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adp-tea-f-fk.cc File Reference

The ADD differential probability of the F-function of TEA for a fixed key and round constants $\mathrm{adp}^{F}(k_0, k_1, \delta |~ da \rightarrow dd)$, where $ F(k_0, k_1, \delta |~ x) = ((x \ll 4) + k_0) \oplus (x + \delta) \oplus ((x \gg 5) + k_1)$ Complexity: $ O(n) < c \le O(2^n) $. More...

#include "common.hh"
#include "tea.hh"

Functions

bool adp_f_check_x (const uint32_t lsh_const, const uint32_t rsh_const, const uint32_t k0, const uint32_t k1, const uint32_t delta, const uint32_t dx, const uint32_t dy, const uint32_t x)
 
bool adp_f_is_sat (const uint32_t mask_i, const uint32_t lsh_const, const uint32_t rsh_const, const uint32_t k0, const uint32_t k1, const uint32_t delta, const uint32_t dx, const uint32_t dy, int32_t x)
 
uint32_t adp_f_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 k0, const uint32_t k1, const uint32_t delta, const uint32_t dx, const uint32_t dy, uint32_t *x_cnt, double *prob)
 
double adp_f_fk (const uint32_t n, const uint32_t dx, const uint32_t dy, const uint32_t k0, const uint32_t k1, const uint32_t delta, const uint32_t lsh_const, const uint32_t rsh_const)
 
uint32_t adp_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 k0, const uint32_t k1, const uint32_t delta, const uint32_t dx, const uint32_t dy, uint64_t *x_cnt, double *ret_prob, uint32_t *ret_dx)
 
double max_dx_adp_f_fk (const uint32_t n, uint32_t *ret_dx, const uint32_t dy, const uint32_t k0, const uint32_t k1, const uint32_t delta, const uint32_t lsh_const, const uint32_t rsh_const)
 
uint32_t adp_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 k0, const uint32_t k1, const uint32_t delta, const uint32_t dx, const uint32_t dy, uint64_t *x_cnt, double *ret_prob, uint32_t *ret_dy)
 
double max_dy_adp_f_fk (const uint32_t n, const uint32_t dx, uint32_t *ret_dy, const uint32_t k0, const uint32_t k1, const uint32_t delta, const uint32_t lsh_const, const uint32_t rsh_const)
 
double all_dy_adp_f_fk (const uint32_t n, const uint32_t dx, uint32_t *ret_dy, const uint32_t k0, const uint32_t k1, const uint32_t delta, const uint32_t lsh_const, const uint32_t rsh_const, uint64_t *x_cnt)
 
uint32_t adp_f_assign_bit_x_dx_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 k0, const uint32_t k1, const uint32_t delta, const uint32_t dx, const uint32_t dy, differential_t *x_cnt, double *ret_prob, uint32_t *ret_dx, uint32_t *ret_dy)
 
double max_dx_dy_adp_f_fk (const uint32_t n, uint32_t *ret_dx, uint32_t *ret_dy, const uint32_t k0, const uint32_t k1, const uint32_t delta, const uint32_t lsh_const, const uint32_t rsh_const)
 
uint64_t *** x_cnt_alloc ()
 
void x_cnt_free (uint64_t ***x_cnt)
 
void x_cnt_print (uint32_t ***x_cnt)
 
uint32_t adp_f_assign_bit_x_dx_key (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 k0, const uint32_t k1, 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 *ret_k0, uint32_t *ret_k1)
 
double max_key_dx_adp_f_fk (const uint32_t n, uint32_t *ret_dx, const uint32_t dy, uint32_t *ret_k0, uint32_t *ret_k1, const uint32_t delta, const uint32_t lsh_const, const uint32_t rsh_const)
 
double adp_f_fk_v2 (const uint32_t da, const uint32_t dd, const uint32_t k0, const uint32_t k1, const uint32_t delta, const uint32_t lsh_const, const uint32_t rsh_const)
 
void f_sfun (const uint32_t n, const uint32_t x_word, const uint32_t dx_word, const uint32_t delta_word, const uint32_t k0_word, const uint32_t k1_word)
 
