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[Powered by Google Translate] [RSA]

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[Rob Bowden] [Tommy MacWilliam] [Harvard University]

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[Hoc est CS50.] [CS50.TV]

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Lets 'take a inviso RSA, a late algorithm pro encrypting notitia.

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Encryption algorithms similem quoque Caesari et Vigenère cyphris non sunt multum securus.

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Cum Caesare notas invasorem solummodo indiget ut tentaret XXV diversis claves

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ad adepto nuntius velit aequoris text.

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Dum Vigenère cyphra tutior est Caesaris cyphra

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propter majores search spatium claves, semel invasorem

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Vigenère clavem scienti longum notas

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determinari poterunt via analysi exemplaria in encrypted text,

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in Vigenère cyphra non est quod multo magis tutis quam Caesar cyphra.

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RSA e manibus arma non sic vulnerari.

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Caesar cyphra et Vigenère cyphra utor idem eadem idem key

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ad utrumque encrypt quod minutum nuntium.

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Hanc proprietatem efficit ut hae cyphris symmetrica key algorithms.

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A fundamentalis forsit per symmetrica key algorithms

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est quod illi inniti unum encrypting et mittens nuntiante

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et recipientis et decrypting nuntiante

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ad iam consenserint upfront in key erunt utrumque utor.

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Hic satus ad propositum nobis est pauca.

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Quam operor II computers quod egestas communicare constituere secretum key inter eos?

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Si occultum sit amet, tunc requiritur ad minutum encrypt amet.

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Si omnes have est symmetrica key cryptography

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tunc redibit eadem quaestio nuper.

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RSA e contrario duo usus clavium

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unum pro encryption et alterum pro decryption.

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Dicitur amet publicum et privatum illud clavis.

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Publicum key est adsuesco assuesco encrypt nuntiandi.

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Sicut vos vires coniicere per nomen eius, possumus nostrum publica key cum

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quis nos volo sine conponendi securitatem of an encrypted nuntius.

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Messages encrypted usura a publicis key

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potest nisi decrypted cum suum correspondens privata key.

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Dum vos potest particeps tuis quas publice key, esses semper custodiat privatum tuum key occulto.

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et de solo privato key potest dici quod minutum perferentes

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si II users volo ut nuntia mittere encrypted cum RSA

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Suspendisse eget citroque habent, et publice et privatim amet par.

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Nuntiis ex user I usorum II

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tantum utor user II scriptor key coniugatione, et nuntiis ex user II usorum I

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tantum utor user I scriptor key coniugatione.

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Hoc quod sunt II separata claves encrypt quod minutum perferentes

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facit RSA an asymmetric key algorithm.

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Non amet ut in publicum emittat encrypt alium computatrum

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cum key est publicum usquam.

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Is opes ut RSA non habent idem satus forsit

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sicut symmetrica key algorithms.

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Ita si volo mittam nuncium usura RSA encryption

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ad expoliandum, Peius primus postulo Rob scriptor publicus key.

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Generare par claves, Rob indiget pick II magna numeros primos.

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In utroque publicis privatisque sit amet hae claves,

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sed publicam key mos tantum uti productum horum II numeris,

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multitudo, non se ipsos.

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Quondam Ive 'encrypted nuntiante usura Rob scriptor publicus key

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Mitte ad me Rob.

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Enim computer, factoring numeris Durus est forsit.

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Publicum key, memini, usus est productum ex II numeros primos.

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Is uber tunc oportet habent solum II factores,

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qui numeri efficiunt in occulto fiunt amet.

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In ordine ad minutum nuntio, RSA mos utor hac privata key

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vel producendo in publicum amet numeri inter se multiplicati.

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Quoniam suus 'computationally difficile PROCURATOR numerum

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usus est in publico key in II numeris usus est in privata key

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suus 'enim difficile invasorem ut instar sicco privata key

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oportet quod verbum minutum.

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Nunc eamus in aliquam gradu inferiore retineo of RSA.

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Primum videamus quomodo duo sint claves generare.

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Primo, puteus 'postulo II numeros primos.

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Puteus 'haec vocare II numeri p et q.

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In ordine ad pick p et q, in praxi volumus pseudorandomly generare

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turn multa an determinetur amet

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isti sunt numeri forsit primus.

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Nos custodire potest generandi temere numerorum super super iterum

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donec habemus II primorum uti possumus.

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Hic lets pick p = XXIII et q = XLIII.

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Memento opere multum PQ plures.

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Quantum scimus, quo maior numerus maior est

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crack an encrypted nuntius.

