# ENIGMA Detailed Explanation - - I have tried “Secret Sharing”

I wish to explain about ENIGMA’S “Secret Sharing” today. Actually, it is very complicated if you study about “Enigma’s Secret Sharing”, so that my purpose is that you can feel something from my following explanations.

Let’s say here is three (3) Bitcoin holders. They only talk about “Virtual Currency” or “Girls/ Why they cannot find girlfriends”... However, because of their pride, they do not want to talk about how many years they do not have their girlfriends.

So, I have suggested… “It is no need to tell how many years, but it is possible to find your average years you do not have girlfriends if I use the “Secret Sharing””.

Nobody knows about the “Secret Sharing”, but because of their pride. Everybody agreed as if they knew the “Secret Sharing”. So, I said… “Everybody, please think function f(x) = s+px+qx2… You can put how many years you have not had girlfriends in “S”, and any single numbers in “P” and “Q””… Their functions came as follows…

Bitcoin Holder (1) f1(x) = 24 + 3x + 6x2

Bitcoin Holder (2) f2(x) = 30 + 4x + 7x2

Bitcoin Holder (3) f3(x) = 18 + 5x + 8x2

Then, I told them if the functions were ready… Please answer the functions using “1”, “2” and “3” in “x”…

So, the Bitcoin Holder (1) finds following answers…

F1(1) = 24 + (3 x 1) + (6 x 1 x 1) = 33

F1(2) = 24 + (3 x 2) + (6 x 2 x 2) = 54

F1(3) = 24 + (3 x 3) + (6 x 3 x 3) = 87

Bitcoin Holder (2) finds…

F2(1) = 30 + (4 x 1) + (7 x 1 x 1) = 41

F2(2) = 30 + (4 x 2) + (7 x 2 x 2) = 66

F2(3) = 30 + (4 x 3) + (7 x 3 x 3) = 105

Bitcoin Holder (3) finds…

F3(1) = 18 + (5 x 1) + (8 x 1 x 1) = 31

F3(2) = 18 + (5 x 2) + (8 x 2 x 2) = 60

F3(3) = 18 + (5 x 3) + (8 x 3 x 3) = 105

Nobody, including myself, knows how many years they have no girlfriends. However, the reader (you) can tell from the above functions, Bitcoin Holder (1) does not have girlfriends for 24 (years), (2) doesn’t have for 30 (years) and (3) doesn’t have for 18 (years)…

I told them if the functions were ready, please tell the answer only to the Holder used his number. (The Bitcoin Holder (1) told the answer 54 to the Holder (2) and 87 to the Holder (3)… The Bitcoin Holder (2) told 41 to the Holder (1) and 105 to the Holder (3) and the Holder Number (3) told 31 to the Holder (1) and 60 to the Holder (2).)

Now, the Bitcoin Holder (1) has 3 numbers, such as f1(1)=33, f2(1)=41, f3(1)=31 and total of these 3 numbers are 105. The Bitcoin Holder (2) has f1(2)=54, f2(2)=66, f3(2)=60 and total of these 3 numbers are 180. The Bitcoin Holder (3) has f1(3)=87, f2(3)=105, f3(3)=105 and total of 297.

I told them that I found the average was 24 years, but I do not know anybody how many years they don’t have… I could find only the average of years...

The reader (you) may solve/find the average from these 105, 180 and 297 total numbers… Even though, you cannot solve/find for each person from these functions.

Each functions are…

F1(x) = s1 + p1x + p2x2

F2(x) = s2 + q1x + q2x2

F3(x) = s3 + r1x + r2x2

So, we can write as follows…

F1(1)+f2(1)+f3(1) = (s1+s2+s3)+(p1+q1+r1)+(p2+q2+r2)=105

F1(2)+f2(2)+f3(2) = (s1+s2+s3)+2(p1+q1+r1)+4(p2+q2+r2)=180

F1(3)+f2(3)+f3(3) = (s1+s2+s3)+3(p1+q1+r1)+9(p2+q2+r2)=297

All the functions has (s1+s2+s3), (p1+q1+r1) and (p2+q2+r2), therefore, we can change to S = (s1+s2+s3), P = (p1+q1+r1) and Q = (p2+q2+r2). So, we can change above functions as follows…

S + P + Q = 105

S + 2P + 4Q = 180

S + 3P + 9Q = 297

Let’s solve above simultaneous… (S,P,Q,)=(72,12,21) Therefore, we can find the average of no girlfriends… S = 72 divided 3 = 24

However, we cannot find each by each.