pas grave
de
musclor74
, posté le 01 janvier 2010 à 19h43
franchement je me fou d'être écouter c'est pas bien grave , de plus les militaires ne doivent pas se gener , la cia et le fbi on du casser les codes y'a bien longtemps !!! de même que tout les militaires de tout les pays !!! zut ils vont m'entendre dire à ma copine que le l'aime !!! trève de plaisanterie vos communications sont elle "secret" défence à ce point ? bien sur que non ! même si ils savent que vous avez une maitresse ou un amant ils s'en foutent grave !!! donc rien de méchant à être écouter point ...
...
de
darshounet
, posté le 04 janvier 2010 à 18h37
Après le hack du gprs, bluetooth, wifi (wep, wpa et wpa2) voici venir les conversations...
Et ils disent que ce n'est pas grave...
Pourtant énormément de logiciels ont "tournés" sur le piratage automatique d'un bluetooth juste après les découvertes des hacks...
_____________________
http://hadopi.over-blog.com/
http://mouvement-zeitgeist.fr/
Et ils disent que ce n'est pas grave...
Pourtant énormément de logiciels ont "tournés" sur le piratage automatique d'un bluetooth juste après les découvertes des hacks...
_____________________
http://hadopi.over-blog.com/
http://mouvement-zeitgeist.fr/
SECURITY
de
SLIMONUE
, posté le 04 janvier 2010 à 19h21
RSA : FACTORING, SECURITY & COMPUTER APPLICATIONS
As we will note it the logarithms play a big role in an operation of factorization. The great numbers do not offer only the advantage of solving a expensive problem with all the mathematicians, they invite us to question us on the laws which govern our universe, medicine, the nanotechs, inter alia, and various opportunities deliver to us on the technological change of information: compression ratios higher than 1 per 10000, more compact programs, transport of bulky data, etc
Thus, it will be permissible for us to store 10.000 films with the DivX format on a support CD and, associated with crypto-compression, to make it possible the world to exchange quantities of information without Big Brother not being able to decipher the few impulses collected.
In addition to the transfer of information bulky, it will be possible to develop new chips of encoding making it possible to ensure the whole safety of the Chinese military communications.
All the tests were carried out on 150 numbers of 1024 bits whose factors are known. Calculations presented below were carried out using a PC Notebook ACER ASPIRES 5920G equipped with a processor Core Duo T7300. The first tests related to a study of the influence of the weight of the base on the speed of the computers and allowed me to reconstitute the first 156 figures in 6 hours.
Thereafter, the rebuilding of the first 170 digits took place in a few seconds.
Example 1: Extract of tables resulting from the basic Algorithm of the factors ©
1.0035695081046852201152666761291779998530643488631872388340107793979864498017825579908660108063465878637050512874197975356538150509791624097937134422495305 10e+154
*
1.3458600503026249556854391675989495759324687551055421000988051942571357566785824617386316197964812400422231492964572095945530111067356858171563935508338806 10e+154
=
135066410865995223349603216278805969938881475605667027524485143851526510604859533833940287150571909441798207282164471551373680419703964191743046496589274242997185495044902494354468514498718464015533419752872326052737902428260293725679867905230916132597008114369547166434146073730468931445127020217937884305830
Example 2: Extract of tables resulting from a formula
10316818314917763325702151276313025303946768901631629013679495438858798953997978991824010769850008487294313392162565425193401875193212097570602920613038011
*
13091866769689435490760893105301876025091350111093293010265880610926442105302611591815350286126670784862076800863403566069087711519681771450475969485570443
=
135066410865995223349603216278805969938881475605667027524485143851526510604859533833940287150571909441798207282164471551373680419703964191743046496589274256284791009980155226485382948738956525917141673045692979002887401859301436547460803919706901566161070455452115171855253348177425634502736978224357577108873
The two examples which are presented to you (Example 1 < RSA1024 < Exemple 2) aim at showing that a number can be reconstituted from left to right according to the weight of the digits (Factors Magnitude Algorithm © describes in the Algorithmes chapter).
As we will discover it in the next chapters, it is possible to rebuild a number from left to right, from right to left, to divide this last into several portions and to reconstitute each one of them from left to right and vice versa. The algorithm describes in question could be adapted of structure out of Wallace's tree in order to accelerate the computing speed.