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Tamen suus 'quoque magis cari encrypt quod minutum nuntiandi.

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Hodie suus 'saepe commendatur ut p et q sunt saltem MXXIV addit frena

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quae ponit quisque numerus ad super CCC decimales constet.

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Sed puteus 'pick haec parua numeri pro isto exemplo.

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Iam puteus multiplicabo p et q pariter ad adepto a 3 numero,

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quod puteus 'vocare n.

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In nostro casu, n = XXIII * XLIII, quae = CMLXXXIX.

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Sumus N = CMLXXXIX.

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Next puteus 'multiplicabo p - I cum q - I

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ad obtinendam 4 numerus, quod puteus 'vocare m.

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In nostro casu, m = XXII * XLII, quae = CMXXIV.

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Habemus m = CMXXIV.

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E numero primus est secundum quod iam opust m

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et minus quam m.

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Duo numeri inter se primi sunt aut coprime

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sed si utrumque aequaliter divisa est I numerus integer positivus.

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Id est, m divisor communis maximus est e,

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oportet esse I.

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In praxi, suus 'communi pro e ad esse numerum primum (LXV)DXXXVII

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numerum non habet esse quamdiu ipsius M.

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Enim nostra claves, puteus 'pick e = V

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quia V est respective primi CMXXIV.

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Denique una numero opust quas feres d.

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D oportet esse aliquam valoris satiat aequatio de = I (mod m).

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Hoc mod m significat puteus 'uti aliquo vocavit modularis arithmetica.

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In modularis arithmetica, semel numerus gets altior quam quidam superiorem ligatus

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is mos involvent se circa 0.

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A horologium, pro exemplo, utitur modularis arithmetica.

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Uno minuto post 1:59, verbigratia, est 2:00,

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non 1:60.

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Minute manus circumfusa ad 0

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super pertingens superiori tenetur ex LX.

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Sic, possumus dicere LX aequivalens sit 0 (mod LX)

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et CXXV aequivalens sit LXV aequivalens sit V (mod LX).

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Publicæ key erit par e et n

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Vbi hic igitur e est V et n CMLXXXIX.

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Privatam, key erit par d et n,

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quae in nostro casu CLXXXV et CMLXXXIX.

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PQ primis animadvertimus origo non apparet

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usquam in nostris priuatis seu publicis claves.

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Claves autem duo nobis est, quomodo est inspice encrypt

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quod minutum nuntium.

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Praereptam velim mittite,

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par erit, ut hac clave generare.

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Tum ego inquies Rob públice key, quae utar

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ad encrypt nuntium mittere ad eum.

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Recordare, suus 'totaliter okay pro Rob consortem publica key mecum.

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Sed non esset esse okay consortem privata key.

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Non est clave uti quales.

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Nos irritum fieri potest auditui nostro m in plura chunks

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minoris omnes n et tunc encrypt singulis illis chunks.

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Puteus 'encrypt chorda CS50, quae nos irritum fieri potest ascendit in IV chunks,

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unum per litteras.

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In ordine ad encrypt mandatique mei, ego puteus 'postulo ut convertam eam in

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aliquod genus, numericae repraesentatione.

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Lets IUNCTUS in ASCII in valoribus characteres in verba mea.

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In ordine ad encrypt data nuntius m

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Ego puteus 'postulo ut supputant c = m ad e (mod n).

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Sed m ​​minor esse debet quam n,

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n modulo vel inenarrabilia verba.

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Chunks m solvere potest in plura, quae minores quam n,

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et encrypt singulis illis chunks.

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Encrypting de his singulis chunks, exurgit C1 = LXVII ad V (mod CMLXXXIX)

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quo fit = DCLVIII.

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Enim noster secundus FRUSTUM habemus LXXXIII ad V (mod CMLXXXIX)

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quo fit = XV.

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Enim nostra tertius FRUSTUM habemus LIII ad V (mod CMLXXXIX)

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quo fit = DCCXCIX.

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Et ad extremum quia nostram ultimam FRUSTUM habemus XLVIII ad V (mod CMLXXXIX)

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quo fit = CMLXXV.

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Autem possumus mittere super has encrypted valores Rob.

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Hic vos vade, Rob.

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Dum nostri nuntius in fuga est, lets accipiamus aliam inviso

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ad quam nos accepisti valor pro d.

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Numerus noster d opus satisfacere 5D = I (mod CMXXIV).

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Hoc facit ut d multiplicative inversa V modulo CMXXIV.

