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/*
* stats.c
*
* statistical tests for randomness (FIPS 140-2, Section 4.9)
*
* David A. McGrew
* Cisco Systems, Inc.
*/
#include "stat.h"
debug_module_t mod_stat = {
0, /* debugging is off by default */
(char *)"stat test" /* printable module name */
};
/*
* each test assumes that 20,000 bits (2500 octets) of data is
* provided as input
*/
#define STAT_TEST_DATA_LEN 2500
err_status_t
stat_test_monobit(uint8_t *data) {
uint8_t *data_end = data + STAT_TEST_DATA_LEN;
uint16_t ones_count;
ones_count = 0;
while (data < data_end) {
ones_count += octet_get_weight(*data);
data++;
}
debug_print(mod_stat, "bit count: %d", ones_count);
if ((ones_count < 9725) || (ones_count > 10275))
return err_status_algo_fail;
return err_status_ok;
}
err_status_t
stat_test_poker(uint8_t *data) {
int i;
uint8_t *data_end = data + STAT_TEST_DATA_LEN;
double poker;
uint16_t f[16] = {
0, 0, 0, 0, 0, 0, 0, 0,
0, 0, 0, 0, 0, 0, 0, 0
};
while (data < data_end) {
f[*data & 0x0f]++; /* increment freq. count for low nibble */
f[(*data) >> 4]++; /* increment freq. count for high nibble */
data++;
}
poker = 0.0;
for (i=0; i < 16; i++)
poker += (double) f[i] * f[i];
poker *= (16.0 / 5000.0);
poker -= 5000.0;
debug_print(mod_stat, "poker test: %f\n", poker);
if ((poker < 2.16) || (poker > 46.17))
return err_status_algo_fail;
return err_status_ok;
}
/*
* runs[i] holds the number of runs of size (i-1)
*/
err_status_t
stat_test_runs(uint8_t *data) {
uint8_t *data_end = data + STAT_TEST_DATA_LEN;
uint16_t runs[6] = { 0, 0, 0, 0, 0, 0 };
uint16_t gaps[6] = { 0, 0, 0, 0, 0, 0 };
uint16_t lo_value[6] = { 2315, 1114, 527, 240, 103, 103 };
uint16_t hi_value[6] = { 2685, 1386, 723, 384, 209, 209 };
int state = 0;
uint16_t mask;
int i;
/*
* the state variable holds the number of bits in the
* current run (or gap, if negative)
*/
while (data < data_end) {
/* loop over the bits of this byte */
for (mask = 1; mask < 256; mask <<= 1) {
if (*data & mask) {
/* next bit is a one */
if (state > 0) {
/* prefix is a run, so increment the run-count */
state++;
/* check for long runs */
if (state > 25) {
debug_print(mod_stat, ">25 runs: %d", state);
return err_status_algo_fail;
}
} else if (state < 0) {
/* prefix is a gap */
if (state < -25) {
debug_print(mod_stat, ">25 gaps: %d", state);
return err_status_algo_fail; /* long-runs test failed */
}
if (state < -6) {
state = -6; /* group together gaps > 5 */
}
gaps[-1-state]++; /* increment gap count */
state = 1; /* set state at one set bit */
} else {
/* state is zero; this happens only at initialization */
state = 1;
}
} else {
/* next bit is a zero */
if (state > 0) {
/* prefix is a run */
if (state > 25) {
debug_print(mod_stat, ">25 runs (2): %d", state);
return err_status_algo_fail; /* long-runs test failed */
}
if (state > 6) {
state = 6; /* group together runs > 5 */
}
runs[state-1]++; /* increment run count */
state = -1; /* set state at one zero bit */
} else if (state < 0) {
/* prefix is a gap, so increment gap-count (decrement state) */
state--;
/* check for long gaps */
if (state < -25) {
debug_print(mod_stat, ">25 gaps (2): %d", state);
return err_status_algo_fail;
}
} else {
/* state is zero; this happens only at initialization */
state = -1;
}
}
}
/* move along to next octet */
data++;
}
if (mod_stat.on) {
debug_print(mod_stat, "runs test", NULL);
for (i=0; i < 6; i++)
debug_print(mod_stat, " runs[]: %d", runs[i]);
for (i=0; i < 6; i++)
debug_print(mod_stat, " gaps[]: %d", gaps[i]);
}
/* check run and gap counts against the fixed limits */
for (i=0; i < 6; i++)
if ( (runs[i] < lo_value[i] ) || (runs[i] > hi_value[i])
|| (gaps[i] < lo_value[i] ) || (gaps[i] > hi_value[i]))
return err_status_algo_fail;
return err_status_ok;
}
/*
* the function stat_test_rand_source applys the FIPS-140-2 statistical
* tests to the random source defined by rs
*
*/
#define RAND_SRC_BUF_OCTETS 50 /* this value MUST divide 2500! */
err_status_t
stat_test_rand_source(rand_source_func_t get_rand_bytes) {