double adp_f_fk_exper (const uint32_t da, const uint32_t db, const uint32_t k0, const uint32_t k1, const uint32_t delta, uint32_t lsh_const, uint32_t rsh_const)
 
double max_dx_adp_f_fk_exper (uint32_t *max_dx, const uint32_t dy, const uint32_t k0, const uint32_t k1, const uint32_t delta, uint32_t lsh_const, uint32_t rsh_const)
 
double max_dy_adp_f_fk_exper (const uint32_t dx, uint32_t *max_dy, const uint32_t k0, const uint32_t k1, const uint32_t delta, uint32_t lsh_const, uint32_t rsh_const)
 
double max_dx_dy_adp_f_fk_exper (uint32_t *max_dx, uint32_t *max_dy, const uint32_t k0, const uint32_t k1, const uint32_t delta, uint32_t lsh_const, uint32_t rsh_const)
 

Detailed Description

The ADD differential probability of the F-function of TEA for a fixed key and round constants $\mathrm{adp}^{F}(k_0, k_1, \delta |~ da \rightarrow dd)$, where $ F(k_0, k_1, \delta |~ x) = ((x \ll 4) + k_0) \oplus (x + \delta) \oplus ((x \gg 5) + k_1)$ 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.

Function Documentation

uint32_t adp_f_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  k0,
const uint32_t  k1,
const uint32_t  delta,
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 TEA 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_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.
k0first round key.
k1second round key.
deltaround constant.
dxinput difference.
dyoutput difference.
x_cntnumber of values satisfying $(dx \rightarrow dy)$.
probthe fixed-key ADD probability of F: $\mathrm{adp}^{F}(k_0, k_1, \delta |~ dx \rightarrow dy)$.
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_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  k0,
const uint32_t  k1,
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).
lsh_constLSH constant.
rsh_constRSH constant.
k0first round key.
k1second round 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 dx.
ret_probthe maximum probability over all input differences $\mathrm{max}_{dx} ~\mathrm{adp}^{F}(k_0, k_1, \delta |~ dx \rightarrow dy)$.
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, max_dx_adp_f_fk
uint32_t adp_f_assign_bit_x_dx_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  k0,
const uint32_t  k1,
const uint32_t  delta,
const uint32_t  dx,
const uint32_t  dy,
differential_t *  x_cnt,
double *  ret_prob,
uint32_t *  ret_dx,
uint32_t *  ret_dy 
)

For the TEA F-functuion with fixed key and round constant, compute all differentials $(dx \rightarrow dy)$ and their probabilities.

The function works by recursively assigning the bits of x, dx 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.
k0first round key.
k1second round key.
deltaround constant.
dxinput difference.
dyoutput difference.
x_cntarray of $2^{2n}$ differentials $(dx \rightarrow dy)$ and their probabilities.
ret_probthe maximum probability over all input and output differences $\mathrm{max}_{dy,dy} ~\mathrm{adp}^{F}(k_0, k_1, \delta |~ dx \rightarrow dy)$.
ret_dxthe input difference of the maximum probability differential.
ret_dythe output difference of the maximum probability differential.
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, adp_f_assign_bit_x_dy.
uint32_t adp_f_assign_bit_x_dx_key ( 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  k0,
const uint32_t  k1,
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 *  ret_k0,
uint32_t *  ret_k1 
)

For the TEA F-function with fixed round constant, and for a fixed output difference dy, compute all differentials $(dx \rightarrow dy)$ and their probabilities for all values of the round keys k0, k1.

The function works by recursively assigning the bits of x, dx, k0 and k1 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.
k0first round key.
k1second round key.
deltaround constant.
dxinput difference.
dyoutput difference.
x_cntarray of $2^{3n}$ differentials $(dx \rightarrow dy)$ and their probabilities.
ret_probthe maximum probability over all input differences and round keys $\mathrm{max}_{dx,k_0,k_1} ~\mathrm{adp}^{F}(k_0, k_1, \delta |~ dx \rightarrow dy)$.
ret_dxthe input difference of the maximum probability differential.
ret_k0the first round key for the maximum probability differential.
ret_k1the second round key for the maximum probability differential.
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_key, adp_f_assign_bit_x_dx_dy.
uint32_t adp_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  k0,
const uint32_t  k1,
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.
k0first round key.
k1second round 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 $\mathrm{max}_{dy} ~\mathrm{adp}^{F}(k_0, k_1, \delta |~ dx \rightarrow dy)$.
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_f_check_x ( const uint32_t  lsh_const,
const uint32_t  rsh_const,
const uint32_t  k0,
const uint32_t  k1,
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 TEA F-function.