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Datum II integri, a et b, prorogati Euclidaeum algorithm

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Haec possunt invenire II integri divisorem communem maximum.

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II Item dant alios x et y,

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ex aequatione ax + satisfacientes divisor communis maximus = a et b.

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Quomodo hic adiuves nos?

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Bene, plugging in e = V pro

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et m = CMXXIV ipsi b

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iam scimus quod hi numeri sunt coprime.

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I maximus divisor communis est.

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Hoc dat nobis 5x + 924y = I

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aut 5x = I - 924y.

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Sed si nos tantum curant omnia modulo CMXXIV

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tunc potest occumbo - 924y.

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Cogitare retro ad horologium.

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Si scrupula est in I et tunc exacte X horas,

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I scrupula adhuc in novimus.

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Hic nos satus procul I et tunc CONVELO exacte y temporibus,

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at usque apud nos I.

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Habemus 5x = I (mod CMXXIV).

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Atque hoc idem x d quaerebatur ante

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ita si utimur prorogati Euclidaeum algorithm

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ut numerus x, sicut utendum est numerus d.

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Nunc lets 'currere prorogati Euclidaeum algorithm pro a = V

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et b = CMXXIV.

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Puteus 'utor a Methodus quam vocant mensam methodo.

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Columnas habebit mensam IV, x, y, d, k.

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Tabula nostra incipit cum II remigat.

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In primo versu erit I, 0, valor noster est V;

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et secundi ordinis 0: I, pretium et B, quae CMXXIV.

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4 agmen pretium K, fiet

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dividendi valor ipsius d in ordine supra eam cum valor ipsius d

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in eadem remigant.

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Habemus V divisa per CMXXIV est 0 cum aliqua cetera manerent.

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Ut opes habemus k = 0.

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Cetera erit valor ipsius celle superius versus cellam II

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minus valor row supra illud temporibus k.

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Lets 'satus per d in 3 remigant.

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Habemus V - CMXXIV * 0 = V.

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Mox 0 - 0 * 0 I

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et I - 0 0 I *.

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Non nimis, ita ut nec movere sequentem ordinem instituunt.

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Primum quidem nostri valor ipsius k.

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CMXXIV divisa per V = CLXXXIV cum aliqua reliquam,

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ita noster valor pro k est CLXXXIV.

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Nunc CMXXIV - V * CLXXXIV = IV.

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I - 0 * CLXXXIV est I - et 0 I * CLXXXIV est -184.

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Bene, faciamus sequentem ordinem instituunt.

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Nostri valor ipsius k erit I quia

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V divisa per IV = I cum aliqua cetera manerent.

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Lets replete in altera columns.

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V - IV * I = I.

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0 - I * I = -1.

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Et I - CLXXXIV * I est CLXXXV.

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Lorem ipsum dolor sit k deinceps fore.

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Bene nobis videtur I IV divisa est IV.

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In hoc casu ubi erant 'dividendo per I talis, ut k est equalis

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valor ipsius d in supra row pertinet quo 'perfectus cum nostris algorithm.

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Et hic potest y = x = -1 in ultima CLXXXV.

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Nunc ergo ad propositum nostrum exemplar sit amet.

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Dictum est valor ipsius x ex hac cursus algorithm

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esset multiplicative inversa a (mod b).

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Id est CLXXXV est multiplicative inversa V (mod CMXXIV)

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per quae intelligitur quod habemus valorem CLXXXV pro d.

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I, quod in ultima d =

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certificat e erat coprime ad m.

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I ergo si non vult e novo eligo.

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Nunc lets 'vide si Rob meam suscepit nuntius.

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Quando aliquis mittit mihi encrypted nuntius

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quamdiu Ive 'mea custodierit privata key secretum

249
00:15:38,000 --> 00:15:41,000
Curabitur quis minutum unum verbum.

250
00:15:41,000 --> 00:15:46,000
Ad minutum a FRUSTUM c possum calculare originali nuntius

251
00:15:46,000 --> 00:15:53,000
FRUSTUM d aequalis potentiae (mod n).

252
00:15:53,000 --> 00:15:57,000
Memento mei secreta clavem d et n.

253
00:15:57,000 --> 00:16:01,000
Impetro a plenus nuntius a suo chunks nos minutum singulis FRUSTUM

254
00:16:01,000 --> 00:16:04,000
et IUNCTUS praecessi.

255
00:16:04,000 --> 00:16:08,000
Exigo quam tutum est RSA?

256
00:16:08,000 --> 00:16:10,000
Verum sit, nescio.

