# RSA and El Gamal Public Keys for Cryptology I

I have now added El Gamal keys for those who have submitted them.

Please continue to inform me of any errors!

Any student may submit a new key at any time. Any student who can break another student's key should inform me (and be able to show me how they did it).

## Girault Protocol

n := 117362022886962066410845266469052466544075833684945829581761298846344425671722652582856114930051680392738007025143613

e := 32572895698750165108650217

alpha := 116279989102598462436005640568726075050856622302062743925424632813610977202603746947195589484848827464612889775643037

Each of you needs to get a public key from me for the Girault protocol. To do this, choose an ID number ID(U) for yourself (say 10 digits) choose a secret exponent a_U (keep this to yourself) and send me b_U = alpha^a mod n, I will post your public value p_U and your ID.

• Shepperd: ID:=3747019416;

pU := 51103719419925022268001990052828686737228853400289861355274461437839557114910242247180097077479402923670183213511046

• N. Pham: ID:=5768431789

pU := 106909548125375171654195088170545836333234761099035354263026484425295349921142435165809471346394027217983589440307678

• K Sarkar: UID := 1523112129

pU := 8731010780846616049620807549634181416998322612542250322173134315360224209192298517747470600063811579513739232634755

• W. Zhang: UID := 6666666666;

pU := 72448997614218747412244051798625413133082851267655832924250674754913788291949859076706953682482660087933543630246305;

• K Theobald: UID := 2805607434;

pU := 31817965562241827380270884303168249035543532073671944378349887720690028768120816187453505594455678995443332317445557;

• Li Ren: UID := 3748246244858548757435;

pU := 37849622034095532293384691761111973170809213721647876401892092797047965361039843310666273048716579588917415358293302;

## MTI Protocol

Use the following prime p and primitive element alpha:

p:=59287651265891759018758967186157862617896289072863872690687876398073086980639083687649376832778268036789367089278986937686877699;

alpha := 9578917521075897581

The next step is for each student to choose an exponent a secretly and send b = alpha^a mod p to me to be posted publicly in this space.

• Zhang: b := 13524028216771142451065125504585220439685035411368686253217547764793086913013665808875189646459782727507944307150391783366960840;
• Shepperd: b:=35824228692123971244545573538968751087236073094448892313746284251109574302539084372212003978981910124904826023448111706553419561;
• Li Ren: b:=57791064740632032706728840698504108386178438938352429458015678811192582557688758539504912861525277197233664487508383523700281024;
• Randall Holmes: b:= 48234743120496370173398816433330281668302320826789491635152159529582501822079918646719194407347439872855903014713089136969571626;
• N. Pham: b:=35064621467133093647666855255927386411713206525037508527090504075267143772656977395885766442642836800483356228788820205486608152;
• K. Theobald: b := 11056171217089890141237222467503504811736691550546216035775433100551040077840645235848972625626393094118320692742898862381623628
• K. Sarkar: b:=42215941579479197846767384472145603119584187220691411573370251855860930227195757112432842786183013473780993991083098804810969227

## RSA and El Gamal Public Keys

I'm still expecting exchanges of El Gamal messages...

• Kaushik Sarkar sarkark@baron.boisestate.edu:

RSA key:

e := 571

N:=220354130013701314270583524275316998795291374510675103200935386441440286673655013316820299325010218313289721089075783786462826844613759723627041173641521275514855783537720513244917168891438894896583266738330875106070315636349;

El Gamal Key:

P := 244242642564291678987676788723478787876757674685486546563563375375337375375375375375375375365375336535375375374912444423423444444444444444234444456181;

alpha := 132323212329637682736803496787367534533276502659277;

beta := 487231898236050875017335945406693815107391943051645824371288327016575105663535194489765002970004303432494851854743622858285346069744169746658848442295;

• Li Ren lren@baron.boisestate.edu:

RSA key:

N := 383165244669547479883516514481564749294982300417989537228621671081118659422089511088090905809973954763757267153255528579590637568485614085665563506788299089376810113714915265833445009160537654026828544130746621

e := 79

El Gamal Key:

p:=2589715687968069600011099097509088983;

alpha :=33947473949243774243523623861848463686;

beta :=114207883704225845800803699416522452;