RSA1024:
135066410865995223349603216278805969938881475605667027524485143851526510604859533833940287150571909441798207282164471551373680419703964191743046496589274256239341020864383202110372958725762358509643110564073501508187510676594629205563685529475213500852879416377328533906109750544334999811150056977236890927563
The results presented in next page were obtained using the same computer and required only a few seconds. A formula is thus possible by an elimination of the residues. That makes it possible to show that the security of algorithm RSA is by no means dependant on the nature or unspecified property of a number (Prime or not).
AFTER TEST OF FORMULA 1: to see chapter Algorithms
1.050788840365072685950352450587047798144934746687995398404115927062658409146104634405124999120263716291629060853699170754696535656431200243664334363835601044734153757066070668175087097633853162381165628665739466431573704611593532659525473834774653833270054346313155441028079965034601318673086077678131315431331504540481356357123977 10e+154
*
1.285381093494193091377241869898479371149607913660777195854400617119003267924312932545198632604892222981270558035126104991868488558113630335497950206940640721248987282347468445508826291927816988328939232913225233553606813790516037914562107477769308489401201737122827642993768526231967780881271596440010975647935645918602438264828495 10e+154
=
1.350664108659952233496032162788059699388814756056670275244851438515265106048595338339402871505719094417982072821644715513736804197039641917430464965892742562393410208643832021103729587257623585096431105640735015081875106765946292055636855294752135008528794163773285339061097505443349998111500569772368909275630000000000000000000466 10e+308
AFTER TEST OF FORMULA 2: see chapter Algorithms
1.0046474111793196477281392153465338694873306095899242918222857249750057273166141409565831411015348561096814902049911905165932505993252032096002254686961257748522176591417844332696630590871648168108665587527485705265134171790498836928350768206450033077347902641728132875925050697090918156986419488976261777082475680132200848060955473 10e+154
*
1.3444160544588035774178934088252278366563098442918880224331406055466905348866747070660101661501032736103644434552532492358003467109134361105364260927149650510776957958453910771574950434465626504775680044730480121691970201754716102375466972069803074585515362365192257360628005577221043657252566312130020518078305097906428784585578538 10e+154
=
1.3506641086599522334960321627880596993888147560566702752448514385152651060485953383394028715057190944179820728216447155137368041970396419174304649658927425623934102086438320211037295872576235850964311056407350150818751067659462920556368552947521350085287941637732853390610975054433499981115005697723689092756299999999999999999997118 10e+308
To factorize is thus summarized to solve a linear function. As it will be shown through the various chapters, the choice of the base of the logarithm influences the linearity and the speed of the computers (simple base or multiple bases).
Note: Neural networks can contribute in an important way to various operations of factorization.
In the same way for RSA2048 : Example 1 < RSA2048 < Example 2 (Computation required only a few seconds).
25195908475657893494027183240048398571429282126204032027777137836043662020707595556264018525880784406918290641249515082189298559149176184502808489120072844992687392807287776735971418347270261896375014971824691165077613379859095700097330459748808428401797429100642458691817195118746121515172654632282216869987549182422433637259085141865462043576798423387184774447920739934236584823824281198163815010674810451660377306056201619676256133844143603833904414952634432190114657544454178424020924616515723350778707749817125772467962926386356373289912154831438167899885040445364023527381951378636564391212010397122822120720357
Example 1:
147964689457797841047066565046278313839088189432388123095307129102409188489470471937032843570795143971891390654789545942159070973008367696524422513142471408432317328058634623998409713802920982540347106658317859297945112627938898934649650078144847454212434920322214762866323864726309077020353636708858369808155
* 170283251821673402385829600686247358732092030186896729440025731250263704572435310252050374757369996831328058037941316712068111191419969084691136376788694541256036152089536478905157026282118450688603498493321129210961511331193332223475832841088033987577327022483936750144526903503305810547115713642582719119817
= 25195908475657893494027183240048398571429282126204032027777137836043662020707595556264018525880784406918290641249515082189298559149176184502808489120072844992687392807287776735971418347270261896375014971824691165077613379859095700097330459748808428401797429100642458691817195118746121515172654632282216869987548267513273542921999454242887605445293850478033108327398246445049736303167909492829147712370879179892408290955218915970494672718456012212312319520831873609108292812428079343250867928075555567689759209545120560317743941145165347731246489211806062916188769546109965585941791679450193420530386292031568748707635
Example 2:
