Matlab scripts 1.0 for RainbowCrack update

Zhu Shuanglei <shuanglei@hotmail.com>
http://www.antsight.com/zsl/rainbowcrack/

There is a problem in script "calc_success_probability.m". 
When key space is small, the calc_success_probability.m script works well. However, the formula in the script is not in a good form and the error accumulates so much when key space is large.

I have written another version of the script to fix this:

-------------------- calc_success_probability.m --------------------
function ret = calc_success_probability(N, t, m)
arr = zeros(1, t - 1);
arr(1) = N * (1 - exp(-m/N));
for i = 2 : t - 1
	arr(i) = N * (1 - exp(-arr(i-1)/N));
end;

ret = 1;
for i = 1 : t - 1
	ret = ret * (1 - arr(i)/N);
end;
ret = 1 - ret;
----------------------------- cut here -----------------------------

You can replace the corresponding script in package rainbowcrack-matlabscripts-1.0.zip with this one.


some results of the old calc_success_probability.m script:
	1 - (1 - calc_success_probability(8353082582,    2100, 8000000    )) ^ 5 = 0.9990
	1 - (1 - calc_success_probability(80603140212,   2400, 40000000   )) ^ 5 = 0.9904
	1 - (1 - calc_success_probability(797193877550,  5700, 200000000  )) ^ 6 = 0.9990
	1 - (1 - calc_success_probability(6823331935124, 9000, 1000000000 )) ^ 8 = 0.9990

some results of the updated calc_success_probability.m script:
	1 - (1 - calc_success_probability(8353082582,    2100, 8000000    )) ^ 5 = 0.9990
	1 - (1 - calc_success_probability(80603140212,   2400, 40000000   )) ^ 5 = 0.9906
	1 - (1 - calc_success_probability(797193877550,  5700, 200000000  )) ^ 6 = 0.9985
	1 - (1 - calc_success_probability(6823331935124, 9000, 1000000000 )) ^ 8 = 0.9997

In configuration #3, the accurate success rate is 0.9985, instead of 0.9990.

In configuration #4, it seems the success rate 0.9997 is unnecessarily high.
For example, if we use l = 7
1 - (1 - calc_success_probability(6823331935124, 9000, 1000000000 )) ^ 7 = 0.9992
We can still control the success rate above 0.999, saving 15GB of disk space at the same time.


Thanks "I Am" <om_sh@hotmail.com> for pointing out this problem.

2004/01/25