In our order system, we want you to choose 60 words,
which represents your seed and a group of additional words.
In this section, we want to show you that our system is safe enough,
your seed can not be found out. Let's show it on some easy examples.
In case we determine the exact number of arrangements consisting
of 24 words. The outcome is easily gained using combinatorics.
In case of reverse word order consisting of strictly given group of 24 words,
we are talking about permutation.
We use the following formula:
P(k) = k!
Calculation:
k = 24, then P(k) = 24! = 24×23×22×... ×2×1 = 620 448 401 733 239 409 999 872
≈ 6,2045 × 10^23 permutations.
Number of permutations = 6.204484×10^23.
That means, even if you gave us exact words representing your seed, it would take 6.204484×10^23 combinations to find out.
In case we are choosing 24 words using strictly given group of 60 words,
there is important the order of words. We are talking about finding variations consisting of 24 words created out of 60 words.
We use the following formula:
V(k,n) = n×(n–1)×(n–2)×...×(n–k+1) = n! / (n–k)!
Calculation:
V(24,60) = 60! / 36! = 22 368 646 191 981 329 482 560 015 901 851 648 000 000
≈ 2.2369 × 10^40 variations.
Number of variations = 2.236865 × 10^40.
That means, even if you gave us exact words representing your seed, it would take 2.236865 × 10^40 combinations to find out.
Finally, one display for comparison:
9 year research of NASA project WMAP, which ended in 2012,
revealed the approximate age of our space on 1,3772±10^10 years,
which is 13,772 miliard years with toleration of 59 milion years.
Source: https://en.wikipedia.org/wiki/Age_of_the_universe
1 year = 60x60x24x365 = 31536000 second = 3,1536 x 10^7.
It is approximately 1,3772 ± 0,0059 × 10^10 x 3,1536 x 10^7 = 4,34 x 10^17
seconds from the BIG BANG.
How long does it take to calculate the all group of 24 SEEDs from 24 words?
6.204484×1023 / 4,34 x 10^17 = 1,429 x 10^6 = 1 429 604 verifications per second from the begining of our space.
How long does it take to calculate the all group of 24 SEEDs from 60 words?
2.236865×10^40 / 4,34 x 10^17 = 5,15 x 10^22 = 51 540 668 202 764 976 958 525 verifications per second from the begining of our space.
So, it is not so easy, right?