Parameters
lsh_constLSH constant.
rsh_constRSH constant.
k0first round key.
k1second round key.
deltaround constant.
dxinput difference.
dyoutput difference.
xinput value.
Returns
TRUE if $k_0, k_1, \delta:~ dy = F(x + dx) - F(x)$.
double adp_f_fk ( const uint32_t  n,
const uint32_t  dx,
const uint32_t  dy,
const uint32_t  k0,
const uint32_t  k1,
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 TEA: $\mathrm{adp}^{F}(k_0, k_1, \delta |~ dx \rightarrow dy)$. Complexity: $ O(n) < c \le O(2^n) $.

Parameters
nword size.
dxinput difference.
dyoutput difference.
k0first round key.
k1second round key.
deltaround constant.
lsh_constLSH constant.
rsh_constRSH constant.
Returns
$\mathrm{adp}^{F}(k_0, k_1, \delta |~ dx \rightarrow dy)$.
See Also
adp_f_assign_bit_x
double adp_f_fk_exper ( const uint32_t  da,
const uint32_t  db,
const uint32_t  k0,
const uint32_t  k1,
const uint32_t  delta,
uint32_t  lsh_const,
uint32_t  rsh_const 
)

Compute the fixed-key, fixed-constant ADD differential probability of the F-function of block cipher TEA: $\mathrm{adp}^{F}(k_0, k_1, \delta |~ dx \rightarrow dy)$ through exhaustive search over all input values. Complexity: $O(2^n)$.

Parameters
dainput difference.
dboutput difference.
k0first round key.
k1second round key.
deltaround constant.
lsh_constLSH constant.
rsh_constRSH constant.
Returns
$\mathrm{adp}^{F}(k_0, k_1, \delta |~ dx \rightarrow dy)$.
See Also
adp_f_fk, adp_f_fk_v2.
double adp_f_fk_v2 ( const uint32_t  da,
const uint32_t  dd,
const uint32_t  k0,
const uint32_t  k1,
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 TEA: $\mathrm{adp}^{F}(k_0, k_1, \delta |~ dx \rightarrow dy)$.

The function works by dividing the input to F into independent parts and iterating over the values in each part. The resulting complexity is equivalent to exhaustive search over all inputs: $O(2^n)$.

Parameters
dainput difference.
ddoutput difference.
k0first round key.
k1second round key.
deltaround constant.
lsh_constLSH constant.
rsh_constRSH constant.
Returns
$\mathrm{adp}^{F}(k_0, k_1, \delta |~ dx \rightarrow dy)$.
See Also
adp_f_fk
bool adp_f_is_sat ( const uint32_t  mask_i,
const uint32_t  lsh_const,
const uint32_t  rsh_const,
const uint32_t  k0,
const uint32_t  k1,
const uint32_t  delta,
const uint32_t  dx,
const uint32_t  dy,
int32_t  x 
)

Check if the differential $(dx \rightarrow dy)$ for F is satisfied on the i LS bits of x i.e. check if $k_0, k_1, \delta:~ dy[i-1:0] = F(x[i-1:0] + dx[i-1:0]) - F(x[i-1:0]) ~\mathrm{mod} ~2^{i}$.

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.
k0first round key.
k1second round key.
deltaround constant.
dxinput difference.
dyoutput difference.
xinput value of size at least (i + rsh_const).
Returns
TRUE if $k_0, k_1, \delta:~ dy[i-1:0] = F(x[i-1:0] + dx[i-1:0]) - F(x[i-1:0]) ~\mathrm{mod} ~2^{i}$.
double all_dy_adp_f_fk ( const uint32_t  n,
const uint32_t  dx,
uint32_t *  ret_dy,
const uint32_t  k0,
const uint32_t  k1,
const uint32_t  delta,
const uint32_t  lsh_const,
const uint32_t  rsh_const,
uint64_t *  x_cnt 
)

For given input difference dx, compute all output differences dy for the TEA F-function with fixed keys and round constants. Returns the maximum output probability.

