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adp-xtea-f-fk.cc File Reference

The ADD differential probability of the F-function of XTEA for a fixed key and round constants $\mathrm{adp}^{F}(k, \delta |~ da \rightarrow dd)$. Complexity: $ O(n) < c \le O(2^n) $. More...

#include "common.hh"
#include "adp-xor.hh"
#include "max-adp-xor.hh"
#include "adp-xor-fi.hh"
#include "max-adp-xor-fi.hh"
#include "adp-shift.hh"
#include "xtea.hh"

Functions

double adp_xtea_f_exper (const uint32_t da, const uint32_t db, const uint32_t k, const uint32_t delta, const uint32_t lsh_const, const uint32_t rsh_const)
 
double adp_xtea_f_approx (const uint32_t ninputs, const uint32_t da, const uint32_t db, const uint32_t k, const uint32_t delta, const uint32_t lsh_const, const uint32_t rsh_const)
 
double max_dy_adp_xtea_f_exper (const uint32_t dx, uint32_t *dy_max, const uint32_t k, const uint32_t delta, const uint32_t lsh_const, const uint32_t rsh_const)
 
double max_dx_adp_xtea_f_exper (uint32_t *dx_max, const uint32_t dy, const uint32_t k, const uint32_t delta, const uint32_t lsh_const, const uint32_t rsh_const)
 
double adp_xtea_f_lxr_exper (const uint32_t da, const uint32_t db, uint32_t lsh_const, uint32_t rsh_const)
 
double adp_xtea_f_lxr_approx (const uint32_t ninputs, const uint32_t da, const uint32_t db, uint32_t lsh_const, uint32_t rsh_const)
 
bool adp_xtea_f_lxr_check_x (const uint32_t lsh_const, const uint32_t rsh_const, const uint32_t dx, const uint32_t dy, const uint32_t x)
 
bool adp_xtea_f_lxr_is_sat (const uint32_t mask_i, const uint32_t lsh_const, const uint32_t rsh_const, const uint32_t dx, const uint32_t dy, int32_t x)
 
uint32_t adp_xtea_f_lxr_assign_bit_x (const uint32_t n, const uint32_t i, const uint32_t mask_i, const uint32_t x, const uint32_t lsh_const, const uint32_t rsh_const, const uint32_t dx, const uint32_t dy, uint32_t *x_cnt, double *prob)
 
double adp_xtea_f_lxr (const uint32_t n, const uint32_t dx, const uint32_t dy, const uint32_t lsh_const, const uint32_t rsh_const)
 
double adp_xtea_f_approx (const uint32_t n, gsl_matrix *A[2][2][2], const uint32_t dx, const uint32_t dy, const uint32_t k, const uint32_t delta, const uint32_t lsh_const, const uint32_t rsh_const)
 
bool adp_xtea_f_check_x (const uint32_t lsh_const, const uint32_t rsh_const, const uint32_t k, const uint32_t delta, const uint32_t dx, const uint32_t dy, const uint32_t x)
 
bool adp_xtea_f_is_sat (const uint32_t mask_i, const uint32_t lsh_const, const uint32_t rsh_const, const uint32_t k, const uint32_t delta, const uint32_t dx, const uint32_t dy, const uint32_t x)
 
uint32_t adp_xtea_f_assign_bit_x (const uint32_t n, const uint32_t i, const uint32_t mask_i, const uint32_t x, const uint32_t key, const uint32_t delta, const uint32_t lsh_const, const uint32_t rsh_const, const uint32_t dx, const uint32_t dy, uint32_t *x_cnt, double *prob)
 
uint32_t adp_xtea_f_assign_bit_x_dx (const uint32_t n, const uint32_t i, const uint32_t mask_i, const uint32_t x, const uint32_t lsh_const, const uint32_t rsh_const, const uint32_t key, const uint32_t delta, const uint32_t dx, const uint32_t dy, uint64_t *x_cnt, double *ret_prob, uint32_t *ret_dx)
 
