+++ /dev/null
-/* -*-c-*-
- *
- * Simple and efficient universal hashing for hashtables
- *
- * (c) 2003 Straylight/Edgeware
- */
-
-/*----- Licensing notice --------------------------------------------------*
- *
- * This file is part of the mLib utilities library.
- *
- * mLib 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.
- *
- * mLib 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 mLib; if not, write to the Free
- * Software Foundation, Inc., 59 Temple Place - Suite 330, Boston,
- * MA 02111-1307, USA.
- */
-
-#ifndef MLIB_UNIHASH_H
-#define MLIB_UNIHASH_H
-
-#ifdef __cplusplus
- extern "C" {
-#endif
-
-
-/*----- Concept -----------------------------------------------------------*
- *
- * Let %$\gf{q}$% be a finite field. Choose an arbitrary %$k \inr \gf{q}$%.
- * Let %$M$% be a message. Injectively pad %$M$% and split it into blocks
- * $m_{n-1}, m_{n-2}, \ldots, m_2, m_1, m_0$% in %$\gf{q}%.
- * Then we compute
- *
- * %$H_k(M) = k^{n+1} + \sum_{0\le i<n} m_i k^{i+1}.$%
- *
- * Note that %$H_0(M) = 0$% for all messages %$M$%.
- *
- * If we deal with messages at most %$\ell$% blocks long then %$H_k(\cdot)$%
- * is %$(\ell + 1)/q$%-almost universal. Moreover, if %$q = 2^f$% then
- * %$H_k(\cdot)$% is %$(\ell + 1)/q$%-almost XOR-universal.
- *
- * Proof. Let %$A$% and %$B$% be two messages, represented by
- * %$a_{n-1}, \ldots, a_0$% and %$b_{m-1}, \ldots, b_0$% respectively; and
- * choose any %$\delta \in \gf{q}$%. We must bound the probability that
- *
- * %$k^{n+1} + a_{n-1} k^{n} + \cdots + a_1 k^2 + a_0 k - {}$%
- * %$k^{m+1} - b_{m-1} k^{m} - \cdots - b_1 k^2 - b_0 k = \delta$%.
- *
- * Firstly, we claim that if %$A$% and %$B$% are distinct, there is some
- * nonzero coefficient of %$k$%. For if %$n \ne m$% then, without loss of
- * generality, let %$n > m$%, and hence the coefficient of %$k_n$% is
- * nonzero. Alternatively, if %$n = m$% then there must be some
- * %$i \in \{ 0, \ldots, n - 1 \}$% with %$a_i \ne b_i$%, for otherwise the
- * messages would be identical; but then the coefficient of %$k^{i+1}$% is
- * %$a_i - b_i \ne 0$%.
- *
- * Hence we have a polynomial equation with degree at most %$\ell + 1$%;
- * there must be at most %$\ell + 1$% solutions for %$k$%; but we choose
- * %$k$% at random from a set of %$q$%; so the equation is true with
- * probability at most %$(\ell + 1)/q$%.
- *
- * This function can be used as a simple MAC with provable security against
- * computationally unbounded adversaries. Simply XOR the hash with a random
- * string indexed from a large random pad by some nonce sent with the
- * message. The probability of a forgery attempt being successful is then
- * %$(\ell + 1)/2^t$%, where %$t$% is the tag length and %$\ell$% is the
- * longest message permitted.
- */
-
-/*----- Practicalities ----------------------------------------------------*
- *
- * We work in %$\gf{2^32}$%, represented as a field of polynomials modulo
- * %$\texttt{104c11db7}_x$% (this is the standard CRC-32 polynomial). Our
- * blocks are bytes.
- *
- * The choice of a 32-bit hash is made for pragmatic reasons: we're never
- * likely to actually want all 32 bits for a real hashtable anyway. The
- * truncation result is needed to keep us afloat with smaller tables.
- *
- * We compute hashes using a slightly unrolled version of Horner's rule,
- * using the recurrence:
- *
- * %$a_{i+b} = (a_i + m_i) k^b + m_{i+1} k^{b-1} + \cdots + m_{i+b-1} k$%
- *
- * which involves one full-width multiply and %$b - 1$% one-byte multiplies;
- * the latter may be efficiently computed using a table lookup. Start with
- * %$a_0 = k$%.
- *
- * We precompute tables %$S[\cdot][\cdot][\cdot]$%, where
- *
- * %$S[u][v][w] = k^{u+1} x^{8v} w$%
- * for %$0 \le u < b$%, %$0 \le v < 4$%, %$0 \le w < 256)$%.
- *
- * A one-byte multiply is one lookup; a full-width multiply is four lookups
- * and three XORs. The processing required is then %$b + 3$% lookups and
- * %$b + 3$% XORs per batch, or %$(b + 3)/b$% lookups and XORs per byte, at
- * the expense of %$4 b$% kilobytes of tables. This compares relatively
- * favorably with CRC32. Indeed, in tests, this implementation with $b = 4$%
- * is faster than a 32-bit CRC.
- */
-
-/*----- Header files ------------------------------------------------------*/
-
-#include <stddef.h>
-
-#ifndef MLIB_BITS_H
-# include "bits.h"
-#endif
-
-/*----- Data structures ---------------------------------------------------*/
-
-#define UNIHASH_NBATCH 4
-#define UNIHASH_POLY 0x04c11db7 /* From CRC32 */
-
-typedef struct unihash_info {
- uint32 s[UNIHASH_NBATCH][4][256]; /* S-tables as described */
-} unihash_info;
-
-/*----- A global hash-info table ------------------------------------------*/
-
-extern unihash_info unihash_global; /* Key this if you like */
-
-/*----- Functions provided ------------------------------------------------*/
-
-/* --- @unihash_setkey@ --- *
- *
- * Arguments: @unihash_info *i@ = where to store the precomputed tables
- * @uint32 k@ = the key to set, randomly chosen
- *
- * Returns: ---
- *
- * Use: Calculates the tables required for efficient hashing.
- */
-
-extern void unihash_setkey(unihash_info */*i*/, uint32 /*k*/);
-
-/* --- @unihash_hash@ --- *
- *
- * Arguments: @const unihash_info *i@ = pointer to precomputed table
- * @uint32 a@ = @UNIHASH_INIT(i)@ or value from previous call
- * @const void *p@ = pointer to data to hash
- * @size_t sz@ = size of the data
- *
- * Returns: Hash of data so far.
- *
- * Use: Hashes data. Call this as many times as needed.
- */
-
-#define UNIHASH_INIT(i) ((i)->s[0][0][1]) /* %$k$% */
-
-extern uint32 unihash_hash(const unihash_info */*i*/, uint32 /*a*/,
- const void */*p*/, size_t /*sz*/);
-
-/* --- @unihash@ --- *
- *
- * Arguments: @const unihash_info *i@ = precomputed tables
- * @const void *p@ = pointer to data to hash
- * @size_t sz@ = size of the data
- *
- * Returns: The hash value computed.
- *
- * Use: All-in-one hashing function. No faster than using the
- * separate calls, but more convenient.
- */
-
-#define UNIHASH(i, p, sz) (unihash_hash((i), UNIHASH_INIT((i)), (p), (sz)))
-
-extern uint32 unihash(const unihash_info */*i*/,
- const void */*p*/, size_t /*sz*/);
-
-/*----- That's all, folks -------------------------------------------------*/
-
-#ifdef __cplusplus
- }
-#endif
-
-#endif
~mdw / mLib / blobdiff