150853796982129550201437469508437639976684780987005809019824856161943067403356756860335785620017699895632544258248038273135044955333278368189479798094606826964478949885940079972720435608963255564041650674059116030317615470244140977674762158336451573466870061470218126368888221427382487146861252104398234464214
*
167022037096239960225921182033334794940667724353681964121043761715885664479605519236619077817857383695123246792893950303090420258925005739113309222476575787910955363454931873944596386559127258691612529044559449873161611426000784608401569114149584013716438501889077768941096310269110022129183980985707437226987
=
25195908475657893494027183240048398571429282126204032027777137836043662020707595556264018525880784406918290641249515082189298559149176184502808489120072844992687392807287776735971418347270261896375014971824691165077613379859095700097330459748808428401797429100642458691817195118746121515172654632282216869987715459349804152216735959217661660883794205134612666280728018168381530670418289858696786735777237093998766696820718409140780238349358207362920229181728918166633643463624531280279373796751645138057360339384757645476959980899153222199232809378427883272550975803398808599662419750643202210167244186492205846543218
Example of residue obtained after test of formula 1: MP > 2000 digits
1.50376664007301027561914543604940246959761239266141098526167695946250722979226462286013447038404037452462798341791377500612178280165661285109077520633478184507307913569697329157697574286269614769906407044616350683373818897956197392400393574968666170509512194663928805550205482179553873471344335350716268646564800049458979836675509271760927776951900439176086858070623525907032877636083257271260588439353017337883268378183831144098474592915364737338249209840549210737284829048116482385595632622627594290124697958599709475583962806979200659669428568493745617051892486632158929956279682541772173040923146290107010591743292148625629278232548723537406843582447820516494972331809205712974448923604433953736151342644093914645203162970555601073216772341892279218703713379031729547159600221369315081409413067368423927520647296457966472563677809268901073916859739121709832626576991962970383146172784589008670897784373648757388426267621031534721442660303889141148204158447778441680793610336884153316148202327793208434070515753528345117499865758335264356367628202151027090939195597172518785534463723063970617572317593045 .....10e+308
*
1.675519844916535177107010615481407363605811030154897022603153334303302595844389170186936251356982286930931475173272775708334831147782225031629417123478004451091227876990830256504880055817075675754992571332845655134119382271661982171016268299979570759369618729379189190077393463010984206530393282864002174463508135226394606166468257899250079467807475061329315603230196690645676640371928623100754387438493452069575686802531479790622881768813053444163629912985047650188684197627774685661394917317144460003529125451624533396432728181703858131046961990840485388053832935448030330226110824105412071619025386547689903154094425511303928948031323476337300322950106502319161214380228615876686424759626301167477666459465412266955521544270309817413153619618364298112181992978829881464764866414048730900699300198708268899306600541466602949642078893630295523399300505186338587295818062350119599262190857628542132128787864330861169765621997181146863668929943538082356468732541361736248536719049499788736208773247068493981361724805211238448875332115545484873521784634910150965328663594934632295795949930079634330993042880259 .....10e+308
=
2.5195908475657893494027183240048398571429282126204032027777137836043662020707595556264018525880784406918290641249515082189298559149176184502808489120072844992687392807287776735971418347270261896375014971824691165077613379859095700097330459748808428401797429100642458691817195118746121515172654632282216869987549182422433637259085141865462043576798423387184774447920739934236584823824281198163815010674810451660377306056201619676256133844143603833904414952634432190114657544454178424020924616515723350778707749817125772467962926386356373289912154831438167899885040445364023527381951378636564391212010397122822120720357000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000004280876010504929214591364178746797793761497072666091502664133502074811540207737556980431596543709625079152807689750053031631040732583363899826948305353985673524527530343316568727141547571787361488867105609561119571208125418904385336196515239638671049168247466201984807694872366943361231569787238796912658708112545746422293683367352779458209903774405574295307230700320270636967758297289767535173529118478801239207276020824258115393738441719572225802921396612296266633461169849532428819258886869718167585038024549542163652910129290665829918655794892148022618817686610290387319786927224661413950943106959431062734502696819237336602742235291187950271783712516506154086461878180720693237232330545424172526345608767730896973439245531469955627554394732305114978098667071158136132747757626322517619084616337363800391029759905747185650500813238336568937365908388266535929727569640940236077358195408336616776202826867475157540059333503770987 .....10e+616
Thus, it is not difficult to determine the intervals in which are located each factor of RSA2048 (Extract of the matrix of the high-orders digit).