int i;
double poker;
uint8_t *data, *data_end;
uint16_t f[16] = {
0, 0, 0, 0, 0, 0, 0, 0,
0, 0, 0, 0, 0, 0, 0, 0
};
uint8_t buffer[RAND_SRC_BUF_OCTETS];
err_status_t status;
int ones_count = 0;
uint16_t runs[6] = { 0, 0, 0, 0, 0, 0 };
uint16_t gaps[6] = { 0, 0, 0, 0, 0, 0 };
uint16_t lo_value[6] = { 2315, 1114, 527, 240, 103, 103 };
uint16_t hi_value[6] = { 2685, 1386, 723, 384, 209, 209 };
int state = 0;
uint16_t mask;
/* counters for monobit, poker, and runs tests are initialized above */
/* main loop: fill buffer, update counters for stat tests */
for (i=0; i < 2500; i+=RAND_SRC_BUF_OCTETS) {
/* fill data buffer */
status = get_rand_bytes(buffer, RAND_SRC_BUF_OCTETS);
if (status) {
debug_print(mod_stat, "couldn't get rand bytes: %d",status);
return status;
}
#if 0
debug_print(mod_stat, "%s",
octet_string_hex_string(buffer, RAND_SRC_BUF_OCTETS));
#endif
data = buffer;
data_end = data + RAND_SRC_BUF_OCTETS;
while (data < data_end) {
/* update monobit test counter */
ones_count += octet_get_weight(*data);
/* update poker test counters */
f[*data & 0x0f]++; /* increment freq. count for low nibble */
f[(*data) >> 4]++; /* increment freq. count for high nibble */
/* update runs test counters */
/* loop over the bits of this byte */
for (mask = 1; mask < 256; mask <<= 1) {
if (*data & mask) {
/* next bit is a one */
if (state > 0) {
/* prefix is a run, so increment the run-count */
state++;
/* check for long runs */
if (state > 25) {
debug_print(mod_stat, ">25 runs (3): %d", state);
return err_status_algo_fail;
}
} else if (state < 0) {
/* prefix is a gap */
if (state < -25) {
debug_print(mod_stat, ">25 gaps (3): %d", state);
return err_status_algo_fail; /* long-runs test failed */
}
if (state < -6) {
state = -6; /* group together gaps > 5 */
}
gaps[-1-state]++; /* increment gap count */
state = 1; /* set state at one set bit */
} else {
/* state is zero; this happens only at initialization */
state = 1;
}
} else {
/* next bit is a zero */
if (state > 0) {
/* prefix is a run */
if (state > 25) {
debug_print(mod_stat, ">25 runs (4): %d", state);
return err_status_algo_fail; /* long-runs test failed */
}
if (state > 6) {
state = 6; /* group together runs > 5 */
}
runs[state-1]++; /* increment run count */
state = -1; /* set state at one zero bit */
} else if (state < 0) {
/* prefix is a gap, so increment gap-count (decrement state) */
state--;
/* check for long gaps */
if (state < -25) {
debug_print(mod_stat, ">25 gaps (4): %d", state);
return err_status_algo_fail;
}
} else {
/* state is zero; this happens only at initialization */
state = -1;
}
}
}
/* advance data pointer */
data++;
}
}
/* check to see if test data is within bounds */
/* check monobit test data */
debug_print(mod_stat, "stat: bit count: %d", ones_count);
if ((ones_count < 9725) || (ones_count > 10275)) {
debug_print(mod_stat, "stat: failed monobit test %d", ones_count);
return err_status_algo_fail;
}
/* check poker test data */
poker = 0.0;
for (i=0; i < 16; i++)
poker += (double) f[i] * f[i];
poker *= (16.0 / 5000.0);
poker -= 5000.0;
debug_print(mod_stat, "stat: poker test: %f", poker);
if ((poker < 2.16) || (poker > 46.17)) {
debug_print(mod_stat, "stat: failed poker test", NULL);
return err_status_algo_fail;
}
/* check run and gap counts against the fixed limits */
for (i=0; i < 6; i++)
if ((runs[i] < lo_value[i] ) || (runs[i] > hi_value[i])
|| (gaps[i] < lo_value[i] ) || (gaps[i] > hi_value[i])) {
debug_print(mod_stat, "stat: failed run/gap test", NULL);
return err_status_algo_fail;
}
debug_print(mod_stat, "passed random stat test", NULL);
return err_status_ok;
}
err_status_t
stat_test_rand_source_with_repetition(rand_source_func_t source, unsigned num_trials) {
unsigned int i;
err_status_t err = err_status_algo_fail;
for (i=0; i < num_trials; i++) {
err = stat_test_rand_source(source);
if (err == err_status_ok) {
return err_status_ok;
}
debug_print(mod_stat, "failed stat test (try number %d)\n", i);
}
return err;
}
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