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xdp-tea-f-fk.hh File Reference

Header file for xdp-tea-f-fk.cc. More...

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Functions

double xdp_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_xdp_f_fk_dx_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_xdp_f_fk_dy_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)
 
bool xdp_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)
 
bool xdp_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)
 
uint32_t xdp_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 xdp_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 xdp_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_xdp_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 xdp_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_xdp_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)
 

Detailed Description

Header file for xdp-tea-f-fk.cc.

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 max_dx_xdp_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: $\mathrm{max}_{dx} ~\mathrm{xdp}^{F}(k_0, k_1, \delta |~ dx \rightarrow dy)$. 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
$\mathrm{max}_{dx} ~\mathrm{xdp}^{F}(k_0, k_1, \delta |~ dx \rightarrow dy)$.
See Also
xdp_f_assign_bit_x_dx
double max_dy_xdp_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: $\mathrm{max}_{dy} ~\mathrm{xdp}^{F}(k_0, k_1, \delta |~ dx \rightarrow dy)$. 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
$\mathrm{max}_{dy} ~\mathrm{xdp}^{F}(k_0, k_1, \delta |~ dx \rightarrow dy)$.
See Also
xdp_f_assign_bit_x_dy, max_dy_xdp_f_fk
double max_xdp_f_fk_dx_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: $\mathrm{max}_{dx} ~\mathrm{xdp}^{F}(k_0, k_1, \delta |~ dx \rightarrow dy)$ 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
$\mathrm{max}_{dx} ~\mathrm{xdp}^{F}(k_0, k_1, \delta |~ dx \rightarrow dy)$.
See Also
max_dx_xdp_f_fk
double max_xdp_f_fk_dy_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: $\mathrm{max}_{dy} ~\mathrm{xdp}^{F}(k_0, k_1, \delta |~ dx \rightarrow dy)$ 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
$\mathrm{max}_{dx} ~\mathrm{xdp}^{F}(k_0, k_1, \delta |~ dx \rightarrow dy)$.
See Also
max_dy_xdp_f_fk
uint32_t xdp_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 xdp_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 XOR probability of F: $\mathrm{xdp}^{F}(k_0, k_1, \delta |~ dx \rightarrow dy)$.
Returns
1 if $x[i-1:0]$ satisfies $(dx[i-1:0] \rightarrow dy[i-1:0])$; 0 otherwise.
See Also
xdp_f_fk
uint32_t xdp_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 xdp_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 $\mathrm{max}_{dx} ~\mathrm{xdp}^{F}(k_0, k_1, \delta |~ dx \rightarrow dy)$.
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
xdp_f_assign_bit_x, max_dx_xdp_f_fk
uint32_t xdp_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 xdp_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 $\mathrm{max}_{dy} ~\mathrm{xdp}^{F}(k_0, k_1, \delta |~ dx \rightarrow dy)$.
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
xdp_f_assign_bit_x_dx
bool xdp_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 XOR 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 $k_0, k_1, \delta:~ dy = F(x \oplus dx) \oplus F(x)$.
double xdp_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 XOR differential probability of the F-function of block cipher TEA: $\mathrm{xdp}^{F}(k_0, k_1, \delta |~ dx \rightarrow dy)$. 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
$\mathrm{xdp}^{F}(k_0, k_1, \delta |~ dx \rightarrow dy)$.
See Also
xdp_f_assign_bit_x
double xdp_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 XOR differential probability of the F-function of block cipher TEA: $\mathrm{xdp}^{F}(k_0, k_1, \delta |~ dx \rightarrow dy)$ 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
$\mathrm{xdp}^{F}(k_0, k_1, \delta |~ dx \rightarrow dy)$.
See Also
xdp_f_fk
bool xdp_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 $k_0, k_1, \delta:~ dy[i-1:0] = F(x[i-1:0] \oplus dx[i-1:0]) \oplus F(x[i-1:0])$.

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 $k_0, k_1, \delta:~ dy[i-1:0] = F(x[i-1:0] \oplus dx[i-1:0]) \oplus F(x[i-1:0)$.