A polynomial representation of the Diffie-Hellman mapping
Let F-q be the finite field of order q and gamma be an element of F-q of order d. The construction of an explicit polynomial f(X) is an element of F-q [X] of degree less than or equal to d - 1 with the property f (gamma(i)) = gamma(i2) for 0 less than or equal to i less than or equal to d - 1 is described. In particular the exact degree and sparsity of f are determined.
degree sparsity diffie-hellman cryptosystem polynomial interpolation