uint32_t adp_xtea_f_assign_bit_x_dy (const uint32_t n, const uint32_t i, const uint32_t mask_i, const uint32_t x, const uint32_t lsh_const, const uint32_t rsh_const, const uint32_t key, const uint32_t delta, const uint32_t dx, const uint32_t dy, uint64_t *x_cnt, double *ret_prob, uint32_t *ret_dy)
 
double adp_xtea_f (const uint32_t n, const uint32_t dx, const uint32_t dy, const uint32_t key, const uint32_t delta, const uint32_t lsh_const, const uint32_t rsh_const)
 
double max_dy_adp_xtea_f (const uint32_t n, const uint32_t dx, uint32_t *ret_dy, const uint32_t key, const uint32_t delta, const uint32_t lsh_const, const uint32_t rsh_const)
 
double max_dx_adp_xtea_f (const uint32_t n, uint32_t *ret_dx, const uint32_t dy, const uint32_t key, const uint32_t delta, const uint32_t lsh_const, const uint32_t rsh_const)
 
double first_nz_adp_xtea_f (gsl_matrix *A[2][2][2], gsl_matrix *AA[2][2][2], const uint32_t key, const uint32_t delta, const uint32_t da, uint32_t *ret_dd, uint32_t lsh_const, uint32_t rsh_const)
 

Detailed Description

The ADD differential probability of the F-function of XTEA for a fixed key and round constants $\mathrm{adp}^{F}(k, \delta |~ da \rightarrow dd)$. Complexity: $ O(n) < c \le O(2^n) $.

Author
V.Velichkov, vesse.nosp@m.lin..nosp@m.velic.nosp@m.hkov.nosp@m.@uni..nosp@m.lu
Attention
The algorithms in this file have complexity that depends on the input and output differences to F. It is worst-case exponential in the word size, but is sub-exponential on average.
See Also
xdp-xtea-f-fk.cc

Function Documentation

double adp_xtea_f ( const uint32_t  n,
const uint32_t  dx,
const uint32_t  dy,
const uint32_t  key,
const uint32_t  delta,
const uint32_t  lsh_const,
const uint32_t  rsh_const 
)

Compute the fixed-key, fixed-constant ADD differential probability of the F-function of block cipher XTEA: $\mathrm{adp}^{F}(k, \delta |~ dx \rightarrow dy)$. Complexity: $ O(n) < c \le O(2^n) $.

Parameters
nword size.
dxinput difference.
dyoutput difference.
keyround key.
deltaround constant.
lsh_constLSH constant.
rsh_constRSH constant.
Returns
$\mathrm{adp}^{F}(k, \delta |~ dx \rightarrow dy)$.
See Also
adp_f_assign_bit_x
double adp_xtea_f_approx ( const uint32_t  ninputs,
const uint32_t  da,
const uint32_t  db,
const uint32_t  k,
const uint32_t  delta,
const uint32_t  lsh_const,
const uint32_t  rsh_const 
)

An approximation of the ADP of the XTEA F-function (xtea_f) obtained over a number of input chosen plaintext pairs chosen uniformly at random.

Parameters
ninputsnumber of chosen plaintext pairs.
dainput difference.
dboutput difference.
kround key.
deltaround constant.
lsh_constLSH constant.
rsh_constRSH constant.
Returns
$\mathrm{adp}^{F}(k, \delta |~ dx \rightarrow dy)$.
Note
For the exact computation refer to adp_xtea_f
double adp_xtea_f_approx ( const uint32_t  n,
gsl_matrix *  A[2][2][2],
const uint32_t  dx,
const uint32_t  dy,
const uint32_t  k,
const uint32_t  delta,
const uint32_t  lsh_const,
const uint32_t  rsh_const 
)

An approximation of the ADD differential probability (ADP) of the XTEA F-function (xtea_f) with fixed round key and round cnstant, obtained as the multiplication the ADP of its $f_{\mathrm{LXR}}$ component (adp_xtea_f_lxr) and the ADP of XOR with one fixed input (adp_xor_fixed_input):

$\mathrm{adp}^{F}(k, \delta |~ dx \rightarrow dy) = \mathrm{adp}^{f_\mathrm{LXR}}(dx \rightarrow dt) \cdot \mathrm{adp}^{\oplus}_{\mathrm{FI}}(k + \delta, dx + dt \rightarrow dy)$.

