Ciphertexts and Parameters for Assignment 5

RSA Problems

Ciphertext for Programming Problem 1: Short message, small exponent

BOPsNWUf4Wlq0x7slBtDBKBAm8/7DZipepU3kklFB2GcurrqQNuouHpxocau3D5otveYhBw7z2AbETcKMuMkWZdToWSo92mK+UhNeP8wXNqVW7I7Fiy/

Modulus for Programming Problem 1

89925312925763822584710378409033190578053125728910169871227932983692156412020390339531051155939673506480017767823980121411205241896041063847997991270201142150794495706134903691987753153769920552199651886672073876514247298569925380985174185832099311517867889120692301373911817723374815064908214018503193857221

The three ciphertexts for Problem 2-Small Exponent


PBq5gXUhUHA9odbER2Oow3aBRX5VzEPPRCPdcFPZisJSDtoDQtCGiDdcD4q5qNWtA7dMRZxktHzO1kQy1HNmgg6jjUnxuXPIihJgTG4rAQaAFVJrj9THVoaNb+QxovCU61c7N49H+tekr6xyGyGSok6wNnLZtE0GQd8p3zbyIAg=


a11Wynb/5BbzR2+gfZ5vgyJvlk0VHAUP08F2tvEZKCsS4Q0zaHok9FBf3QSJxn7X+e9+bADoV0aycZpXh/8hchNE5jER156vamjQm/9cmLwVcQeK/IFJOOmvuFEWYwOg3L8r2Jsii6cn/XrStNZ4JypnOhzbyhR5Jd8hsC2pPIo=

HlPEAzFjvc1ipxHIaig2o6WwpHfsHmIuS07lM0uKmY0VzcxyiOyB8Q0f4yjo8mu5yPYteO5Kiz5W3sk2j/d5ClmU7yUOVRxm5Q8LXymjpkhLK/I+cxO5P3WRjXF6tUiS/7cz+Koox/r1zC0W4BdfCzr3LSjM/khFHyRyxsmW9Ec=

The three associated moduli

116352696909960426025864851693810318405618117771451092066454825684677043175680039111752172705287741166921435658711582887107841565748470707915492808066623281928343866378761016071751094691691153177015920723800541267192488702040046723176890027878282090184778778793686252497241689941158021804171328580092708776333

113159069239053057823530426012762733579195323934158077138440185385412667833688850511263203419882218256057634130377557866771685834979020529147973323837633935391154851580497106210797073916815264166772985134768913514820393183935763151959349642321950865577799563213986693573189083682991881468336071564883866833467

84645091220488904665996303582605230466879862527671219768265030555132951506114250139685118956675414529710122137796339176130460114790081203074349445462593477716603703644138088562638660083014885373629701703614641595720381677601897924624948376232277832479665238039958287396790532376148968417689500200999461168369

Problem 3: Common Modulus Attack.

Modulus

118655596447903224963869613053944974689306948978385022351313547236325408711597515968013120482999812623684614237188826586513936280546323473924322265897469916282911780567243884859836121621708694140679468147474220271417145483116948895892297437839699778114403528270801117190611396069302409336194794071895031049811

Decryption Exponent for e=5

23731119289580644992773922610788994937861389795677004470262709447265081742319503193602624096599962524736922847437765317302787256109264694784864453179493978848181776281125630457673065339633910037899644296946114786385008468034547208885433370715974640426127989454209067113013826578800440508863151210816724921125

Ciphertext for e=3

LbJFbZa7eoMEQE8uPICTjzxFqvtM2qLPf6OSNOR6bgIJ8IlSWMMIOL4s7qevd77GRtLTz6EgC38EVjbp+ZHKJ5inX582MlxjD6WYcqGEYOnvCFGBpeFJnkAvhFIWxNyIx1tk1xxQgTHU8wMHjq/rMCl6USuZcSH4L1bzUMmgfZE=

Problem 4: Moduli with a common factor, e=65537

First modulus

87750187518907655534583445808737942078016029371855217057442341331127022016930461105786023716013285380470222803872626192434912740863485532564125627646878636545449869643527771922181597178447982975143657375859594541373428795038041796818858805812228886812351199020336314262507362189851970680226889619203804537151

Second modulus

59077605606399909603607705484000546044333045357566473814158491087439387780574866766800852465743470772146755309189078604396507686696592563062056700875467732286553829707195406383141965288479916793429869646143662227281782900822010619445408818002981548245734527538573941174294649831309213962935858200869524073603

First ciphertext

Ur/BIau7ZZBdwxD8P3xDJFJGMfkJDXNU5rbY7GlvlRkGae4NEMo3pMq9r8Jk2akGSj47SZ00L+eTmeMIIfis3RoG7jjBdj03p5lLtgrLwnjP0lzr31fasl5+NVZIvmnoEt56Figi54lIAXEj4ig06MHFG2KfotLYJTnwabangS4=

Second ciphertext

CPEXorDgegEqM6UttzFLaccAN/t4QB1FTDS+NL3TSofQlq3Rs/BebbNn4Qj/Vo4FmTwV3P0+n+hlIhjXzOgEgdgV3BmiBE3rIBHqUc+q0FoVvWJU1+jvFpEeellYZMX8vG7O9us5JKfDAHjPaHWZSwv++BSX4rh+5O01flxzlJA=

Problem 5: Short Message, e=65537

Modulus

104267313539010410259697196441509577894896177181353222939098975044658256653731229369696658803005865075730776171497005390040729021346385892644721558032556950267328480157757202775565554421465561098972037171123794802541382258202303916754661689619425811225128735978214662249095628369305188282273814273882601469489

Ciphertext

j/pGAvf886IqKc4IN6TNPTSymwReGjUxUjB7F7r2aEk9bIuZPuRezm3wGCYBifv7u7kDcLQ9k4f/i5luqD/oFGS8PaJljrftLmlpa6hlUm8S/dU8h1tFW884ddtAoGTfZbN5vN4hNcSBGWPQHNzghDgwzNw/4IrqjGL81DckUdY=

ElGamal (Diffie-Hellman) Problems

Alice's Key Information

Prime Modulus

p=191147927718986609689229466631454649812986246276667354864188503638807260703436799058776201365135161278134258296128109200046702912984568752800330221777752773957404540495707852046983

Generator

g=5

Public power

g^x=176478319826764259370406117740489882944142268114222243573886354279989450112247437716236796057251798300509450763347865746885560883563075519833320667906000345397226327059751213369961

Secret Exponent


x=42694797205671621659845608467948077104282354898632405210027867058530843815065930986742716022222447350595400603633273172816767784236961837688169657044396569579700949515830214254992

Problem 6: Bob's First Message to Alice

First Component

73982478796308483406582889587923018499575337266536017447507799702797406257043632101045569763590982806403627704785985032506296784648293661856246199184245278019913797261546316759270

Second component

1227561673735205443986782574414500194775280963876704725208507831364630528829422611287956320336912905023628854115065478249082243473610928313596901712034514819305660036543382454852

Problem 7: 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 8: 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 that Eve is able to find

138670566126823584879625861326333326312363943825621039220215583346153783336272559955521970357301302912046310782908659450758549108092918331352215751346054755216673005939933186397777

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

112018886720018236580229932176683955946063514397085867696250318378121351302079624330821244744748925197792097406122146093507280201522804485024833199924734248052247065779216659451112