nuclear weapons and shamir secret sharing

1756 days ago by bardg

A = matrix( GF(101), 4, 5, [ 1, 1, 1, 1, 22, 64, 16, 4, 1, 72, 99^3, 99^2, 99, 1, 3, 53^3, 53^2, 53, 1, 63] ) 
       
       
[ 1  1  1  1 22]
[64 16  4  1 72]
[93  4 99  1  3]
[ 3 82 53  1 63]
[ 1  1  1  1 22]
[64 16  4  1 72]
[93  4 99  1  3]
[ 3 82 53  1 63]
A.rref() 
       
[ 1  0  0  0 13]
[ 0  1  0  0  2]
[ 0  0  1  0  3]
[ 0  0  0  1  4]
[ 1  0  0  0 13]
[ 0  1  0  0  2]
[ 0  0  1  0  3]
[ 0  0  0  1  4]
print "Therefore the formula is 13x^3 + 2x^2 + 3x + 4 = y" 
       
Therefore the formula is 13x^3 + 2x^2 + 3x + 4 = y
Therefore the formula is 13x^3 + 2x^2 + 3x + 4 = y
print "Now let's say that person #4 is not certain that he wants to launch, so he uses 62 instead of 63, a tiny change" 
       
Now let's say that person #4 is not certain that he wants to launch, so
he uses 62 instead of 63, a tiny change
Now let's say that person #4 is not certain that he wants to launch, so he uses 62 instead of 63, a tiny change
A_fear = matrix( GF(101), 4, 5, [ 1, 1, 1, 1, 22, 64, 16, 4, 1, 72, 99^3, 99^2, 99, 1, 3, 53^3, 53^2, 53, 1, 62] ) 
       
A_fear.rref() 
       
[ 1  0  0  0 53]
[ 0  1  0  0 84]
[ 0  0  1  0 66]
[ 0  0  0  1 21]
[ 1  0  0  0 53]
[ 0  1  0  0 84]
[ 0  0  1  0 66]
[ 0  0  0  1 21]
print "Now the polynomial is 53x^3 + 84x^2 + 66x + 21 = y, which is completely and utterly different." 
       
Now the polynomial is 53x^3 + 84x^2 + 66x + 21 = y, which is completely
and utterly different.
Now the polynomial is 53x^3 + 84x^2 + 66x + 21 = y, which is completely and utterly different.
print ( 53*1^3 + 84*1^2 + 66*1 + 21 ) % 101 
       
22
22
print ( 53*4^3 + 84*4^2 + 66*4 + 21 ) % 101 
       
72
72
print ( 53*99^3 + 84*99^2 + 66*99 + 21 ) % 101 
       
3
3
print ( 53*53^3 + 84*53^2 + 66*53 + 21 ) % 101 
       
62
62