Algorithm sketch:

  1. Compute $dz$ s.t. $p_1 = \mathrm{max}_{dz}~\mathrm{adp}^{\oplus}_{\mathrm{FI}}(k + \delta, dy \rightarrow dz)$.
    Note
    Note that $\mathrm{adp}^{\oplus}_{\mathrm{FI}}(k + \delta, dy \rightarrow dz) = \mathrm{adp}^{\oplus}_{\mathrm{FI}}(k + \delta, dz \rightarrow dy)$.
  2. Compute the output from $f_{\mathrm{LXR}}$ : $dt = dz - dx$.
  3. Compute $p_2 = \mathrm{adp}^{f_\mathrm{LXR}}(dx \rightarrow dt)$.
  4. Compute $\mathrm{adp}^{F}(k, \delta |~ dx \rightarrow dy) = p_1 \cdot p_2$.
Parameters
nword size.
Atransition probability matrices for $\mathrm{adp}^{\oplus}$ with FI (adp_xor_fixed_input_sf).
dxinput difference.
dyoutput difference.
kround key.
deltaround constant.
lsh_constLSH constant.
rsh_constRSH constant.
Returns
$\mathrm{adp}^{f_\mathrm{LXR}} \cdot \mathrm{adp}^{\oplus}_{\mathrm{FI}}$.
Note
For the exact computation refer to adp_xtea_f.
uint32_t adp_xtea_f_assign_bit_x ( const uint32_t  n,
const uint32_t  i,
const uint32_t  mask_i,
const uint32_t  x,
const uint32_t  key,
const uint32_t  delta,
const uint32_t  lsh_const,
const uint32_t  rsh_const,
const uint32_t  dx,
const uint32_t  dy,
uint32_t *  x_cnt,
double *  prob 
)

Counts the number of values x for which the differential $(dx \rightarrow dy)$ for the F-function of XTEA is satisfied. The function operates by recursively assigning the bits of x starting from bit position i and terminating at the MS bit n. The recursion proceeds to bit $(i+1)$ only if the differential is satisfied on the i LS bits. This is checked by applying adp_xtea_f_is_sat.

Parameters
nword size (terminating bit popsition).
icurrent bit position.
mask_imask on the i LS bits of x.
xinput value of size at least (i + rsh_const).
keyround key.
deltaround constant.
lsh_constLSH constant.
rsh_constRSH constant.
dxinput difference.
dyoutput difference.
x_cntnumber of values satisfying $(dx \rightarrow dy)$.
probthe fixed-key ADD probability of F: $\mathrm{adp}^{F}(k, \delta |~ dx \rightarrow dy)$.
Returns
1 if $x[i-1:0]$ satisfies $(dx[i-1:0] \rightarrow dy[i-1:0])$; 0 otherwise.
See Also
adp_f_fk
uint32_t adp_xtea_f_assign_bit_x_dx ( const uint32_t  n,
const uint32_t  i,
const uint32_t  mask_i,
const uint32_t  x,
const uint32_t  lsh_const,
const uint32_t  rsh_const,
const uint32_t  key,
const uint32_t  delta,
const uint32_t  dx,
const uint32_t  dy,
uint64_t *  x_cnt,
double *  ret_prob,
uint32_t *  ret_dx 
)

For given output difference dy, compute all input differences dx and their probabilities, by counting all values x that satisfy the differential $(dx \rightarrow dy)$ for a fixed key and round constant. At the same time keeps track of the maximum probability input difference.

The function works by recursively assigning the bits of x and dx starting at bit position i and terminating at the MS bit n. The recursion proceeds to bit $(i+1)$ only if the differential is satisfied on the i LS bits. This is checked by applying adp_f_is_sat .

