c4e_gfp.h File Reference

Prime field arithmetic in $\mathbb{F}_p$ . More...

#include "c4e_modn.h"

Include dependency graph for c4e_gfp.h:

Defines
#define	C4E_GFP_INV_SPACE(msize)
	Temp. space calculation (in units of C4eArchDigit) for function c4e_gfp_inv().
Functions
void	c4e_gfp_inv (C4E_CONST C4eElement C4E_RESTRICT x, C4E_CONST C4eElement C4E_RESTRICT m, C4eArchDigit tmp[C4E_RESTRICT], C4eElement *C4E_RESTRICT y)
	Inversion of a field element in $\mathbb{F}_p$ .

Detailed Description

Prime field arithmetic in $\mathbb{F}_p$ .

Definition in file c4e_gfp.h.

#define C4E_GFP_INV_SPACE ( msize )

Temp. space calculation (in units of C4eArchDigit) for function c4e_gfp_inv().

Parameters:

[in] msize Size of modulus in units of C4eArchDigit.

Returns:: Required digit space (in units of C4eArchDigit) when using c4e_gfp_inv() or functions based on it.

Definition at line 48 of file c4e_gfp.h.

void c4e_gfp_inv	(	C4E_CONST C4eElement *C4E_RESTRICT	x,
		C4E_CONST C4eElement *C4E_RESTRICT	m,
		C4eArchDigit	tmp[C4E_RESTRICT],
		C4eElement *C4E_RESTRICT	y
	)

Inversion of a field element in $\mathbb{F}_p$ .

Precondition:: The numbers x and m must be normalized (e.g. by using function c4e_elem_norm()) and must be unequal to zero.; tmp must point to pre-allocated memory space for at least (4U * C4E_GFP_INV_SPACE(m->size)) digits.; Use of restrict qualifier indicates that aliasing x with y or aliasing x->digits with y->digits is not allowed.

Note:: Parameter x can be declared as C4E_CONST because the structure it points to isn't modified. Instead only the digits in x->digits[] will change (and the double indirection prevents any const inheritance, at least when using "C").

Parameters:

`[in]`	x	Big number to be inverted modulo the prime number `m`. Notice that `x` is destroyed. The digits space which must be available at `x->digits` is C4E_GFP_INV_SPACE(`m->size`).
`[in]`	m	Prime number forming the modulus p of the associated field $\mathbb{F}_p$ .
	tmp	Array of temporary space elements (see preconditions for details on size).
`[out]`	y	Big number which is $x^{-1} \pmod m$ , normalized. If the result is zero then `x` seems not to be a valid field element ( $\gcd(x,m)=1$ does not hold true) and so does not have an inverse (error condition). The required C4eArchDigit digits space is C4E_GFP_INV_SPACE(`m->size`).

See also:: c4e_elem_norm(), C4E_ELEM_IS_ZERO(), C4E_GFP_INV_SPACE(), C4eElement, C4E_ELEM_ASGN_MEM()