Parameters
nword size.
dxinput difference.
ret_dymaximum probability output difference.
k0first round key.
k1second round key.
deltaround constant.
lsh_constLSH constant.
rsh_constRSH constant.
x_cntarray of $2^n$ counters - each one keeps track of the number of inputs x satisfying $(dx \rightarrow dy)$ for every dy.
Returns
$\mathrm{max}_{dy} ~\mathrm{adp}^{F}(k_0, k_1, \delta |~ dx \rightarrow dy)$.
See Also
max_dy_adp_f_fk
void f_sfun ( const uint32_t  n,
const uint32_t  x_word,
const uint32_t  dx_word,
const uint32_t  delta_word,
const uint32_t  k0_word,
const uint32_t  k1_word 
)

Compute the S-function for the TEA F function.

Parameters
nword size.
x_wordinput to F.
dx_wordinput difference.
delta_wordround constant.
k0_wordfirst round key.
k1_wordsecond round key.
double max_dx_adp_f_fk ( const uint32_t  n,
uint32_t *  ret_dx,
const uint32_t  dy,
const uint32_t  k0,
const uint32_t  k1,
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: $\mathrm{max}_{dx} ~\mathrm{adp}^{F}(k_0, k_1, \delta |~ dx \rightarrow dy)$. Complexity: $ O(2n) < c \le O(2^{2n}) $. Memory: $4 \cdot 2^n$ Bytes.

Parameters
nword size.
ret_dxmaximum probability input difference.
dyoutput difference.
k0first round key.
k1second round key.
deltaround constant.
lsh_constLSH constant.
rsh_constRSH constant.
Returns
$\mathrm{max}_{dx} ~\mathrm{adp}^{F}(k_0, k_1, \delta |~ dx \rightarrow dy)$.
See Also
adp_f_assign_bit_x_dx
double max_dx_adp_f_fk_exper ( uint32_t *  max_dx,
const uint32_t  dy,
const uint32_t  k0,
const uint32_t  k1,
const uint32_t  delta,
uint32_t  lsh_const,
uint32_t  rsh_const 
)

For given output difference dy, compute the maximum probability input differences dx over all input differences: $\mathrm{max}_{dx} ~\mathrm{adp}^{F}(k_0, k_1, \delta |~ dx \rightarrow dy)$ through exhaustive search over all input values and input differences. Complexity: $O(2^{2n})$.

Parameters
max_dxmaximum probability input difference.
dyoutput difference.
k0first round key.
k1second round key.
deltaround constant.
lsh_constLSH constant.
rsh_constRSH constant.
Returns
$\mathrm{max}_{dx} ~\mathrm{adp}^{F}(k_0, k_1, \delta |~ dx \rightarrow dy)$.
See Also
max_dx_adp_f_fk
double max_dx_dy_adp_f_fk ( const uint32_t  n,
uint32_t *  ret_dx,
uint32_t *  ret_dy,
const uint32_t  k0,
const uint32_t  k1,
const uint32_t  delta,
const uint32_t  lsh_const,
const uint32_t  rsh_const 
)

For the TEA F-functuion with fixed key and round constant, compute the maximum probability differential $(dx \rightarrow dy)$ over all input and output differences. Complexity: $ O(3n) < c \le O(2^{3n}) $. Memory: $12 \cdot 2^{2n}$ Bytes.

Parameters
nword size.
ret_dxthe input difference of the maximum probability differential.
ret_dythe output difference of the maximum probability differential.
k0first round key.
k1second round key.
deltaround constant.
lsh_constLSH constant.
rsh_constRSH constant.
Returns
$\mathrm{max}_{dx,dy} ~\mathrm{adp}^{F}(k_0, k_1, \delta |~ dx \rightarrow dy)$.
See Also
adp_f_assign_bit_x_dx_dy
double max_dx_dy_adp_f_fk_exper ( uint32_t *  max_dx,
uint32_t *  max_dy,
const uint32_t  k0,
const uint32_t  k1,
const uint32_t  delta,
uint32_t  lsh_const,
uint32_t  rsh_const 
)

For the TEA F-functuion with fixed key and round constant, compute the maximum probability differential $(dx \rightarrow dy)$ over all input and output differences. Complexity: $O(2^{3n})$.