Parameters
nword size (terminating bit popsition).
icurrent bit position.
mask_imask on the i LS bits of x.
xinput value of size at least (i + rsh_const).
keyround key.
deltaround constant.
lsh_constLSH constant.
rsh_constRSH constant.
dxinput difference.
dyoutput difference.
x_cntarray of $2^n$ counters - each one keeps track of the number of values satisfying $(dx \rightarrow dy)$ for every dx.
ret_probthe maximum probability over all input differences $\mathrm{max}_{dx} ~\mathrm{adp}^{F}(k, \delta |~ dx \rightarrow dy)$.
ret_dxthe input difference that has maximum probability.
Returns
1 if $x[i-1:0]$ satisfies $(dx[i-1:0] \rightarrow dy[i-1:0])$; 0 otherwise.
See Also
adp_f_assign_bit_x
uint32_t adp_xtea_f_assign_bit_x_dy ( const uint32_t  n,
const uint32_t  i,
const uint32_t  mask_i,
const uint32_t  x,
const uint32_t  lsh_const,
const uint32_t  rsh_const,
const uint32_t  key,
const uint32_t  delta,
const uint32_t  dx,
const uint32_t  dy,
uint64_t *  x_cnt,
double *  ret_prob,
uint32_t *  ret_dy 
)

For given input difference dx, compute all output differences dy and their probabilities, by counting all values x that satisfy the differential $(dx \rightarrow dy)$ for a fixed key and round constant. At the same time keeps track of the maximum probability output difference.

The function works by recursively assigning the bits of x and dy starting at bit position i and terminating at the MS bit n. The recursion proceeds to bit $(i+1)$ only if the differential is satisfied on the i LS bits. This is checked by applying adp_f_is_sat.

Parameters
nword size (terminating bit popsition).
icurrent bit position.
mask_imask on the i LS bits of x.
xinput value of size at least (i + rsh_const).
lsh_constLSH constant.
rsh_constRSH constant.
keyround key.
deltaround constant.
dxinput difference.
dyoutput difference.
x_cntarray of $2^n$ counters - each one keeps track of the number of values satisfying $(dx \rightarrow dy)$ for every dy.
ret_probthe maximum probability over all output differences $\mathrm{max}_{dy} ~\mathrm{adp}^{F}(k, \delta |~ dx \rightarrow dy)$.
ret_dythe output difference that has maximum probability.
Returns
1 if $x[i-1:0]$ satisfies $(dx[i-1:0] \rightarrow dy[i-1:0])$; 0 otherwise.
See Also
adp_f_assign_bit_x_dx
bool adp_xtea_f_check_x ( const uint32_t  lsh_const,
const uint32_t  rsh_const,
const uint32_t  k,
const uint32_t  delta,
const uint32_t  dx,
const uint32_t  dy,
const uint32_t  x 
)

Check if a given value x satisfies the ADD differential $(dx \rightarrow dy)$ for the XTEA F-function.

Parameters
lsh_constLSH constant.
rsh_constRSH constant.
kround key.
deltaround constant.
dxinput difference.
dyoutput difference.
xinput value.
Returns
TRUE if $k, \delta:~ dy = F(x + dx) - F(x)$.
double adp_xtea_f_exper ( const uint32_t  da,
const uint32_t  db,
const uint32_t  k,
const uint32_t  delta,
const uint32_t  lsh_const,
const uint32_t  rsh_const 
)

Compute the fixed-key, fixed-constant ADD differential probability of the F-function of block cipher XTEA: $\mathrm{adp}^{F}(k, \delta |~ dx \rightarrow dy)$ through exhaustive search over all input values. Complexity: $O(2^n)$.

Parameters
dainput difference.
dboutput difference.
kround key.
deltaround constant.
lsh_constLSH constant.
rsh_constRSH constant.
Returns
$\mathrm{adp}^{F}(k, \delta |~ dx \rightarrow dy)$.
bool adp_xtea_f_is_sat ( const uint32_t  mask_i,
const uint32_t  lsh_const,
const uint32_t  rsh_const,
const uint32_t  k,
const uint32_t  delta,
const uint32_t  dx,
const uint32_t  dy,
const uint32_t  x 
)

Check if the differential $(dx \rightarrow dy)$ for F (xtea_f) is satisfied on the i LS bits of x i.e. check if

$k, \delta:~ dy[i-1:0] = F(x[i-1:0] + dx[i-1:0]) - F(x[i-1:0]) ~\mathrm{mod} ~2^{i}$.

