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I have a Crypto assignment, trying different ideas for couple hours landed me nowhere. Supposedly during a Diffie-Hellman key exchange Alice sends bob an encrypted message, the message (cipher) is a large number XORed with the key, We (as sniffer/attacker) have following parameters

Alice : 
A = 957960503740477865499612979799288292279082788682058666143427454603396976995714435704478946030977915114025853816714610085170706057657348243856571774314904068451395018259117003339363154529105539749734853621722859706476015262606587390751976960733494191000395823674358415355778875803193719866529234544468467316561358645583901905380395120833053122330825263060339607548228215379983259574309592403749078271563329954776732460449127958349169887798275776412582343565587731

g = 2

p = 2410312426921032588552076022197566074856950548502459942654116941958108831682612228890093858261341614673227141477904012196503648957050582631942730706805009223062734745341073406696246014589361659774041027169249453200378729434170325843778659198143763193776859869524088940195577346119843545301547043747207749969763750084308926339295559968882457872412993810129130294592999947926365264059284647209730384947211681434464714438488520940127459844288859336526896320919633919

Bob :

B = 720872130619681826724522175108480266747900186063248500957885206489182263493086664815141395808994117691106712356217868879743700420026891797060193009526740433031979860226371717845756100929411189486178116792543051957992807959690784585724734635389258256378408596242222941985025198731054382164547947617594833739534056112202145556230426134219710281333138966897901031828197069509693808501793907180466934782859455682673617835431117327271113044661400126183146597451892644

Alice :

cipher = 327421232546739570358788376618319071226724496311756414828126519923904888855152133241585253190966311281019981779345533668369721441804371622015913493325011909580536781387126547729162684725230955623208862762791680324567166270833967360227520286136228600057308617868908958716473983240720367007532325926750574196002098615696543256992898546982154275933762469991006924040254056416952652977860627241073741649518909861015974113222031842050562668165710983337396704041863869

intial google search showed I have to calculate either of A^b mod p, B^a mod p but these are practically impossible to calculate on my pc and online services, Therefore I'm suspicious of "g" parameter being weak/wired.

Clearly I have no clue what am I doing! any kind of help/POC is appreciated :)

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That particular $p, g$ values are the standard "group 5" DH parameters (see RFC3526) - there are considered quite strong (even if current fashion is to prefer groups just a bit stronger); attempting to compute the discrete log will be essentially impossible,

On the other hand, you might want to compare the listed $p$ and $B$ values; you have likely misentered the $B$ value; if you didn't, well, that looks suspicious (and likely impossible if that's supposed to be the value that Bob sent...)

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