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Dec 12: Crypt-o-Math
Challenge
Crypto? Math? Maybe both?
you remember math classes at school?
hopefully you payed attention - and even if not, there are other ways to solve this challenge.
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-----BEGIN HV16 CHALLENGE-----
m,b,p
260492575707724061121829547730531689268,219331109722881671601619265628380637246,264919855316001119104226076800779561423
177037883108301921298501682022541052670,139010999389216475313896172223515984938,320424365363679773525372180610490277297
201530751445587644733838605908487065258,156283960365344379794603462644218812025,260817421396746284411005790925469586671
243507266865305317073588348849175479231,228672633794460367905186619683512549913,311961837617653522368820984616392093801
235979373536480839808082706396503872744,193357134507240975900584464141934560197,272109227670221371468387040437351965901
230551569853098007600677345727280344755,287930781315318970473254677546577038359,267938315516895485484707051396200706443
243574932572443222972750303823800502163,301120142698243924290763614435454565780,298644815229643145404450351035804160241
227879528304283891530899499744980291425,259647428751561260984852593239590962832,269635859822490692863508746527322139429
193780289185955117334123511554895799539,230518059194860774985531587526031582924,207593226880414101384701594893426311937
195425447990038725090924967791915486200,211074736770197591575170253798012315012,268179617336236355437933191393015865423
182160695615960388203641943769582257756,226052690185182197055109796183513576908,206467790630567275126889799309355179359
270365608703884312725165910007312396490,213419845252996446560398094913250521674,324158008615298179424325819513870548587
201137118708843924452456973486310609161,159816376238003107002192693657105630045,290037217831618223964293971372160917859
173038113384777542289872672569239525188,189558894159177271916644208007912631998,183921485447992361971839173200969564297
203079462849536394511816713024005910404,265255113893859933710071781082768935284,214860441818087898101519465166073705553
175435955454496700514946039667711586185,321302129754052602637931061925096198926,176882035352883165226937995777991718197
200701714682593432395729715130128082931,240366172083509768840032993181552166546,262938198945065824235502495190974734479
299752902236935158362307014205359355636,235711956783855914923056820687273121476,332555996220370247549433065033032955347
215902963387633985679795544753434436743,271635699405692295953353834140161222963,234686602415496986215568540582391915559
205034325176731455396463659428717818520,272071326791294957481838950480920388378,206409649750015144058460651952033121471
186202058515529112089774144624697652752,254056783751113612320599805874190538383,203950808577618100941828939328974427763
287901749499474956286121649902808545796,182193516067311697257425115832952178725,310661715406253093730218700854274682783
188797174721730846063832466557549096934,204289631640363328059573883403131553162,202398097602736311826665715995283701469
173276488624612107075891981111532248427,143340215883386310219352729908142093188,310272112653851647580237588097526878451
300899937001700644581647299928269672025,333680929290782211826332325236347007941,313491113294105066840003438756384124923
179363152345949876980223861387117154037,192660289980311571512766813788452507319,191173487237342005980035033206582186319
274297779066581320003362916911839787292,230968818301666954768423827202499074222,280249595392717543321356899242915413241
173512792712172909456131993539106342879,276670255129140880258696821649524107343,176080436791985260266403840744627297429
217267141898619422837859646397422811530,192415481924499182031594124394175595334,261771203728758901533499406756951694139
m = a * 0x1337 * b % p
a=flag
-----END HV16 CHALLENGE-----
Solution
Seems clear we would need to find a for each set of (m,b,p), since there are 29 such tuples, it is safe to assume each encodes one letter of the flag.
There is surely a direct way to compute this, but my modular arithmetic is a bit rusty, so just going to bruteforce it:
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cts=[[260492575707724061121829547730531689268,219331109722881671601619265628380637246,264919855316001119104226076800779561423],
[177037883108301921298501682022541052670,139010999389216475313896172223515984938,320424365363679773525372180610490277297],
[201530751445587644733838605908487065258,156283960365344379794603462644218812025,260817421396746284411005790925469586671],
[243507266865305317073588348849175479231,228672633794460367905186619683512549913,311961837617653522368820984616392093801],
[235979373536480839808082706396503872744,193357134507240975900584464141934560197,272109227670221371468387040437351965901],
[230551569853098007600677345727280344755,287930781315318970473254677546577038359,267938315516895485484707051396200706443],
[243574932572443222972750303823800502163,301120142698243924290763614435454565780,298644815229643145404450351035804160241],
[227879528304283891530899499744980291425,259647428751561260984852593239590962832,269635859822490692863508746527322139429],
[193780289185955117334123511554895799539,230518059194860774985531587526031582924,207593226880414101384701594893426311937],
[195425447990038725090924967791915486200,211074736770197591575170253798012315012,268179617336236355437933191393015865423],
[182160695615960388203641943769582257756,226052690185182197055109796183513576908,206467790630567275126889799309355179359],
[270365608703884312725165910007312396490,213419845252996446560398094913250521674,324158008615298179424325819513870548587],
[201137118708843924452456973486310609161,159816376238003107002192693657105630045,290037217831618223964293971372160917859],
[173038113384777542289872672569239525188,189558894159177271916644208007912631998,183921485447992361971839173200969564297],
[203079462849536394511816713024005910404,265255113893859933710071781082768935284,214860441818087898101519465166073705553],
[175435955454496700514946039667711586185,321302129754052602637931061925096198926,176882035352883165226937995777991718197],
[200701714682593432395729715130128082931,240366172083509768840032993181552166546,262938198945065824235502495190974734479],
[299752902236935158362307014205359355636,235711956783855914923056820687273121476,332555996220370247549433065033032955347],
[215902963387633985679795544753434436743,271635699405692295953353834140161222963,234686602415496986215568540582391915559],
[205034325176731455396463659428717818520,272071326791294957481838950480920388378,206409649750015144058460651952033121471],
[186202058515529112089774144624697652752,254056783751113612320599805874190538383,203950808577618100941828939328974427763],
[287901749499474956286121649902808545796,182193516067311697257425115832952178725,310661715406253093730218700854274682783],
[188797174721730846063832466557549096934,204289631640363328059573883403131553162,202398097602736311826665715995283701469],
[173276488624612107075891981111532248427,143340215883386310219352729908142093188,310272112653851647580237588097526878451],
[300899937001700644581647299928269672025,333680929290782211826332325236347007941,313491113294105066840003438756384124923],
[179363152345949876980223861387117154037,192660289980311571512766813788452507319,191173487237342005980035033206582186319],
[274297779066581320003362916911839787292,230968818301666954768423827202499074222,280249595392717543321356899242915413241],
[173512792712172909456131993539106342879,276670255129140880258696821649524107343,176080436791985260266403840744627297429],
[217267141898619422837859646397422811530,192415481924499182031594124394175595334,261771203728758901533499406756951694139]]
alphabet="-ABCDEFGHIJKLMNOPQRSTUVWXYZabcdefghijklmnopqrstuwyz0123456789"
pt=''
for (m,b,p) in cts:
for c in alphabet:
if (ord(c)*0x1337*b)%p == m:
pt += c
print pt
This spits out our nugget :)
Flag
HV16-laWz-D5yT-0Uzb-DFj0-FIsL