Attention
x must be of size at least $(i + R)$ bits where R is the RSH constant of F.
Parameters
mask_ii bit mask.
lsh_constLSH constant.
rsh_constRSH constant.
kround key.
deltaround constant.
dxinput difference.
dyoutput difference.
xinput value of size at least (i + rsh_const).
Returns
TRUE if $k, \delta:~ dy[i-1:0] = F(x[i-1:0] + dx[i-1:0]) - F(x[i-1:0]) ~\mathrm{mod} ~2^{i}$.
double adp_xtea_f_lxr ( const uint32_t  n,
const uint32_t  dx,
const uint32_t  dy,
const uint32_t  lsh_const,
const uint32_t  rsh_const 
)

Compute the ADD differential probability of the $f_{\mathrm{LXR}}$ (xtea_f_lxr) function: $\mathrm{adp}^{f_\mathrm{LXR}}(dx \rightarrow dy)$. Complexity c: $ O(n) < c \le O(2^n) $.

Parameters
nword size.
dxinput difference.
dyoutput difference.
lsh_constLSH constant.
rsh_constRSH constant.
Returns
$\mathrm{adp}^{f_\mathrm{LXR}}(dx \rightarrow dy)$.
See Also
adp_xtea_f_lxr_assign_bit_x
double adp_xtea_f_lxr_approx ( const uint32_t  ninputs,
const uint32_t  da,
const uint32_t  db,
uint32_t  lsh_const,
uint32_t  rsh_const 
)

An approximation of the ADP of $f_{\mathrm{LXR}}$ (xtea_f_lxr) obtained over a number of input chosen plaintext pairs chosen uniformly at random.

Parameters
ninputsnumber of input chosen plaintext pairs.
dainput difference.
dboutput difference.
lsh_constLSH constant.
rsh_constRSH constant.
Returns
$\mathrm{adp}^{f_\mathrm{LXR}}(da \rightarrow db)$
Note
For the exact computation refer to adp_xtea_f_lxr_exper
uint32_t adp_xtea_f_lxr_assign_bit_x ( const uint32_t  n,
const uint32_t  i,
const uint32_t  mask_i,
const uint32_t  x,
const uint32_t  lsh_const,
const uint32_t  rsh_const,
const uint32_t  dx,
const uint32_t  dy,
uint32_t *  x_cnt,
double *  prob 
)

Counts the number of values x for which the differential $(dx \rightarrow dy)$ for the $f_{\mathrm{LXR}}$ (xtea_f_lxr) function is satisfied. The algorithm works by recursively assigning the bits of x starting from bit position i and terminating at the MS bit n. The recursion proceeds to bit $(i+1)$ only if the differential is satisfied on the i LS bits. This is checked by applying adp_xtea_f_lxr_is_sat.

Parameters
nword size (terminating bit popsition).
icurrent bit position.
mask_imask on the i LS bits of x.
xinput value of size at least (i + rsh_const).
lsh_constLSH constant.
rsh_constRSH constant.
dxinput difference.
dyoutput difference.
x_cntnumber of values satisfying $(dx \rightarrow dy)$.
probthe probability $\mathrm{adp}^{f_\mathrm{LXR}}(dx \rightarrow dy)$.
Returns
1 if $x[i-1:0]$ satisfies $(dx[i-1:0] \rightarrow dy[i-1:0])$; 0 otherwise.
See Also
adp_xtea_f_lxr
bool adp_xtea_f_lxr_check_x ( const uint32_t  lsh_const,
const uint32_t  rsh_const,
const uint32_t  dx,
const uint32_t  dy,
const uint32_t  x 
)

Check if a given value x satisfies the ADD differential $(dx \rightarrow dy)$ for the function $f_{\mathrm{LXR}}$ (xtea_f_lxr).