257
00:16:10,000 --> 00:16:14,000
Quamdiu voluit ex invasore guinem verba crack

258
00:16:14,000 --> 00:16:16,000
encrypted cum RSA.

259
00:16:16,000 --> 00:16:19,000
Accedit ad publicam meminerint amet invasorem,

260
00:16:19,000 --> 00:16:21,000
quae utrumque continet e et n.

261
00:16:21,000 --> 00:16:26,000
Si oppugnator procurat inferre PROCURATOR n in sua II primorum, p et q,

262
00:16:26,000 --> 00:16:30,000
tunc ipsa coniectare poterat d usura prorogati Euclidaeum algorithm.

263
00:16:30,000 --> 00:16:35,000
Hoc dat privata key, quo uti potest ad minutum ulla nuntius.

264
00:16:35,000 --> 00:16:38,000
Sed quam cito possumus PROCURATOR integri?

265
00:16:38,000 --> 00:16:41,000
Deinde nescio.

266
00:16:41,000 --> 00:16:43,000
Nemo invenit ieiunium via faciendi,

267
00:16:43,000 --> 00:16:46,000
per quae intelligitur quod data magna satis n

268
00:16:46,000 --> 00:16:49,000
foret invasorem unrealistically diu

269
00:16:49,000 --> 00:16:51,000
ad PROCURATOR numerum.

270
00:16:51,000 --> 00:16:54,000
Si quis revelavit ieiunium viam factoring integri

271
00:16:54,000 --> 00:16:57,000
RSA esset confringatur.

272
00:16:57,000 --> 00:17:01,000
Sed etiam si integer factorization est inherently tardus

273
00:17:01,000 --> 00:17:04,000
in RSA algorithm adhuc posset habere aliquod vitium in eam

274
00:17:04,000 --> 00:17:07,000
admittit pro securus decryption de nuntiandi.

275
00:17:07,000 --> 00:17:10,000
, Nemo inventa, et revelaverit talia vitium tamen,

276
00:17:10,000 --> 00:17:12,000
non unus, sed non est.

277
00:17:12,000 --> 00:17:17,000
In theoria posset aliquis esse sicco illic legens tota notitia encrypted cum RSA.

278
00:17:17,000 --> 00:17:19,000
Illic 'alius aliquantulus of a intimitatem semen.

279
00:17:19,000 --> 00:17:23,000
Si Tommy encrypts aliquam legationem usura publice, key

280
00:17:23,000 --> 00:17:26,000
et invasorem encrypts eadem man usura publice, key

281
00:17:26,000 --> 00:17:29,000
oppugnator videbit II perferentes sunt identicae

282
00:17:29,000 --> 00:17:32,000
et sic cognoscunt quid Tommy encrypted.

283
00:17:32,000 --> 00:17:36,000
In ordine ad hoc excludendum, perferentes sunt typice padded cum temere bits

284
00:17:36,000 --> 00:17:39,000
antequam encrypted ita quod idem nuntius encrypted

285
00:17:39,000 --> 00:17:44,000
multiple vicis mos vultus diversis quamdiu padding super nuntius est diversa.

286
00:17:44,000 --> 00:17:47,000
Sed memento quomodo habeamus cessitas perferentes in chunks

287
00:17:47,000 --> 00:17:50,000
ita quod quilibet FRUSTUM minor est quam n?

288
00:17:50,000 --> 00:17:52,000
Padding in chunks: quod significet quod habeamus cessitas res sursum

289
00:17:52,000 --> 00:17:57,000
in magis etiam chunks cum padded FRUSTUM minor esse debet, quam n.

290
00:17:57,000 --> 00:18:01,000
Encryption et decryption sunt respective carus cum RSA,

291
00:18:01,000 --> 00:18:05,000
et sic indigens diducere a nuntius in multas chunks potest esse valde veste pretiosa.

292
00:18:05,000 --> 00:18:09,000
Si magna volumen of notitia esse indiget encrypted et decrypted

293
00:18:09,000 --> 00:18:12,000
possumus miscere beneficia symmetrica key algorithms

294
00:18:12,000 --> 00:18:16,000
cum illis de RSA impetro utrumque securitatem et efficientiae.

295
00:18:16,000 --> 00:18:18,000
Ingredi non licet, hic

296
00:18:18,000 --> 00:18:23,000
Aes est symmetrica key algorithm sicut Vigenère et Caesar cyphris

297
00:18:23,000 --> 00:18:25,000
sed multo durius fatiscat.

