I am implementing Shamir's Secret Sharing, and I find that in (t,n)-threshold scheme, the shares are just using
1,2,3...,n as the key to form the shares
For example, I want share "Hello", and the shares look like this:
01-AAAA1,AAAA2,AAAA3,AAAA4,AAAA5 02-BBBB1,BBBB2,BBBB3,BBBB4,BBBB5 03-CCCC1,CCCC2,CCCC3,CCCC4,CCCC5 04-DDDD1,DDDD2,DDDD3,DDDD4,DDDD5
01,02,03,04 are the keys and
XXXX are the values.
But I find in some place, people are using random numbers as the key. And I want to further extend it by using different key for each character.
For example, the secret is still "Hello", but the share are become:
x1-AAAA1, x2-AAAA2, x3-AAAA3, x4-AAAA4, x5-AAAA5 y1-BBBB1, y2-BBBB2, y3-BBBB3, y4-BBBB4, y5-BBBB5 z1-CCCC1, z2-CCCC2, z3-CCCC3, z4-CCCC4, z5-CCCC5 u1-DDDD1, u2-DDDD2, u3-DDDD3, u4-DDDD4, u5-DDDD5
x1,x2,x3,x4,x5 are random and distinct.
In this way the only disadvantage is that we need more store space for keys, and it may takes more time to generate random number.
But I wonder whether there is some advantages? Say, Safety issue?
I am new with computer security, hope to get answer. Thanks!