Parameters
max_dxthe input difference of the maximum probability differential.
max_dythe output difference of the maximum probability differential.
k0first round key.
k1second round key.
deltaround constant.
lsh_constLSH constant.
rsh_constRSH constant.
Returns
$\mathrm{max}_{dx,dy} ~\mathrm{adp}^{F}(k_0, k_1, \delta |~ dx \rightarrow dy)$.
See Also
max_dx_dy_adp_f_fk
double max_dy_adp_f_fk ( const uint32_t  n,
const uint32_t  dx,
uint32_t *  ret_dy,
const uint32_t  k0,
const uint32_t  k1,
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: $\mathrm{max}_{dy} ~\mathrm{adp}^{F}(k_0, k_1, \delta |~ dx \rightarrow dy)$. 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.
k0first round key.
k1second round key.
deltaround constant.
lsh_constLSH constant.
rsh_constRSH constant.
Returns
$\mathrm{max}_{dy} ~\mathrm{adp}^{F}(k_0, k_1, \delta |~ dx \rightarrow dy)$.
See Also
adp_f_assign_bit_x_dy, max_dy_adp_f_fk
double max_dy_adp_f_fk_exper ( const uint32_t  dx,
uint32_t *  max_dy,
const uint32_t  k0,
const uint32_t  k1,
const uint32_t  delta,
uint32_t  lsh_const,
uint32_t  rsh_const 
)

For given input difference dx, compute the maximum probability output difference dy over all output differences: $\mathrm{max}_{dy} ~\mathrm{adp}^{F}(k_0, k_1, \delta |~ dx \rightarrow dy)$ through exhaustive search over all input values and input differences. Complexity: $O(2^{2n})$.

Parameters
dxinput difference.
max_dymaximum probability output difference.
k0first round key.
k1second round key.
deltaround constant.
lsh_constLSH constant.
rsh_constRSH constant.
Returns
$\mathrm{max}_{dx} ~\mathrm{adp}^{F}(k_0, k_1, \delta |~ dx \rightarrow dy)$.
See Also
max_dy_adp_f_fk
double max_key_dx_adp_f_fk ( const uint32_t  n,
uint32_t *  ret_dx,
const uint32_t  dy,
uint32_t *  ret_k0,
uint32_t *  ret_k1,
const uint32_t  delta,
const uint32_t  lsh_const,
const uint32_t  rsh_const 
)

For the TEA F-functuion with fixed key and round constant, compute the maximum probability differential $(dx \rightarrow dy)$ over all input differences and round keys. Complexity: $ O(4n) < c \le O(2^{4n}) $. Memory: $12 \cdot 2^{3n}$ Bytes.

Parameters
nword size.
dyoutput difference.
ret_dxthe input difference of the maximum probability differential.
ret_k0the first round key for the maximum probability differential.
ret_k1the second round key for the maximum probability differential.
deltaround constant.
lsh_constLSH constant.
rsh_constRSH constant.
Returns
$\mathrm{max}_{dx,k_0,k_1} ~\mathrm{adp}^{F}(k_0, k_1, \delta |~ dx \rightarrow dy)$.
See Also
adp_f_assign_bit_x_dx_key
uint64_t*** x_cnt_alloc ( )

Allocate memory for a 2D array of differentials.

Returns
2D array of differentials.
See Also
x_cnt_free
void x_cnt_free ( uint64_t ***  x_cnt)

Free the memory allocated from a previous call to x_cnt_alloc

Parameters
x_cnt2D array of differentials.
See Also
x_cnt_alloc
void x_cnt_print ( uint32_t ***  x_cnt)

Print the elements of a 2D array of differentials.

Parameters
x_cnt2D array of differentials.