X-Git-Url: https://git.distorted.org.uk/u/mdw/catacomb/blobdiff_plain/ba6e6b64033b1f9de49feccb5c9cd438354481f7..0f00dc4c8eb47e67bc0f148c2dd109f73a451e0a:/rand/maurer.c diff --git a/rand/maurer.c b/rand/maurer.c new file mode 100644 index 0000000..d66194e --- /dev/null +++ b/rand/maurer.c @@ -0,0 +1,233 @@ +/* -*-c-*- + * + * Maurer's universal statistical test + * + * (c) 2000 Straylight/Edgeware + */ + +/*----- Licensing notice --------------------------------------------------* + * + * This file is part of Catacomb. + * + * Catacomb is free software; you can redistribute it and/or modify + * it under the terms of the GNU Library General Public License as + * published by the Free Software Foundation; either version 2 of the + * License, or (at your option) any later version. + * + * Catacomb is distributed in the hope that it will be useful, + * but WITHOUT ANY WARRANTY; without even the implied warranty of + * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the + * GNU Library General Public License for more details. + * + * You should have received a copy of the GNU Library General Public + * License along with Catacomb; if not, write to the Free + * Software Foundation, Inc., 59 Temple Place - Suite 330, Boston, + * MA 02111-1307, USA. + */ + +/*----- Header files ------------------------------------------------------*/ + +#include +#include +#include +#include + +#include +#include + +#include "maurer.h" + +/*----- Data structures ---------------------------------------------------*/ + +typedef struct bitscan { + const octet *p; + unsigned b; + uint32 a; +} bitscan; + +/*----- Main code ---------------------------------------------------------*/ + +/* --- @maurer_init@ --- * + * + * Arguments: @maurer_ctx *m@ = pointer to a context to initialize + * @unsigned l@ = number of bits to take at a time + * + * Returns: Minimum recommended amount of data to test. + * + * Use: Initializes a Maurer testing context. Note that @l@ values + * larger than 16 are not supported, and values less than 6 can + * give bizarre results. + */ + +unsigned long maurer_init(maurer_ctx *m, unsigned l) +{ + size_t i; + + assert(((void)"(maurer_init): chunks larger than 16 bits not supported", + 0 < l && l <= 16)); + + m->l = l; + m->a = 0; + m->b = 0; + m->n = 0; + m->x = 0; + + m->t = xmalloc(sizeof(unsigned long) << l); + for (i = 0; i < (1 << l); i++) + m->t[i] = 0; + return (((1000ul << l) * l + 7)/8); +} + +/* --- @bits@ --- * + * + * Arguments: @maurer_ctx *m@ = pointer to testing context + * @const octet **p@ = address of a buffer pointer + * @const octet *q@ = limit of the buffer pointer + * @unsigned *x@ = address to store next chunk + * + * Returns: Nonzero if some more bits arrived. + * + * Use: Reads some bits from a buffer. + */ + +static int bits(maurer_ctx *m, const octet **p, const octet *q, unsigned *x) +{ + while (m->b < m->l) { + if (*p >= q) + return (0); + m->a |= U8(*(*p)++) << m->b; + m->b += 8; + } + *x = m->a & ((1 << m->l) - 1); + m->a >>= m->l; + m->b -= m->l; + m->n++; + return (1); +} + +/* --- @maurer_test@ --- * + * + * Arguments: @maurer_ctx *m@ = pointer to a Maurer testing context + * @const void *buf@ = pointer to a buffer of data + * @size_t sz@ = size of the buffer + * + * Returns: --- + * + * Use: Scans a buffer of data and updates the testing context. + */ + +void maurer_test(maurer_ctx *m, const void *buf, size_t sz) +{ + const octet *p = buf, *l = p + sz; + unsigned long q = 10 << m->l; + unsigned x; + + /* --- Initialize the table --- */ + + while (m->n < q) { + if (!bits(m, &p, l, &x)) + return; + m->t[x] = m->n; + } + + /* --- Update the statistic --- */ + + while (bits(m, &p, l, &x)) { + m->x += log(m->n - m->t[x]); + m->t[x] = m->n; + } +} + +/* --- @maurer_done@ --- * + * + * Arguments: @maurer_ctx *m@ = pointer to a Maurer testing context + * + * Returns: The statistic %$Z_u = (X_u - \mu)/\sigma$%, which should be + * normally distributed with a mean of 0 and variance of 1. + * + * Use: Returns the result of Maurer's universal statistical test. + * Also frees the memory allocated during initialization. + * + * If insufficient data was received, the value @HUGE_VAL@ is + * returned. + */ + +double maurer_done(maurer_ctx *m) +{ + double x, mu, c, sigma; + unsigned long q = 10 << m->l, k; + + /* --- Table for means and variances --- */ + + struct { double mu, var_1; } vtab[] = { + { 0.7326495, 0.690 }, + { 1.5374383, 1.338 }, + { 2.4016068, 1.901 }, + { 3.3112247, 2.358 }, + { 4.2534266, 2.705 }, + { 5.2177052, 2.945 }, + { 6.1962507, 3.125 }, + { 7.1836656, 3.238 }, + { 8.1764248, 3.311 }, + { 9.1723243, 3.356 }, + { 10.170032 , 3.384 }, + { 11.168765 , 3.401 }, + { 12.168070 , 3.410 }, + { 13.167693 , 3.416 }, + { 14.167488 , 3.419 }, + { 15.167379 , 3.421 } + }; + + /* --- Check for bogus requests --- */ + + if (m->n < q) { + x = HUGE_VAL; + goto done; + } + + /* --- Do the maths --- * + * + * This produces %$X_u$%, which should be normally distributed with a mean + * and variance we can compute. + */ + + k = m->n - q; + x = m->x/(k * log(2)); + + /* --- Now translate this into %$Z_u$% distributed as %$N(0, 1)$% --- */ + + mu = vtab[m->l - 1].mu; + c = 0.7 - 0.8/m->l + (1.6 + 12.8/m->l) * pow(k, -4.0/m->l); + sigma = sqrt(c * c * vtab[m->l - 1].var_1 / k); + x = (x - mu)/sigma; + + /* --- Done (phew!) --- */ + +done: + xfree(m->t); + return (x); +} + +/* --- @maurer@ --- * + * + * Arguments: @const octet *p@ = pointer to a buffer of data + * @size_t sz@ = size of the buffer + * @unsigned l@ = number of bits to take at a time + * + * Returns: The statistic %$Z_u$%. + * + * Use: Simple interface to Maurer's universal statistical test. For + * large %$l$% you should use the more complicated restartable + * interface. + */ + +double maurer(const octet *p, size_t sz, unsigned l) +{ + maurer_ctx m; + + maurer_init(&m, l); + maurer_test(&m, p, sz); + return (maurer_done(&m)); +} + +/*----- That's all, folks -------------------------------------------------*/