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Is there an algorithm for dividing information into several parts, with the ability to restore the original information with only two parts?
I want to find an algorithm that can do the following:
Encodes and divides the original information into X parts, with the ability to restore the original information if the parts are missing (ideally - from 2 parts).
But so that the information could not be restored from only one part.
Real life example: encode and distribute a password between 4 people. To recover the password, at least two people must put their parts together.
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System of equations (A,B,C,D - unique):
A+B=C+D
A+C=B+D
A+D=B+C
A+B: X=F(A,f(A,B ))
A+C: X=F(A,f(A,C))
A+D: X=F(A,f(A,D))
.....(and so on for the right parts: 3 more lines)
Now, you need to make a function: X=F(M,f(M,L)), S=f(M,L)
Easier, general form: X=F(M,S) It
remains to come up with 2 -th functions: F(M,S) and f(M,L)...
On the "fingers": let it be sum and multiplication: F(M,S)=M+S and f(M,L)= M*L
After substitution, all F(M,S) should be equal to the same value: X
We can use it (X) as a parameter of the encoding function of the original (shared) data.
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