Parameters
lsh_constLSH constant.
rsh_constRSH constant.
dxinput difference.
dyoutput difference.
xinput value.
Returns
TRUE if $dy = f_{\mathrm{LXR}}(x + dx) - f_{\mathrm{LXR}}(x)$.
double adp_xtea_f_lxr_exper ( const uint32_t  da,
const uint32_t  db,
uint32_t  lsh_const,
uint32_t  rsh_const 
)

Compute the ADD differential probability of the $f_{\mathrm{LXR}}$ (xtea_f_lxr) component of the F-function of block cipher XTEA, through exhaustive search over all input values. Complexity: $O(2^n)$.

Parameters
dainput difference.
dboutput difference.
lsh_constLSH constant.
rsh_constRSH constant.
Returns
$\mathrm{adp}^{f_\mathrm{LXR}}(da \rightarrow db)$
bool adp_xtea_f_lxr_is_sat ( const uint32_t  mask_i,
const uint32_t  lsh_const,
const uint32_t  rsh_const,
const uint32_t  dx,
const uint32_t  dy,
int32_t  x 
)

Check if the differential $(dx \rightarrow dy)$ for the function $f_{\mathrm{LXR}}$ (xtea_f_lxr) is satisfied on the i LS bits of x i.e. check if

$dy[i-1:0] = f_{\mathrm{LXR}}(x[i-1:0] + dx[i-1:0]) - f_{\mathrm{LXR}}(x[i-1:0]) ~\mathrm{mod} ~2^{i}$.

Attention
x must be of size at least $(i + R)$ bits where R is the RSH constant of $f_{\mathrm{LXR}}$.
Parameters
mask_ii bit mask.
lsh_constLSH constant.
rsh_constRSH constant.
dxinput difference.
dyoutput difference.
xinput value of size at least (i + rsh_const).
Returns
TRUE if $dy[i-1:0] = f_{\mathrm{LXR}}(x[i-1:0] + dx[i-1:0]) - f_{\mathrm{LXR}}(x[i-1:0]) ~\mathrm{mod} ~2^{i}$.
double first_nz_adp_xtea_f ( gsl_matrix *  A[2][2][2],
gsl_matrix *  AA[2][2][2],
const uint32_t  key,
const uint32_t  delta,
const uint32_t  da,
uint32_t *  ret_dd,
uint32_t  lsh_const,
uint32_t  rsh_const 
)

For the XTEA F-function (xtea_f), for fixed input difference da, compute an arbitrary dd such that the differential $(da \rightarrow dd)$ has non-zero probability.

The procedure approximates the ADP of the TEA F-function as a multiplication of the ADP of its three non-linear components (w.r.t. ADD differences): the two XOR operations and the RSH operation (see xtea_f):

$\mathrm{adp}^{F}(k, \delta |~ dx \rightarrow dy) = \mathrm{adp}^{\oplus} \cdot \mathrm{adp}^{\gg} \cdot \mathrm{adp}^{\oplus}_{\mathrm{FI}}$

Algorithm sketch:

  1. Compute $ dy: \mathrm{max}_{dc[i]}~\mathrm{adp}^{\oplus}(db, dc[i] \rightarrow dy) $, where $dc[i] \in \{(da \gg 5), (da \gg 5) + 1, (da \gg 5) - 2^{n-5}, (da \gg 5) - 2^{n-5} + 1\}$, is one of the four possible ADD differences after RSH (adp_rsh).
  2. Compute $dt = dy + da$.
  3. Compute $ dd:\mathrm{max}_{dd}~\mathrm{adp}^{\oplus}((k + \delta), dt \rightarrow dd)$.
  4. For the computed da and dd experimenttaly re-adjust the probability using adp_xtea_f_approx.
    Note
    At this step the exact probability can also be computed with adp_xtea_f which is more accurate but less efficient.
  5. Return the adjusted probability p and dd.
Attention
it is still possible that p = 0.0 for some da.
Parameters
Atransition probability matrices for $\mathrm{adp}^{\oplus}$ (adp_xor_sf).
AAtransition probability matrices for $\mathrm{adp}^{\oplus}$ with FI (adp_xor_fixed_input_sf).
keyround key.
deltaround constant.
dainput difference.
ret_ddoutput difference.
lsh_constLSH constant.
rsh_constRSH constant.
Returns
$\mathrm{adp}^{F}(k, \delta |~ da \rightarrow dd)$
double max_dx_adp_xtea_f ( const uint32_t  n,
uint32_t *  ret_dx,
const uint32_t  dy,
const uint32_t  key,
const uint32_t  delta,
const uint32_t  lsh_const,
const uint32_t  rsh_const 
)

