Low complexity normal bases

David W. Ash, Ian F. Blake, Scott A. Vanstone
1989 Discrete Applied Mathematics  
A normal basis in GF(qm) is a basis of the form {a p9, fig', . . . , flqm-'], i.e., a basis of conjugate elements in the field. In GF(2'") squaring with respect to a normal basis representation becomes simply a cyclic shift of the vector. For hardware design this is one of the very attractive features of these bases. Multiplication with respect to a normal basis can be defined in terms of a certain bilinear form. Define the complexity of the normal basis to be the number of nonzero terms in
more » ... form. Again, for hardware design, it is important to find normal bases with low complexity. In this paper we investigate low complexity normal bases, give a construction for such bases and apply it to a number of cases of interest.
doi:10.1016/0166-218x(89)90001-2 fatcat:i44sqckagbdgtays6mnjiz2t24