Level - Hard
Description:
[rsa4.txt]
p1 = 177511594509894023662530054533955528832351144228260971892266194164923826324164037548822690203261179955180294705980244671526172824416596077425676394216077098790159989463576993609910356482334757318277053948213771265250744095530251047776831849580814137335085935564909657740080235796277866916967979641132008420797
q1 = 141990234651907173281229610691964462620483885241337739424485415398906507801727107095892937218463053452882902118836801148586780915135326945813037568830777543305414546734469000367895951494322167037998086132122540084224805984599083137234527325031095951958077807553870792586755117189401387717937506623415204682013
p2 = 147891546902283079479020038978501155491976849905915195300105660032040161983374061995258103731629996151394494765563629375444840842572126323082165215428198693765257146747156445511048384598229870826406399200672206570442559885840660169255586210231378135933575282323425595058757409983050934367057777158301477823037
q2 = 119891317365940250126124802379223074064800022239783382623184268255212340570282555937088773325249707977597789414029101394887940067638656169271662037715774739879450242737833382102027915181096149902698830515285545766637900113024213341496390740916807972483974149995409942270819468508313708660518295749022662948167
p3 = 175269909528279729088054136514482269464968453452038573648264046577285747782198679765138942274820404738544835558950325626205276019886629675376140873077602909714625335246342743473563997929189939896397585648918952185990772299212310881635422288079031626849255334862313335388170340067161446764254399910560122570543
q3 = 135185050394274690877464056556141855729087007972999156477744877698690967858984524027521857566325438763430596797726797548562898502170504958757257786295381340086753181113707049960117978493628521636179508665791534607985306013295743497057772408343116097551729309473394750347256048496459288718636993457860734833227
Hastad's broadcast attack applies when an identical message is sent out >= e times. In this case, e was 3, and the same message was put out 3 times. Using the Chinese Remainder Theorem, the plaintext message can be deciphered (see solve.py).
Flag - byuctf{hastad_broadcast_attack_is_why_e_needs_to_be_very_large}