For given output difference dy, compute the maximum probability input differences dx over all input differences: $\mathrm{max}_{dx} ~\mathrm{adp}^{F}(k, \delta |~ dx \rightarrow dy)$ through exhaustive search over all input values and input differences. Complexity: $O(2^{2n})$.

Parameters
nword size.
ret_dxmaximum probability input difference.
dyoutput difference.
keyround key.
deltaround constant.
lsh_constLSH constant.
rsh_constRSH constant.
Returns
$\mathrm{max}_{dx} ~\mathrm{adp}^{F}(k, \delta |~ dx \rightarrow dy)$.
See Also
max_dx_adp_f_fk
double max_dx_adp_xtea_f_exper ( uint32_t *  dx_max,
const uint32_t  dy,
const uint32_t  k,
const uint32_t  delta,
const uint32_t  lsh_const,
const uint32_t  rsh_const 
)

For given output difference dy, compute the maximum probability input differences dx over all input differences: $\mathrm{max}_{dx} ~\mathrm{adp}^{F}(k, \delta |~ dx \rightarrow dy)$ through exhaustive search over all input values and input differences. Complexity: $O(2^{2n})$.

Parameters
dx_maxmaximum probability input difference.
dyoutput difference.
kround key.
deltaround constant.
lsh_constLSH constant.
rsh_constRSH constant.
Returns
$\mathrm{max}_{dx} ~\mathrm{adp}^{F}(k, \delta |~ dx \rightarrow dy)$.
See Also
max_dx_adp_f_fk
double max_dy_adp_xtea_f ( const uint32_t  n,
const uint32_t  dx,
uint32_t *  ret_dy,
const uint32_t  key,
const uint32_t  delta,
const uint32_t  lsh_const,
const uint32_t  rsh_const 
)

For given input difference dx, compute the maximum probability output difference dy over all output differences: $\mathrm{max}_{dy} ~\mathrm{adp}^{F}(k, \delta |~ dx \rightarrow dy)$. Complexity: $ O(2n) < c \le O(2^{2n}) $. Memory requirement: $4 \cdot 2^n$ Bytes.

Parameters
nword size.
dxinput difference.
ret_dymaximum probability output difference.
keyround key.
deltaround constant.
lsh_constLSH constant.
rsh_constRSH constant.
Returns
$\mathrm{max}_{dx} ~\mathrm{adp}^{F}(k, \delta |~ dx \rightarrow dy)$.
See Also
adp_f_assign_bit_x_dy, max_dx_adp_f_fk
double max_dy_adp_xtea_f_exper ( const uint32_t  dx,
uint32_t *  dy_max,
const uint32_t  k,
const uint32_t  delta,
const uint32_t  lsh_const,
const uint32_t  rsh_const 
)

For given input difference dx, compute the maximum probability output difference dy over all output differences: $\mathrm{max}_{dy} ~\mathrm{adp}^{F}(k, \delta |~ dx \rightarrow dy)$ through exhaustive search over all input values and input differences. Complexity: $O(2^{2n})$.

Parameters
dxinput difference.
dy_maxmaximum probability output difference.
kround key.
deltaround constant.
lsh_constLSH constant.
rsh_constRSH constant.
Returns
$\mathrm{max}_{dx} ~\mathrm{adp}^{F}(k, \delta |~ dx \rightarrow dy)$.
See Also
max_dy_adp_f_fk