# [pycrypto] getStrongPrime() implementation

Lorenz Quack don at amberfisharts.com
Fri Oct 30 10:43:58 CST 2009

```Hi there!

Here comes my monster patch.
It includes a python and C version of getStrongPrime, rabinMillerTest and isPrime.
there are also two small unit tests and some helper functions.
They all take a randfunc and propagate them (or so I hope).
The Rabin-Miller-Test uses random bases (non-deterministic).
getStrongPrime and isPrime take an optional parameter "false_positive_prob"
where one can specify the maximum probability that the prime is actually
composite. Internally the functions calculate the Rabin-Miller rounds from
this. It defaults to 1e-6 (1:1000000) which results in 10 rounds of Rabin-Miller
testing.

Please review this carefully. Even though I tried hard to get things right some
bugs always slip through.
maybe you could also review the way I acquire and release the GIL. It felt kind
of ugly the way I did it but I don't see a better way just now.

Concerning the public exponent e:
I now know why it needs to be coprime to p-1 and q-1. The private exponent d is
the inverse of e mod ((p-1)(q-1)).
If e is not coprime to ((p-1)(q-1)) then the inverse does not exist [1].

The getStrongPrime take an optional argument e. if provided the function will
make sure p-1 and e are coprime. if e is even (p-1)/2 will be coprime.
if e is even then there is a additional constraint: p =/= q mod 8.
I can't check for that in getStrongPrime of course but since we hardcoded e to
be odd in _RSA.py this should pose no problem.

The Baillie-PSW-Test is not included.

I tried hard not to use any functionality new than 2.1 but if you find anything
feel free to criticize. Also if I didn't get the coding style right either tell
me or feel free to correct it yourself.

have fun.
//Lorenz

[1] http://mathworld.wolfram.com/ModularInverse.html

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