> For the complete documentation index, see [llms.txt](https://pentest.mxhx.org/llms.txt). Markdown versions of documentation pages are available by appending `.md` to page URLs; this page is available as [Markdown](https://pentest.mxhx.org/05-passwords-ciphers/04-cipher-decrypt-rsa-wiener.md).

# Cipher RSA Wiener P-Q-E

* [htb-brainfuck](/05-passwords-ciphers/04-cipher-decrypt-rsa-wiener.md)
* <https://crypto.stackexchange.com/questions/19444/rsa-given-q-p-and-e>

## Definitions

* p - prime random 1
* q - prime random 2
* n
* e
* ct - cipher text
* pt - plain text

## Encryption:

```
> cat encrypt.sage 


nbits = 1024
password = open("/root/root.txt").read().strip()
enc_pass = open("output.txt","w")
debug = open("debug.txt","w")
m = Integer(int(password.encode('hex'),16))

p = random_prime(2^floor(nbits/2)-1, lbound=2^floor(nbits/2-1), proof=False)
q = random_prime(2^floor(nbits/2)-1, lbound=2^floor(nbits/2-1), proof=False)
n = p*q
phi = (p-1)*(q-1)
e = ZZ.random_element(phi)
while gcd(e, phi) != 1:
    e = ZZ.random_element(phi)

c = pow(m, e, n)
enc_pass.write('Encrypted Password: '+str(c)+'\n')
debug.write(str(p)+'\n')
debug.write(str(q)+'\n')
debug.write(str(e)+'\n')

```

## Debug Outputs

```
> cat debug.txt 

7493025776465062819629921475535241674460826792785520881387158343265274170009282504884941039852933109163193651830303308312565580445669284847225535166520307
7020854527787566735458858381555452648322845008266612906844847937070333480373963284146649074252278753696897245898433245929775591091774274652021374143174079
30802007917952508422792869021689193927485016332713622527025219105154254472344627284947779726280995431947454292782426313255523137610532323813714483639434257536830062768286377920010841850346837238015571464755074669373110411870331706974573498912126641409821855678581804467608824177508976254759319210955977053997


> cat output.txt 

Encrypted Password: 44641914821074071930297814589851746700593470770417111804648920018396305246956127337150936081144106405284134845851392541080862652386840869768622438038690803472550278042463029816028777378141217023336710545449512973950591755053735796799773369044083673911035030605581144977552865771395578778515514288930832915182
```

## Decode Script

```python
def egcd(a, b):
    x,y, u,v = 0,1, 1,0
    while a != 0:
        q, r = b//a, b%a
        m, n = x-u*q, y-v*q
        b,a, x,y, u,v = a,r, u,v, m,n
        gcd = b
    return gcd, x, y

def main():

    p = 7493025776465062819629921475535241674460826792785520881387158343265274170009282504884941039852933109163193651830303308312565580445669284847225535166520307
    q = 7020854527787566735458858381555452648322845008266612906844847937070333480373963284146649074252278753696897245898433245929775591091774274652021374143174079
    e = 30802007917952508422792869021689193927485016332713622527025219105154254472344627284947779726280995431947454292782426313255523137610532323813714483639434257536830062768286377920010841850346837238015571464755074669373110411870331706974573498912126641409821855678581804467608824177508976254759319210955977053997
    ct = 44641914821074071930297814589851746700593470770417111804648920018396305246956127337150936081144106405284134845851392541080862652386840869768622438038690803472550278042463029816028777378141217023336710545449512973950591755053735796799773369044083673911035030605581144977552865771395578778515514288930832915182

    # compute n
    n = p * q

    # Compute phi(n)
    phi = (p - 1) * (q - 1)

    # Compute modular inverse of e
    gcd, a, b = egcd(e, phi)
    d = a

    print( "n:  " + str(d) );

    # Decrypt ciphertext
    pt = pow(ct, d, n)
    print( "pt: " + str(pt) )

if __name__ == "__main__":
    main()
```

## Execution

```
> python3 crack.py 
n:  8730619434505424202695243393110875299824837916005183495711605871599704226978295096241357277709197601637267370957300267235576794588910779384003565449171336685547398771618018696647404657266705536859125227436228202269747809884438885837599321762997276849457397006548009824608365446626232570922018165610149151977
pt: 24604052029401386049980296953784287079059245867880966944246662849341507003750
```

## Human Readable

```
Python2:

>>> pt = 24604052029401386049980296953784287079059245867880966944246662849341507003750
>>> str(hex(pt))
'0x3665666331613564626238393034373531636536353636613330356262386566L'
>>> str(hex(pt)[2:-1])
'3665666331613564626238393034373531636536353636613330356262386566'
>>> str(hex(pt)[2:-1]).decode('hex')
'6efc1a5dbb8904751ce6566a305bb8ef'


Python3:

>>> pt = 24604052029401386049980296953784287079059245867880966944246662849341507003750
>>> pt = pt.to_bytes(((pt.bit_length() + 7) // 8), "big").decode()
>>> print(pt)
6efc1a5dbb8904751ce6566a305bb8ef  ..flag!!
```


---

# Agent Instructions
This documentation is published with GitBook. GitBook is the documentation platform designed so that both humans and AI agents can read, navigate, and reason over technical content effectively. Learn more at gitbook.com.

## Querying This Documentation
If you need additional information that is not directly available in this page, you can query the documentation dynamically by asking a question.

Perform an HTTP GET request on the current page URL with the `ask` query parameter, and the optional `goal` query parameter:

```
GET https://pentest.mxhx.org/05-passwords-ciphers/04-cipher-decrypt-rsa-wiener.md?ask=<question>&goal=<endgoal>
```

`ask` is the immediate question: it should be specific, self-contained, and written in natural language.
`goal` is optional and describes the broader end goal you are ultimately trying to accomplish on behalf of the user. GitBook uses it to tailor the answer towards what is most useful for that goal.

The response will contain a direct answer to the question and relevant excerpts and sources from the documentation.

Use this mechanism when the answer is not explicitly present in the current page, you need clarification or additional context, or you want to retrieve related documentation sections.