├── README.md
└── fermats_factorizer.py


/README.md:
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1 | # rsa_tool
2 | 
3 | A python script written with the intend to demonstrate a vulnerability in [rsa cryptography](https://en.wikipedia.org/wiki/RSA_(cryptosystem)).
4 | 
5 | The vulnerability exists only if the two large primes that are chosen to compute n are very close to each other (the distance between the numbers can be iterated in feasible time limits).
6 | 
7 | In such a scenario on can use [fermat factorization](https://en.wikipedia.org/wiki/Fermat%27s_factorization_method).
8 | 


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/fermats_factorizer.py:
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 1 | import math
 2 | import gmpy2
 3 | 
 4 | N=gmpy2.mpz(E8953849F11E932E9127AF35E1000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000051F8EB7D0556E09FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFBAD55)
 5 | 
 6 | gmpy2.get_context().precision=2048
 7 | a=int(gmpy2.sqrt(n))
 8 | 
 9 | a2=a*a
10 | b2=gmpy2.sub(a2,N)
11 | 
12 | while not(gmpy2.is_square(b2)):
13 |     a=a+1
14 |     b2=a*a-N
15 | 
16 | b2=gmpy2.mpz(b2)
17 | gmpy2.get_context().precision=2048
18 | b=int(gmpy2.sqrt(b2))
19 | 
20 | print a+b
21 | 
22 | print a-b
23 | 


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