25195908475657893494027183240048398571429282126204032027777137836043662020707595556264018525880784406918290641249515082189298559149176184502808489120072844992687392807287776735971418347270261896375014971824691165077613379859095700097330459748808428401797429100642458691817195118746121515172654632282216869987549182422433637259085141865462043576798423387184774447920739934236584823824281198163815010674810451660377306056201619676256133844143603833904414952634432190114657544454178424020924616515723350778707749817125772467962926386356373289912154831438167899885040445364023527381951378636564391212010397122822120720357
Factor 1 is higher than:
103672031906951053623947441426514013084516767552219487151306210059006889609014612268034793945656305588603952925576709915679174156682928486219835893428182536652469099063223463008816014180182453133593899587075484130932570201493364804764920076880814392591950513840246864398759993143762298801236664695486126949517
And lower than:
160566559884233726650546447809140208245454254331048557333174632052519210507323250271792956262309668239183736106871075377479646207322834007579407963656384883208946107211302017794468125764038293541827340635892138959103263333422298544049962868942319668575518784768847057679039275999685961201047236292788173557525
Factor 2 is higher than:
156918778691053702101098219916929907095707992706905177559929437154331963727096373732841065560273170416700664715274656923963499842118665928897228995739228119959375434923971858101152147245130724275869544346084032277230907854980268987985209737247789756740388316193980799845678656944921255048040421014728671823543
And lower than:
243034770441000161126465146022739160410548547609503313622989361907329958650766602167702851722442843650127501854315620459398004439036301253662401358684009829459735524825756900968245233284476538643092084054461139999369593406028547097675253570507367414788307418470447697302794934211368999328501932309380268452820
OR
103672031906951053623947441426514013084516767552219487151306210059006889609014612268034793945656305588603952925576709915679174156682928486219835893428182536652469099063223463008816014180182453133593899587075484130932570201493364804764920076880814392591950513840246864398759993143762298801236664695486126949517
*
243034770441000161126465146022739160410548547609503313622989361907329958650766602167702851722442843650127501854315620459398004439036301253662401358684009829459735524825756900968245233284476538643092084054461139999369593406028547097675253570507367414788307418470447697302794934211368999328501932309380268452820
=
25195908475657893494027183240048398571429282126204032027777137836043662020707595556264018525880784406918290641249515082189298559149176184502808489120072844992687392807287776735971418347270261896375014971824691165077613379859095700097330459748808428401797429100642458691817195118746121515172654632282216869987351136698979061355037939898594525507081434979124047013628823559769184684573478985618011864902497861390989014844844362845349008351828710467630695685634603600782089364195343946529373990689987491961025790041201276592676379385175977542000411539890036692244455383333187236534787068838403688223820177619935836287940
AND
160566559884233726650546447809140208245454254331048557333174632052519210507323250271792956262309668239183736106871075377479646207322834007579407963656384883208946107211302017794468125764038293541827340635892138959103263333422298544049962868942319668575518784768847057679039275999685961201047236292788173557525
* 156918778691053702101098219916929907095707992706905177559929437154331963727096373732841065560273170416700664715274656923963499842118665928897228995739228119959375434923971858101152147245130724275869544346084032277230907854980268987985209737247789756740388316193980799845678656944921255048040421014728671823543
=
25195908475657893494027183240048398571429282126204032027777137836043662020707595556264018525880784406918290641249515082189298559149176184502808489120072844992687392807287776735971418347270261896375014971824691165077613379859095700097330459748808428401797429100642458691817195118746121515172654632282216869987376442144809790263733523494772552609177243296914361150584677599102340273336517163017862080932994710827908674546061640403490009778309444907472298196352369688222426021819717480568367224285826392796847861339605137071054629721605627016961934672514962553877988237073859695017066384725959609349517316336115359811075
A linear algorithm able to factorize numbers of unspecified size (ie: 8192 bits or 2472 decimal digits) will be available on Bejaia University web site.
