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RSA - puzzle no 5 Mystery Cache

Hidden : 5/5/2015
Difficulty:
5 out of 5
Terrain:
1 out of 5

Size: Size:   micro (micro)

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Geocache Description:


In the same town as Hr. Vænge lived Fru Stræde--also an avid geocacher. She had a lot of fun with Hr. Vænge's puzzles and had also written her own encrypt/decrypt program. Fru Stræde wanted to make a RSA puzzle as well, but she was not fond of the new rule that the solution method should be given to the reviews on the cache page. She preferred to email it directly, and so she did. The three messages are identical, but encrypted with each reviewers public key.

To Toa Takanuva she wrote:
c1=124496133005695781591769264156107282974066666938198285891554888613380933414114969918658481944491853286144240513666492985887235487033784202383362479988669035505163825911535061422290225000071952627352090804820693830077147438659027048823381408641312023216560427964051101258567011188647386424543351303656125148281472623512320668339791482752477185788810621623715660521184140067194131202107164741680978170890

To Toa Onua she emailed:
c2=72481886459434819214698968986703866000570485145505187479339109043647541409285306178212469874959641595631074412597987170014907982442706274438248357082035122863208257973678528280600720220522963310531899013109197663919693635136446760702850418342325999262438891671058536578067584857917694050150633290358102456096612860757936449582069030923871848026626929691634005496810642697841138814452525195751022493976

And for Toa Ignika:
c3=86094768742426505264407800460067959354662482272048054225342799829165612481358470797179408747609520938827725139659092596795558425263226000008567147193642521179031804836688926885607883262466214205825624918728266429644579995120282705667975596028291990279907243605859951231401861759079596012026078202579542189123136084640054272606173856079559264889787533298083462544999670256004506535250676697125692670607

So for the reviewers it was easy to solve the puzzle and get to the coordinates.

But was this a safe way to mail the information?

The reviewers public RSA keys are:
n1=131496786049513314968587695133222405876958604224059496786042313314967867695133150405876951404224058776786042241314967860495133149685876951332224058769586042240594967860423133149678676951331504058769586778971536714260790035062442639869880627623351699125971533548960789718532442608216880624458051698809441533517307789715367142607900350624426398698806276233516991259715335489607897185324426082168806251143
e1=3

n2=151496786053513314969187695133302405876968604224060696786042453314967883695133152205876951604224058798786042243714967860755133149713876951335224058769906042240628967860426733149679056951331544058770141421395801758503216537486685289912304892607594125622395776198403213983456685034707304867106894123074305775943792213958015385032165154866852877123048923875941256003957761962032139832366850346853049183461
e2=3

n3=91496786041513314967387695133062405876938604224057096786042033314967835695133146805876951004224058732786042236514967859975133149629876951326224058768946042240526967860415933149677916951331424058769545536547291030018365470638200183827456382059109274573547291094118365473088200183676456382004409274564117291092779365472914700183655146382001882274563824991092746175472910985183654735282001837204563823937
e3=3

Dansk udgave på forespørgsel.

Additional Hints (Decrypt)

Cvpgher va trbgwrxxre

Decryption Key

A|B|C|D|E|F|G|H|I|J|K|L|M
-------------------------
N|O|P|Q|R|S|T|U|V|W|X|Y|Z

(letter above equals below, and vice versa)