298
00:18:25,000 --> 00:18:30,000
Nimirum, non possumus uti aes sine constituendum corresponsabilitate abscondito key

299
00:18:30,000 --> 00:18:34,000
inter II systemata, et vidimus forsit per quod ante.

300
00:18:34,000 --> 00:18:40,000
Sed nunc uti possumus RSA ad stabiliendam corresponsabilitate abscondito key inter II ratio.

301
00:18:40,000 --> 00:18:43,000
Puteus 'vocare computer mittens notitia mittentis

302
00:18:43,000 --> 00:18:46,000
et computer suscipiens notitia recipientis.

303
00:18:46,000 --> 00:18:49,000
Accipientis habet RSA key par et mittit

304
00:18:49,000 --> 00:18:51,000
clavis mittitur publica.

305
00:18:51,000 --> 00:18:54,000
Mittentis generat aes key,

306
00:18:54,000 --> 00:18:57,000
encrypts eam cum accipientis est scriptor RSA publica key,

307
00:18:57,000 --> 00:19:00,000
et mittit amet aes recipientis.

308
00:19:00,000 --> 00:19:04,000
Accipientis decrypts nuntiante, cum suo RSA privata key.

309
00:19:04,000 --> 00:19:09,000
Utrumque mittentis et recipientis nunc habent communi aes key inter eos.

310
00:19:09,000 --> 00:19:14,000
Aes, quae est multo velocior in encryption et decryption quam RSA,

311
00:19:14,000 --> 00:19:18,000
Mauris sit amet nunc libros mittere encrypt accipienti magnum,

312
00:19:18,000 --> 00:19:21,000
qui potest minutum usura idem eadem idem key.

313
00:19:21,000 --> 00:19:26,000
Aes, quae est multo velocior in encryption et decryption quam RSA,

314
00:19:26,000 --> 00:19:30,000
Mauris sit amet nunc libros mittere encrypt accipienti magnum,

315
00:19:30,000 --> 00:19:32,000
qui potest minutum usura idem eadem idem key.

316
00:19:32,000 --> 00:19:36,000
Nos iustus opus RSA transferre partita key.

317
00:19:36,000 --> 00:19:40,000
RSA iam non usum fuisse.

318
00:19:40,000 --> 00:19:46,000
Videntur verba teneo.

319
00:19:46,000 --> 00:19:49,000
Quid refert si in charta legerent Vivamus ante incidissent

320
00:19:49,000 --> 00:19:55,000
quia solus non sum de propriae amet.

321
00:19:55,000 --> 00:19:57,000
Lets minutum singulis chunks in auditui.

322
00:19:57,000 --> 00:20:07,000
FRUSTUM primum, DCLVIII, levamus d, quod est CLXXXV,

323
00:20:07,000 --> 00:20:18,000
mod n, CMLXXXIX, erit LXVII,

324
00:20:18,000 --> 00:20:24,000
quae est C littera in ASCII.

325
00:20:24,000 --> 00:20:31,000
Nunc, onto secundo FRUSTUM.

326
00:20:31,000 --> 00:20:35,000
Secundo FRUSTUM valet XV,

327
00:20:35,000 --> 00:20:41,000
quae levamus ad 185th potentia,

328
00:20:41,000 --> 00:20:51,000
mod CMLXXXIX, et hoc est aequalis LXXXIII

329
00:20:51,000 --> 00:20:57,000
quae est litterae S in ASCII.

330
00:20:57,000 --> 00:21:06,000
Jam tertius FRUSTUM, quae habet valorem DCCXCIX, nos suscitábunt CLXXXV,

331
00:21:06,000 --> 00:21:17,000
mod CMLXXXIX, et hoc est aequalis LIII,

332
00:21:17,000 --> 00:21:24,000
V ASCII in qua ratio valet.

333
00:21:24,000 --> 00:21:30,000
Nunc ultimo FRUSTUM, quae habet valorem CMLXXV,

334
00:21:30,000 --> 00:21:41,000
levamus ad CLXXXV, mod CMLXXXIX,

335
00:21:41,000 --> 00:21:51,000
et hoc est aequalis XLVIII, quae est valor character 0 ASCII.

336
00:21:51,000 --> 00:21:57,000
Est nomen meum Rob Bowden, et hoc est CS50.

337
00:21:57,000 --> 00:22:00,000
[CS50.TV]

338
00:22:06,000 --> 00:22:08,000
RSA omnino.

339
00:22:08,000 --> 00:22:14,000
RSA omnino. [Risus]

340
00:22:14,000 --> 00:22:17,000
Omnino.