satised, unpredicatibility, requiringa, againstqsc, hainwith, puried, converted, purely, hachieves, cj, i], sinceiis, bya, simplies, considerably, thecoutput, ias, consisting, ofiwires, measurexdirectly, ifi, sincehis, measurec, thatciis, repeat, reachx, complete, theflipfunction, otherwisea, iwould, flipj, escapes, messagesm, principle, usingflipwould, illustrated, unable, efcacy, construction, largely, complex, nature, potential, substantial, glance, conclusionwe, offpufor, denitionqfpuis, ofqfpu, decided, examined, finally, formal, subproblem