Hello,
just a few comments:
Exactly for the purpose of implementing AES (and generalisations) we
looked at using the gf-package in the past, and we used it for some
time, but then abandoned the gf-package, since it was very slow, and
also not convenient to use: due to the reliance on global variables, we
needed to write a wrapper function for every gf-function, which first
calls gf_set, and that permanent calling of gf_set (since otherwise you
don't know what's happening!) makes is even slower.
Apparently the design is taken over, and so I doubt that the package can
be much of use for us.
It would be very helpful if the gf-package itself would provide the
wrapper-functions, to make the functionalities of the package
"functional", i.e., not depending on global variables.
To achieve that, the gf_set function should return a (light-weight)
object, which contains all the information, and overloaded versions
of all the functions would take as additional, last parameter this
object. Then we would have proper, reliably usable functions, and the
need to permanently call gf_set would disappear.
Oliver
On Thu, Oct 25, 2012 at 10:00:38PM +0200, Volker van Nek wrote:
> 2012/10/25 Robert Dodier <robert.dodier at gmail.com>
>
> > On 2012-10-25, Volker van Nek <volkervannek at gmail.com> wrote:
> >
> > > I am working on a package for Galois Fields. I nearly finished coding the
> > > functions but unfortunately at the moment most of them are not
> > documented.
> >
> > Well, in a sense that's good, since I'd like to suggest changing the
> > name of the function.
> >
> > > (%i2) gf_irr_p(x^4+x+1, 2);
> > > (%o2) true
> > >
> > > which means that x^4+x+1 is irredicible over F2,
> >
> > I'd like to suggest spelling out "irreducible" in this function name.
> > Maxima has a tremendous number of functions and variables and it is hard
> > to keep track of them all, so spelling out names makes Maxima as a whole
> > more comprehensible, especially for names which are not widely used.
> >
> > It's OK to use abbreviations for commonly-used names. In this case, I
> > think it's OK to abbreviate Galois field as gf. (Also, 'GF' is a typical
> > abbreviation anyway.)
> >
> > So the name I'll suggest is gf_irreducible_p or maybe gf_irreduciblep.
> >
>
> Robert,
> gf_irreducible_p is OK by me.
>
> The following list shows all the GF-functions I put to src. I hope the very
> short and quick comments explain what these functions do. Feel free to make
> any suggestions about other names.
>
> As I posted in a previous mail to this list I coded AES encryption as an
> application and test case for these functions. That showed me which of
> these are used frequently.
> E.g. the conversion functions gf_p2n and friends are used quite often and I
> would like to keep them as short as possible.
> Frequently used are also the arithmetic functions like gf_add and (in small
> fields) the lookup arrays gf_powers and gf_logs.
>
> gf_set : set the field parameters and global variables
> gf_unset : reset the globals to nil
> gf_minset : set a minimum of information to allow simple GF-arithmetics
> gf_rat : option variable - the returned polys are of cre or of general form
> gf_char : return the field characteristic set by gf_set
> gf_prim : return the primitive element computed by gf_set
> gf_red : return the reduction polynomial set or computed by gf_set
> gf_info : print information about globals
> gf_make_arrays : compute the lookup arrays gf_powers and gf_logs
> gf_powers : global variable - all powers of gf_prim stored in an array
> gf_logs : global variable - the corresponding logarithms
> gf_mult_table : show a multiplication table of the field
> gf_power_table : show a power table of the field
> gf_add : add field elements
> gf_sub : subtract field elements
> gf_mult : mulitply field elements
> gf_inv : return the inverse of a field element
> gf_div : divide field elements
> gf_exp : return the power of a field element
> gf_exp : return the field exponent when used with no args
> gf_ind : return the index of a field element
> gf_log : return a logarithm wrt the primitive or another element
> gf_p2n : convert a poly to the corresponding number
> gf_n2p : convert a number to the corresponding poly
> gf_p2l : convert a poly to a list of coefficients
> gf_l2p : convert a list of coefficients to a poly
> gf_l2n : convert a list of coefficients to a number
> gf_n2l : convert a number to a list of coefficients
> gf_irr_p : test of irreducibility
> gf_prim_p : test of primitivity
> gf_next_prim : find the next primitive element
> gf_eval : evaluate an arbitrary poly in the context of the field
> gf_rand : return a random field element
> gf_factor : factor an arbitrary poly in the context of the field
> gf_gcd : return the gcd of two field elements
> gf_gcdex : return the ext gcd of two field elements
> gf_ord : return the order of the field
> gf_deg : return the degree of a field element
> gf_minpoly : return the minimum poly of a field element
> gf_normal_p : test if an element is normal
> gf_normal : find a normal element by brute force
> gf_random_normal : find a normal element by random
> gf_normal_basis : compute a normal base
> gf_nbrep : return a normal base representation of a field element
> gf_matadd : add two matrices
> gf_matmult : multiply two matrices
> gf_matinv : return the inverse of a matrix
>
>
> Greetings
> Volker
>
>