Blinding polynomials are mathematical constructs used in zero-knowledge proof systems, particularly in polynomial commitment schemes, to hide or "blind" the actual polynomials being proved while maintaining their mathematical properties and structure. A blinding polynomial is essentially a random polynomial that's added to the original polynomial to mask its coefficients, the resulting sum preserves the mathematical properties needed for the proof while hiding the actual values.
Mathematical Representation:
Let's say you have an original polynomial
The blinding polynomial
rand_polynomial
.vanishing_polynomial
; it is important to note, vanishing polynomial
construction varies with the nature of domain of the polynomial (e.g. Real numbers, Roots of unity and so on).blinding_polynomial
is not given by; blinded_polynomial
, perform this operation; Constructing Vanishing Polynomial when Domain = Real Numbers
The vanishing polynomial
impling these properties;
Constructing Vanishing Polynomial when Domain = Roots of Unity
Constructing the vanishing polynomial in this domian is alot more less complicated, it can be represented by the given equation;
Understanding blinding polynomials is crucial for implementing secure and private zero-knowledge proof systems while maintaining the mathematical integrity of the underlying computations.