Decrypt the ciphertext encrypted by RSA method.

 The encoding for the RSA is as following: 1) divide the plaintext into blocks. 2) each block forms a big number as following: (because all characters are from a 10X10 matrix) find the row and column number from the matrix for the first character and the row number and column number are connected together to form a partial number; find the row and column number from the matrix for the second character, then append the row number and column number to the above number,... for example: This homework.... will be encoded to 527273830072798275... (because T is in row 5 and column 2. Note: the row and column numbers begin from Zero.) 3) encrypt each block using RSA method. 4) Therefore, after your decryption, you need to decode by changing every pair of two numbers (as row number and column number) into a character by looking up the matrix. 5) you can get the ciphertext and matrix 28595220443600602493861284158505136951947525031399288434 8583332019843725719035358849983839773527043582016587146 66494131875652588636818002146640797785842102112664516948 21766978308791263221790991236477530195767134102253299032 2011901812366724852815466394393632330917455268906212193 53780511593259203188425204918488872477401283846868940458 9002524462353371497194637333089717545398571470046542035 67399271610075989668193494413821155272956266004775848861 52244147782063847115711382443808670530254828651119522612 25057637774563543629109780513728226958682951544575410174 31217575966160537869566909766276687083638414331912019448 67134941179545159798913281084561154655966873270252577010 35459253212292336238794442610648542675416266381716091795 7668288731298413756522562260452112742850173913131504257 18480745628847153241937307313533897787560871830128313520 30906439164674530252930115205065868691432849878820863259 61000903274571342140093085620255870692057508182235229968 32299474857653266184541827525031303046430816468360056255 56416442806270589225520834453898315081929224878740785359 23452728066419872208351385396432055614221625189933191439 57617399262639085725683231487022275549230170516356575012 57717667055182700528787373683344750577902684571940548064 64214915462404185999171911607833026260029353668368894453 18768691964254940081053168895143417579180097292444309591 3325352648157122881829775328084235565579724027742781576 55820635056259716311462000643768397941083057069184074595 24056141723947944409563449522899868289154050712414166453 43257550822568835865579206074674999919161144760058787536 8155694341405464452373161743551411594189638874622168022 59182210098509297351852773856270751953007624527209991872 28519142786600036166291504820031094163998598032294920992 64966347957674296431731646654792121745867347321834030503 45528845766863895217443518395898430263653836953199736188 2856106083220625420399304227392938492459656027635367376 12564424882667686905694141162257311673187673395020552391 54816357625731708980552498190676302901326132505536009781 60564692344000820619717312777643296113369786675913181058 64927154726319568061305344153574652059818025393060810181 11477522098129021353110162819847657897508298676436888042 1220849147780401389550201283351361295900611981260390342 19419925240237200949007246202928998839942640031344763543 11244797903104951704959784971177291819345616208041349543 30752104717808879580601701808810065648123907746002953703 14044047026423651442214107059244478265581512619483664716 24564807550432223319181124926128028923111976250669862300 10644881234730037271447107199791291229427575990799215397 15465713882924445853320933523021389781707889511205781399 19870321987104654760202157913523500589113483152729219718 26837526078828499028277768424255638235852346909207619258 48511321922220877688574678996368695025781936515257026278 25424488066140008029616665755020489655936454004648035029 10412242847875630428193362869351404485339331224446887726 48147761606202595457015991018784118774497903428503902080 47926531852796209051957209196831109400408496512983443312 4027817379140408798989279698703450011584855880008309013 67269361983066969667280050798200707813325823158746093005 57798411861576100416253991414898804636404966734816873030 39405518990192570707582782297935303117837267190554990861 65863179345305417238447619063940579041947288273679825305 11217142381083883785942726811544642416337671104048046098 63829174577326499556835672515697850672986476480526843637 56124399920691724575725495594676797136586367640634889435 398723915895759999407628806171621433707957051286467834 4639126249719519155309978324804656888246227236164380475 6) Every row in the ciphertext is an encrypted RSA number. So you need to decrypt the ciphertext row by row. 7) Here is the public key for this RSA system: n = 68102916241556953901301068745501609390192169871097881297 (modulo) b = 36639088738407540894550923202224101809992059348223191165 (public exponent) 8) This problem needs big integer. There are several possibilities: a). use Java which contains BigInteger class. b). use GMP C library which contains operations on big integers and has been installed in pegasus. Here is a simple program to let you test and get familar with the usage of GMP library. Here are the manual link: http://gmplib.org/manual/ and the integer function link: http://gmplib.org/manual/Integer-Functions.html#Integer-Functions c). download Crypto++ Library from http://www.eskimo.com/~weidai/cryptlib.html. following instructions in readme. You may need to play for a while. Crypto++ Library can be run on both Windows and Unix/Linux. d). download LiDIA library from http://www.informatik.tu-darmstadt.de/TI/LiDIA/. LiDIA is only for Unix/Linux. 9) There is a need to add one ZERO before the numbers having odd number of digits. 10) Since there is no factorization function in the above Libraries you need to write your only Pollard p-1 factoring program to find the factor of n in this problem. Note: set B=1500 or lager.