Computation carried out by Behnous Salah (Algeria)
As we will note it the logarithms play a big role in an operation of factorization. The great numbers do not offer only the advantage of solving a expensive problem with all the mathematicians, they invite us to question us on the laws which govern our universe, medicine, the nanotechs, inter alia, and various opportunities deliver to us on the technological change of information: compression ratios higher than 1 per 10000, more compact programs, transport of bulky data, etc
Thus, it will be permissible for us to store 10.000 films with the DivX format on a support CD and, associated with crypto-compression, to make it possible the world to exchange quantities of information without Big Brother not being able to decipher the few impulses collected.
In addition to the transfer of information bulky, it will be possible to develop new chips of encoding making it possible to ensure the whole safety of the Chinese military communications.
All the tests were carried out on 150 numbers of 1024 bits whose factors are known. Calculations presented below were carried out using a PC Notebook ACER ASPIRES 5920G equipped with a processor Core Duo T7300. The first tests related to a study of the influence of the weight of the base on the speed of the computers and allowed me to reconstitute the first 156 figures in 6 hours.
Thereafter, the rebuilding of the first 170 digits took place in a few seconds.
Example 1: Extract of tables resulting from the basic Algorithm of the factors ©
1.0035695081046852201152666761291779998530643488631872388340107793979864498017825579908660108063465878637050512874197975356538150509791624097937134422495305 10e+154
*
1.3458600503026249556854391675989495759324687551055421000988051942571357566785824617386316197964812400422231492964572095945530111067356858171563935508338806 10e+154
=
135066410865995223349603216278805969938881475605667027524485143851526510604859533833940287150571909441798207282164471551373680419703964191743046496589274242997185495044902494354468514498718464015533419752872326052737902428260293725679867905230916132597008114369547166434146073730468931445127020217937884305830
Example 2: Extract of tables resulting from a formula
10316818314917763325702151276313025303946768901631629013679495438858798953997978991824010769850008487294313392162565425193401875193212097570602920613038011
*
13091866769689435490760893105301876025091350111093293010265880610926442105302611591815350286126670784862076800863403566069087711519681771450475969485570443
=
135066410865995223349603216278805969938881475605667027524485143851526510604859533833940287150571909441798207282164471551373680419703964191743046496589274256284791009980155226485382948738956525917141673045692979002887401859301436547460803919706901566161070455452115171855253348177425634502736978224357577108873
The two examples which are presented to you (Example 1 < RSA1024 < Exemple 2) aim at showing that a number can be reconstituted from left to right according to the weight of the digits (Factors Magnitude Algorithm © describes in the Algorithmes chapter).
As we will discover it in the next chapters, it is possible to rebuild a number from left to right, from right to left, to divide this last into several portions and to reconstitute each one of them from left to right and vice versa. The algorithm describes in question could be adapted of structure out of Wallace's tree in order to accelerate the computing speed.
RSA1024:
135066410865995223349603216278805969938881475605667027524485143851526510604859533833940287150571909441798207282164471551373680419703964191743046496589274256239341020864383202110372958725762358509643110564073501508187510676594629205563685529475213500852879416377328533906109750544334999811150056977236890927563
The results presented in next page were obtained using the same computer and required only a few seconds. A formula is thus possible by an elimination of the residues. That makes it possible to show that the security of algorithm RSA is by no means dependant on the nature or unspecified property of a number (Prime or not).
