The ADD differential probability of right shift followed by XOR: $\mathrm{adp}^{\gg\oplus}$ . More...

#include "common.hh"
#include "adp-xor.hh"
#include "adp-shift.hh"
#include "adp-rsh-xor.hh"

Functions
uint32_t	rsh_xor (uint32_t a, uint32_t x, int r)

double	adp_rsh_xor_exper (const uint32_t da, const uint32_t dx, const uint32_t db, const int r)

void	adp_rsh_xor_alloc_matrices (gsl_matrix *A[3][2][2][2])

void	adp_rsh_xor_free_matrices (gsl_matrix *A[3][2][2][2])

void	adp_rsh_xor_normalize_matrices (gsl_matrix *A[3][2][2][2])

void	adp_rsh_xor_print_matrices (gsl_matrix *A[3][2][2][2])

void	adp_rsh_xor_sf (gsl_matrix *A[3][2][2][2])

double	adp_rsh_xor (gsl_matrix *A[3][2][2][2], uint32_t da, uint32_t dx, uint32_t db, int r)

double	adp_rsh_xor_approx (uint32_t da, uint32_t dx, uint32_t db, int r)

Detailed Description

The ADD differential probability of right shift followed by XOR: $\mathrm{adp}^{\gg\oplus}$ .

Author: V.Velichkov, vesse.nosp@m.lin..nosp@m.velic.nosp@m.hkov.nosp@m.@uni..nosp@m.lu

Date: 2012-2013

Function Documentation

double adp_rsh_xor	(	gsl_matrix *	A[3][2][2][2],
		uint32_t	da,
		uint32_t	dx,
		uint32_t	db,
		int	r
	)

The ADD differential probability of $({\gg\oplus})$ (RSH-XOR) computed experimentally over all inputs. Complexity: $O(n)$ .

Parameters

A	transition probability matrices for $\mathrm{adp}^{\gg\oplus}$ .
da	input difference.
dx	input difference.
db	output difference.
r	shift constant.

Returns: $\mathrm{adp}^{\gg\oplus}(r | da, dx \rightarrow db)$ .

See Also: adp_rsh_xor_exper

void adp_rsh_xor_alloc_matrices ( gsl_matrix * A[3][2][2][2] )

Allocate memory for the transition probability matrices for $\mathrm{adp}^{\gg\oplus}$ .

Parameters

A	transition probability matrices for $\mathrm{adp}^{\gg\oplus}$ .

See Also: adp_rsh_xor_free_matrices

double adp_rsh_xor_approx	(	uint32_t	da,
		uint32_t	dx,
		uint32_t	db,
		int	r
	)

Approximation of $\mathrm{adp}^{\gg\oplus}$ obtained as the multiplication of the differential probabilities $\mathrm{adp}^{\gg}$ and $\mathrm{adp}^{\oplus}$ .

Parameters

da	input difference.
dx	input difference.
db	output difference.
r	shift constant.

Returns: $\mathrm{adp}^{\gg\oplus}(r | da, dx \rightarrow db) \approx \mathrm{adp}^{\gg} \cdot \mathrm{adp}^{\oplus}$ .

See Also: adp_xor, adp_rsh

double adp_rsh_xor_exper	(	const uint32_t	da,
		const uint32_t	dx,
		const uint32_t	db,
		const int	r
	)

The ADD differential probability of RSH-XOR computed experimentally over all inputs. Complexity: $O(2^{2n})$ .

Parameters

da	input difference.
dx	input difference.
db	output difference.
r	shift constant.

Returns: $\mathrm{adp}^{\gg\oplus}(r | da, dx \rightarrow db)$ .

See Also: adp_rsh_xor

void adp_rsh_xor_free_matrices ( gsl_matrix * A[3][2][2][2] )

Free memory reserved for the transition probability matrices for $\mathrm{adp}^{\gg\oplus}$ .

Parameters

A	transition probability matrices for $\mathrm{adp}^{\gg\oplus}$ .

See Also: adp_rsh_xor_alloc_matrices

void adp_rsh_xor_normalize_matrices ( gsl_matrix * A[3][2][2][2] )

Transform the elements of A into probabilities.

Parameters

A	transition probability matrices for $\mathrm{adp}^{\gg\oplus}$ .

void adp_rsh_xor_print_matrices ( gsl_matrix * A[3][2][2][2] )

Print the elements of A.

Parameters

A	transition probability matrices for $\mathrm{adp}^{\gg\oplus}$ .

void adp_rsh_xor_sf ( gsl_matrix * A[3][2][2][2] )

S-function for the operation $({\gg\oplus})$ (RSH-XOR).

Parameters

A	zero-initialized set of matrices.

Returns: Transition probability matrices A for $\mathrm{adp}^{\gg\oplus}$ .

$A[3][2][2][2] = A[j][da[i]][dx[i+r]][db[i]]$ , where $da[i]$ denotes the i-th bit of $da$ , $n$ is the word size, $r$ is the shift constant, $i$ is the bit position and $j$ is a special bit position with three possible values: