B has two polynomials of the same degree whose coefficients are defined over Zp and gives both polynomials to A. A picks a list of random X values, evaluates one of the polynomial and gives the result which is Y's values back to B. It is evident that he first evaluates then mod N.
Note: Both polynomials either are complete or have the same number of terms (e.g. ($x^2+1$ , $x^2+18$), as both have two terms is considered in our case, but ($x^2$ , $x^2+1$ ) is not allowed in here)
(1) Can B figure out which polynomial, A has used.
(2) What if two polynomials have different degrees. ** In this case the x values cab be defined as : x>(N/2)+1
Thanks