AFTER TEST OF FORMULA 1: to see chapter Algorithms
1.050788840365072685950352450587047798144934746687995398404115927062658409146104634405124999120263716291629060853699170754696535656431200243664334363835601044734153757066070668175087097633853162381165628665739466431573704611593532659525473834774653833270054346313155441028079965034601318673086077678131315431331504540481356357123977 10e+154
*
1.285381093494193091377241869898479371149607913660777195854400617119003267924312932545198632604892222981270558035126104991868488558113630335497950206940640721248987282347468445508826291927816988328939232913225233553606813790516037914562107477769308489401201737122827642993768526231967780881271596440010975647935645918602438264828495 10e+154
=
1.350664108659952233496032162788059699388814756056670275244851438515265106048595338339402871505719094417982072821644715513736804197039641917430464965892742562393410208643832021103729587257623585096431105640735015081875106765946292055636855294752135008528794163773285339061097505443349998111500569772368909275630000000000000000000466 10e+308
AFTER TEST OF FORMULA 2: see chapter Algorithms
1.0046474111793196477281392153465338694873306095899242918222857249750057273166141409565831411015348561096814902049911905165932505993252032096002254686961257748522176591417844332696630590871648168108665587527485705265134171790498836928350768206450033077347902641728132875925050697090918156986419488976261777082475680132200848060955473 10e+154
*
1.3444160544588035774178934088252278366563098442918880224331406055466905348866747070660101661501032736103644434552532492358003467109134361105364260927149650510776957958453910771574950434465626504775680044730480121691970201754716102375466972069803074585515362365192257360628005577221043657252566312130020518078305097906428784585578538 10e+154
=
1.3506641086599522334960321627880596993888147560566702752448514385152651060485953383394028715057190944179820728216447155137368041970396419174304649658927425623934102086438320211037295872576235850964311056407350150818751067659462920556368552947521350085287941637732853390610975054433499981115005697723689092756299999999999999999997118 10e+308
To factorize is thus summarized to solve a linear function. As it will be shown through the various chapters, the choice of the base of the logarithm influences the linearity and the speed of the computers (simple base or multiple bases).
Note: Neural networks can contribute in an important way to various operations of factorization.
In the same way for RSA2048 : Example 1 < RSA2048 < Example 2 (Computation required only a few seconds).
25195908475657893494027183240048398571429282126204032027777137836043662020707595556264018525880784406918290641249515082189298559149176184502808489120072844992687392807287776735971418347270261896375014971824691165077613379859095700097330459748808428401797429100642458691817195118746121515172654632282216869987549182422433637259085141865462043576798423387184774447920739934236584823824281198163815010674810451660377306056201619676256133844143603833904414952634432190114657544454178424020924616515723350778707749817125772467962926386356373289912154831438167899885040445364023527381951378636564391212010397122822120720357
Example 1:
147964689457797841047066565046278313839088189432388123095307129102409188489470471937032843570795143971891390654789545942159070973008367696524422513142471408432317328058634623998409713802920982540347106658317859297945112627938898934649650078144847454212434920322214762866323864726309077020353636708858369808155
* 170283251821673402385829600686247358732092030186896729440025731250263704572435310252050374757369996831328058037941316712068111191419969084691136376788694541256036152089536478905157026282118450688603498493321129210961511331193332223475832841088033987577327022483936750144526903503305810547115713642582719119817
= 25195908475657893494027183240048398571429282126204032027777137836043662020707595556264018525880784406918290641249515082189298559149176184502808489120072844992687392807287776735971418347270261896375014971824691165077613379859095700097330459748808428401797429100642458691817195118746121515172654632282216869987548267513273542921999454242887605445293850478033108327398246445049736303167909492829147712370879179892408290955218915970494672718456012212312319520831873609108292812428079343250867928075555567689759209545120560317743941145165347731246489211806062916188769546109965585941791679450193420530386292031568748707635
Example 2:
150853796982129550201437469508437639976684780987005809019824856161943067403356756860335785620017699895632544258248038273135044955333278368189479798094606826964478949885940079972720435608963255564041650674059116030317615470244140977674762158336451573466870061470218126368888221427382487146861252104398234464214
*
