@Article{Riv01c,
  author = 	 { Ronald L. Rivest },
  title = 	 { Permutation polynomials modulo $2^w$ },
  journal = 	 { Finite Fields and Their Applications },
  issn =         { 1071-5797 },
  OPTyear = 	 { 2001 },
  OPTmonth = 	 { April },
  date =         { 2001-04 },                  
  volume = 	 { 7 },
  number = 	 { 2 },
  pages = 	 { 287--292 },
  doi =          { 10.1006/ffta.2000.0282 },
  url =          { http://www.sciencedirect.com/science/article/pii/S107157970090282X },
  keywords =     { permutation polynomial, latin square, multipermutation },                  
  abstract =     { 
                  We give an exact characterization of permutation
                  polynomials modulo $n=2^w$, $w\ge 2$: a polynomial
                  $P(x)=a_0+a_1x +\cdots + a_dx_d$ with integral coefficients is
                  a permutation polynomial modulo $n$ if and only if $a_1$
                  is odd, $(a_2+a_4+a_6+\cdots)$ is even, and 
                  $(a_3+a_5+a_7+\cdots)$
                  is even. We also characterize polynomials defining
                  latin squares modulo $n=2^w$, but prove that polynomial
                  multipermutations (that is, a pair of polynomials
                  defining a pair of orthogonal latin squares) modulo
                  $n=2^w$ do not exist.  
                  },
}