Interpolation and Approximation of Polynomials in Finite Fields over a   Short Interval from Noisy Values
  Motivated by a recently introduced HIMMO key distribution scheme, we consider a modification of the noisy polynomial interpolation problem of recovering an unknown polynomial $f(X) \in Z[X]$ from approximate values of the residues of $f(t)$ modulo a prime $p$ at polynomially many points $t$ taken from a short interval. 
Oscar Garcia-Morchon, Ronald Rietman, Igor E. Shparlinski and Ludo   Tolhuizen
math.NT cs.CR cs.DS