167022037096239960225921182033334794940667724353681964121043761715885664479605519236619077817857383695123246792893950303090420258925005739113309222476575787910955363454931873944596386559127258691612529044559449873161611426000784608401569114149584013716438501889077768941096310269110022129183980985707437226987
=
25195908475657893494027183240048398571429282126204032027777137836043662020707595556264018525880784406918290641249515082189298559149176184502808489120072844992687392807287776735971418347270261896375014971824691165077613379859095700097330459748808428401797429100642458691817195118746121515172654632282216869987715459349804152216735959217661660883794205134612666280728018168381530670418289858696786735777237093998766696820718409140780238349358207362920229181728918166633643463624531280279373796751645138057360339384757645476959980899153222199232809378427883272550975803398808599662419750643202210167244186492205846543218
Example of residue obtained after test of formula 1: MP > 2000 digits
1.50376664007301027561914543604940246959761239266141098526167695946250722979226462286013447038404037452462798341791377500612178280165661285109077520633478184507307913569697329157697574286269614769906407044616350683373818897956197392400393574968666170509512194663928805550205482179553873471344335350716268646564800049458979836675509271760927776951900439176086858070623525907032877636083257271260588439353017337883268378183831144098474592915364737338249209840549210737284829048116482385595632622627594290124697958599709475583962806979200659669428568493745617051892486632158929956279682541772173040923146290107010591743292148625629278232548723537406843582447820516494972331809205712974448923604433953736151342644093914645203162970555601073216772341892279218703713379031729547159600221369315081409413067368423927520647296457966472563677809268901073916859739121709832626576991962970383146172784589008670897784373648757388426267621031534721442660303889141148204158447778441680793610336884153316148202327793208434070515753528345117499865758335264356367628202151027090939195597172518785534463723063970617572317593045 .....10e+308
*
1.675519844916535177107010615481407363605811030154897022603153334303302595844389170186936251356982286930931475173272775708334831147782225031629417123478004451091227876990830256504880055817075675754992571332845655134119382271661982171016268299979570759369618729379189190077393463010984206530393282864002174463508135226394606166468257899250079467807475061329315603230196690645676640371928623100754387438493452069575686802531479790622881768813053444163629912985047650188684197627774685661394917317144460003529125451624533396432728181703858131046961990840485388053832935448030330226110824105412071619025386547689903154094425511303928948031323476337300322950106502319161214380228615876686424759626301167477666459465412266955521544270309817413153619618364298112181992978829881464764866414048730900699300198708268899306600541466602949642078893630295523399300505186338587295818062350119599262190857628542132128787864330861169765621997181146863668929943538082356468732541361736248536719049499788736208773247068493981361724805211238448875332115545484873521784634910150965328663594934632295795949930079634330993042880259 .....10e+308
=
2.5195908475657893494027183240048398571429282126204032027777137836043662020707595556264018525880784406918290641249515082189298559149176184502808489120072844992687392807287776735971418347270261896375014971824691165077613379859095700097330459748808428401797429100642458691817195118746121515172654632282216869987549182422433637259085141865462043576798423387184774447920739934236584823824281198163815010674810451660377306056201619676256133844143603833904414952634432190114657544454178424020924616515723350778707749817125772467962926386356373289912154831438167899885040445364023527381951378636564391212010397122822120720357000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000004280876010504929214591364178746797793761497072666091502664133502074811540207737556980431596543709625079152807689750053031631040732583363899826948305353985673524527530343316568727141547571787361488867105609561119571208125418904385336196515239638671049168247466201984807694872366943361231569787238796912658708112545746422293683367352779458209903774405574295307230700320270636967758297289767535173529118478801239207276020824258115393738441719572225802921396612296266633461169849532428819258886869718167585038024549542163652910129290665829918655794892148022618817686610290387319786927224661413950943106959431062734502696819237336602742235291187950271783712516506154086461878180720693237232330545424172526345608767730896973439245531469955627554394732305114978098667071158136132747757626322517619084616337363800391029759905747185650500813238336568937365908388266535929727569640940236077358195408336616776202826867475157540059333503770987 .....10e+616
Thus, it is not difficult to determine the intervals in which are located each factor of RSA2048 (Extract of the matrix of the high-orders digit).