• Nhan Pham npham@baron.boisestate.edu

RSA key:

e:= 453

N := 15233345415005179066337563203356147068710700859929425788524478879135593900287229753283909088731614177355920852981599608677411434598155638076057652560794981762883833092592137480100506816483840242572677;

El Gamal key:

alpha:=124;

beta:=27444602282354702216537377774425168962564300471072217808681284292280433964647171885122650104387748914071850418224870866711491374116051720046027204254681640712230;

p := 38289228209900896169259300945983022437554490741296629623342778147682683054396306009619251813682235907042118253578878565336618411407698658877052366733551025509603;

• Kristine Theobald ktheobal@baron.boisestate.edu:

RSA key:

N := 3680174353598791240614133251959357156227672596036658562367417070292122738361521733424834476625055829;

e := 54654652147;

El Gamal key:

p:=4587916516516516849879846546456131321654684799465465132132465498798465415468804423;

alpha := 54654654612654987989

beta := 43096512471661589511814515955758095405895847761202703492\ 77122605966956184020073834

• Jon Fenn jfenn@baron.boisestate.edu: (if I've posted the wrong version, please tell me).

RSA key:

N:= 3032627867705576768403152843610944027145279615865730279797432274820606505664356678986111326216812469130121543534272199259885112016157844899707242579377962274026104995120772583814343186664042130282732169567966917018946794746885831382611249526039225103279194039570167843416245536734437801798323410446414628875941835044949459885994211838617198983213799923977049473044514657843206075667869750392394913423

e:= 14176753

• Wei Zhang wzhang@baron.boisestate.edu:

RSA key:

the public key is:

e:= 174887470365515213

N:= 7068399054598314480507675356110917912695311563463304716087747909403657061826219667344776881849462776545265788315130246573106732482050841305321738798964169136881268798009642061953065785741037581703415470207764553866007145193262066288111069049996251634101450019867491537550342056263089585370107245804064034140330151633748600615487463279342022909029799528201356712924969944327091586607681593960813494158592165726695658796777181800362769837615421842232114755203466789016411093421555273641303724279

El Gamal key:

p := 4759775887759568686648988686919171717719373751919919999999998864086197070818870957317757113067096906670909070913779579751066709137959746648588906965808477080939 ;

alpha := 97653555563476776666666666637682736803496787363276502659277;

beta := 2966933188201715769735691267223649664288273769075507557874683492676255234017342707523059916377715251801109363919223205676976283665419516490276229016832348619422 ;

• Jonathan Williams jwilliam@baron.boisestate.edu:

RSA key:

N:=24197236474023414893264161714715506609171001931395415005573599990483803670679168555471548070501304000183316469223633985952469975203649075908323845350379713362189976181118887986691309800995634089123091

e:=47

El Gamal Key:

p:=7813456112218514379304323579144215163535785123131453178033014528447;

alpha:=98748937948789011329148791239;

beta:=2755947232323072156758081913602490530812819323249764817765248695335;

• Jason Shepperd jshepper@baron.boisestate.edu:

RSA key:

N:=23432204100224173813412043144310746881783668889694327971429508949542088159284886137272287412608958200547604577769268914821103885211223720044593917435119378532688256672300802000563923527290773125819931;

e:=9053675621;

El Gamal key:

p := 58113437925619123712357286396144796112995713780295780351783414367;

alpha := 395837294875624892485619203894189723487623498723498523987234876125;

beta := 57988259849880591253435680597953569528307313472486098962175455342;

• Jared Hopkins jahopkin@baron.boisestate.edu:

RSA key:

N:=1856099719865917915693338982214281440175115973412172264015191272311046526788529898949657174365393006308085898418872014411731911563944172626362905472666586133388157737770264234671538305276424922213200937848749389701967162546929309637405322204036635822150091; e:=981997736892577;

El Gamal key:

p:=11975139719691967896933097918997487150910969515138688717951975139719691966996879687749152710910969515138688716444444666953178396016879697754247817504367;

alpha:=863487643876459090688677;

beta:=9134854409245306586633771498520336878536428953025147589348587746206503991033550740222902286916791733775370050589472291201731367431138427720553635214221;