Question

can anyone explain it for me how can I calculated ? Example: •(t, n)=(2, 4)-threshold secret...


can anyone explain it for me how can I calculated ?


Example:

(t, n)=(2, 4)-threshold secret sharing

s=9,p=17

Given x1=1,x2=2,x3=3,x4=4

A polynomial equation can be defined as

f(x) ≡ 9+13x mod 17

Then f(1)=5, f(2)=1, f(3)=14, f(4)=10

Four points: (1,5), (2,1), (3,14), (4,10)

.


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Answer #1

f(x) = (9+13x) mod 17

= (9+13x) % 17

= Reminder on dividing (9+13x) by 17

Here x1=1, x2=2, x3=3, x4=4

So, f(x1)=f(1) = (9+13*1)%17

= (9+13)%17

= 22%17

= 5 (Reminder on dividing 22 by 17),

f(x2)=f(2) = (9+13*2)%17

= (9+26)%17

= 35%17

= 1 (Reminder on dividing 35 by 17),

f(x3)=f(3) = (9+13*3)%17

= (9+39)%17

= 48%17

= 14 (Reminder on dividing 48 by 17),

f(x4)=f(4) = (9+13*4)%17

= (9+52)%17

= 61%17

= 10 (Reminder on dividing 61 by 17),

So, Four points are (1,5), (2,1), (3,14), (4,10) [ taking (x, f(x)) values for x1,x2,x3,x4 ]

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