25195908475657893494027183240048398571429282126204032027777137836043662020707595556264018525880784406918290641249515082189298559149176184502808489120072844992687392807287776735971418347270261896375014971824691165077613379859095700097330459748808428401797429100642458691817195118746121515172654632282216869987549182422433637259085141865462043576798423387184774447920739934236584823824281198163815010674810451660377306056201619676256133844143603833904414952634432190114657544454178424020924616515723350778707749817125772467962926386356373289912154831438167899885040445364023527381951378636564391212010397122822120720357
Factor 1 is higher than:
103672031906951053623947441426514013084516767552219487151306210059006889609014612268034793945656305588603952925576709915679174156682928486219835893428182536652469099063223463008816014180182453133593899587075484130932570201493364804764920076880814392591950513840246864398759993143762298801236664695486126949517
And lower than:
160566559884233726650546447809140208245454254331048557333174632052519210507323250271792956262309668239183736106871075377479646207322834007579407963656384883208946107211302017794468125764038293541827340635892138959103263333422298544049962868942319668575518784768847057679039275999685961201047236292788173557525
Factor 2 is higher than:
156918778691053702101098219916929907095707992706905177559929437154331963727096373732841065560273170416700664715274656923963499842118665928897228995739228119959375434923971858101152147245130724275869544346084032277230907854980268987985209737247789756740388316193980799845678656944921255048040421014728671823543
And lower than:
243034770441000161126465146022739160410548547609503313622989361907329958650766602167702851722442843650127501854315620459398004439036301253662401358684009829459735524825756900968245233284476538643092084054461139999369593406028547097675253570507367414788307418470447697302794934211368999328501932309380268452820
OR
103672031906951053623947441426514013084516767552219487151306210059006889609014612268034793945656305588603952925576709915679174156682928486219835893428182536652469099063223463008816014180182453133593899587075484130932570201493364804764920076880814392591950513840246864398759993143762298801236664695486126949517
*
243034770441000161126465146022739160410548547609503313622989361907329958650766602167702851722442843650127501854315620459398004439036301253662401358684009829459735524825756900968245233284476538643092084054461139999369593406028547097675253570507367414788307418470447697302794934211368999328501932309380268452820
=
25195908475657893494027183240048398571429282126204032027777137836043662020707595556264018525880784406918290641249515082189298559149176184502808489120072844992687392807287776735971418347270261896375014971824691165077613379859095700097330459748808428401797429100642458691817195118746121515172654632282216869987351136698979061355037939898594525507081434979124047013628823559769184684573478985618011864902497861390989014844844362845349008351828710467630695685634603600782089364195343946529373990689987491961025790041201276592676379385175977542000411539890036692244455383333187236534787068838403688223820177619935836287940
AND
160566559884233726650546447809140208245454254331048557333174632052519210507323250271792956262309668239183736106871075377479646207322834007579407963656384883208946107211302017794468125764038293541827340635892138959103263333422298544049962868942319668575518784768847057679039275999685961201047236292788173557525
* 156918778691053702101098219916929907095707992706905177559929437154331963727096373732841065560273170416700664715274656923963499842118665928897228995739228119959375434923971858101152147245130724275869544346084032277230907854980268987985209737247789756740388316193980799845678656944921255048040421014728671823543
=
25195908475657893494027183240048398571429282126204032027777137836043662020707595556264018525880784406918290641249515082189298559149176184502808489120072844992687392807287776735971418347270261896375014971824691165077613379859095700097330459748808428401797429100642458691817195118746121515172654632282216869987376442144809790263733523494772552609177243296914361150584677599102340273336517163017862080932994710827908674546061640403490009778309444907472298196352369688222426021819717480568367224285826392796847861339605137071054629721605627016961934672514962553877988237073859695017066384725959609349517316336115359811075
A linear algorithm able to factorize numbers of unspecified size (ie: 8192 bits or 2472 decimal digits) will be available on Bejaia University web site.
Computation carried out by Behnous Salah (Algeria)
Sécurité ???
de
Rensk
, posté le 08 janvier 2010 à 17h55
Ce ne sont pas les seuls (les hackers) qui travaillent sur les failles de sécurité… Une Uni à Lausanne par exemple :
Une équipe de scientifiques parmi lesquels des chercheurs de l'EPFL sont parvenus à "casser" une clé de sécurité de 768 bits sur Internet, battant ainsi un record mondial.
Une équipe de scientifiques parmi lesquels des chercheurs de l'EPFL sont parvenus à "casser" une clé de sécurité de 768 bits sur Internet, battant ainsi un record mondial.
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