30 lines
1.3 KiB
Markdown
30 lines
1.3 KiB
Markdown
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# Fermat Attack on RSA
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This is just a little ugly program to
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attack on RSA modul with an approach of Fermat.
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Use: `java -jar fermat_rsa_attack.jar [MODUL] [TRIES]`
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where MODUL is the RSA-modul (generated from both keys you want to evaluate)
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and TRIES the amount of iterations to avoid long runtime.
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TRIES is optional. If not given the default amount of trie is 100.
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If there is no solution found within the tries then give a bigger number up to
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approx. 2 billion (integer 32).
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---
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The modul `N` evaluates from product of two prime numbers (except 2):
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`N = p1 * p2`
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For the two prime numbers exists `a` and `b` with `p1 = a-b` and `p2 = a+b`.
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So `N` can be evaluated as `N = (a-b)(a+b) = a^2 - b^2`.
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The number `a` must lie in between `p1` and `p2` with equal distance `b`.
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A good guess for such an `a` is the square root of `N` as a starting point.
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In each iteration increase `a` by 1 until a solution is found or the amount of tries is exhausted.
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In the iteration itself calculate `b^2 = a^2 - N` then check if `b` is non-negative and a square number.
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If so the solution is found. If not then increase `a` by 1 and try again.
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---
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**This method to calculate `p1` and `p2` for RSA-keys is a good method if the two prime numbers
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are close together. However, if they are not close it takes long.
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So RSA with good key generators are still strong.**
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