Rating:

# RSA-3
## Description

Alright, this is the big leagues. You have someone’s Public Key. This isn’t unusual, if you want to send someone an encrypted message,
you have to have thier public key. Your job is to evaluate this public key, and obtain the value of the secret exponent or decryption
exponent (The value of “d” in an RSA encryption).
Wrap the number that you find with dsc{}!

mykey.pub:

-----BEGIN PUBLIC KEY-----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-----END PUBLIC KEY-----

After a research I found that it's weiner's attack and used online decoder to find n and e

n = 64064959164923876064874945473407049985543119992992738119252749231253142464203647518777455475109972581684732621072998898066728303433300585291527582979430276357787634026869116095391514311111174206395195817672737320837240364944609979844601986221462845364070396665723029902932653368943452652854174197070747631242101084260912287849286644699582292473152660004035330616149016496957012948833038931711943984563035784805193474921164625068468842927905314268942153720078680937345365121129404384633019183060347129778296640500935382186867850407893387920482141216498339346081106433144352485571795405717793040441238659925857198439433

e = 36222680858414256161375884602150640809062958718117141382923099494341733093172587117165920097285523276338274750598022486976083511178091392849986039384975758609343597548039166024042264614496506087597114091663955133779956176941325431822684716988128271384410010471755324833136859652978240297120618458534306923558546176110055737233883129780378153307730890915697357455996361736492022695824172516806204252765904924281272883818154621932085365817823019773860783687666788095035790491006333432295698178378520444810813882117817329847874531809530929345430796600870728736678389479159328119322587647856274762262358880664585675219093



Substituting value in same online decoder i got d as

6393313697836242618414301946448995659516429576261871356767102021920538052481829568588047189447471873340140537810769433878383029164089236876209147584435733

## Flag

dsc{6393313697836242618414301946448995659516429576261871356767102021920538052481829568588047189447471873340140537810769433878383029164089236876209147584435733}

## Tool
https://www.dcode.fr/rsa-cipher

Original writeup (https://github.com/S-H-E-L-L/DeconstructCTF/blob/main/crypto/RSA-3.md).