Ciphertexts and Parameters for Assignment 5

Alice's Key Information

Prime Modulus

p=191147927718986609689229466631454649812986246276667354864188503638807260703436799058776201365135161278134258296128109200046702912984568752800330221777752773957404540495707852046983

Generator

g=5

Public power

g^x=176478319826764259370406117740489882944142268114222243573886354279989450112247437716236796057251798300509450763347865746885560883563075519833320667906000345397226327059751213369961

Secret Exponent


x=42694797205671621659845608467948077104282354898632405210027867058530843815065930986742716022222447350595400603633273172816767784236961837688169657044396569579700949515830214254992

Problem 2: Bob's First Message to Alice

First Component

73982478796308483406582889587923018499575337266536017447507799702797406257043632101045569763590982806403627704785985032506296784648293661856246199184245278019913797261546316759270

Second component

1227561673735205443986782574414500194775280963876704725208507831364630528829422611287956320336912905023628854115065478249082243473610928313596901712034514819305660036543382454852

Problem 3: Bob Foolishly Reuses a Value in Two Messages

First component of both ciphertexts

104862672745740711919811315922065122010281934991422240638097533405207971405689057652673577043484488015740722326384001808611695005135028713487234715202873484670021923322009761545457

Second component of first of the two messages

17606878671981551311137298337848994393797765223509173646178261989274226953505667592410786573428076963287971811161509360601971410344413313700739795932040261074709506491861567699546

Second component of the second of the two messages

116115839773157782821329377087409766815814624668492668098672866213651171163182813304753241741593566110843721045751605192482170477996370202802973966889697676265503034822908949368607

Problem 4: Eve Knows a Discrete Log

Here is the number whose mod p log at base 5 was found, and also the first component of the ciphertext...

68188080109582330879868861330998506151774854600403700625797299927558995162740321112260973638619757922646242302104885437536745080299248852065080008358309735875192480724496530325927

...and here is the logarithm which Eve is able to find

138670566126823584879625861326333326312363943825621039220215583346153783336272559955521970357301302912046310782908659450758549108092918331352215751346054755216673005939933186397777

..and here is the second component of the intercepted ciphertext

112018886720018236580229932176683955946063514397085867696250318378121351302079624330821244744748925197792097406122146093507280201522804485024833199924734248052247065779216659451112