C的rand()有哪些常用的算法？

Question

我知道C规范没有给出任何关于rand()的具体实现的规范。在不同的主要平台上通常使用哪些不同的算法？它们有什么不同？

Answer 1

请参阅本文：http://en.wikipedia.org/wiki/List_of_random_number_generators

这是glibc的rand()的源代码

/* Reentrant random function from POSIX.1c.
   Copyright (C) 1996, 1999, 2009 Free Software Foundation, Inc.
   This file is part of the GNU C Library.
   Contributed by Ulrich Drepper <drepper@cygnus.com>, 1996.

   The GNU C Library is free software; you can redistribute it and/or
   modify it under the terms of the GNU Lesser General Public
   License as published by the Free Software Foundation; either
   version 2.1 of the License, or (at your option) any later version.

   The GNU C Library 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
   Lesser General Public License for more details.

   You should have received a copy of the GNU Lesser General Public
   License along with the GNU C Library; if not, write to the Free
   Software Foundation, Inc., 59 Temple Place, Suite 330, Boston, MA
   02111-1307 USA.  */

#include <stdlib.h>


/* This algorithm is mentioned in the ISO C standard, here extended
   for 32 bits.  */
int
rand_r (unsigned int *seed)
{
  unsigned int next = *seed;
  int result;

  next *= 1103515245;
  next += 12345;
  result = (unsigned int) (next / 65536) % 2048;

  next *= 1103515245;
  next += 12345;
  result <<= 10;
  result ^= (unsigned int) (next / 65536) % 1024;

  next *= 1103515245;
  next += 12345;
  result <<= 10;
  result ^= (unsigned int) (next / 65536) % 1024;

  *seed = next;

  return result;
}

来源：https://sourceware.org/git/?p=glibc.git;a=blob_plain;f=stdlib/rand_r.c;hb=HEAD

如你所见，它只是简单的乘以一个加法和一个移位。这些值经过仔细选择，以确保不会重复RAND_MAX迭代的输出。

注意，这是一个旧的实现，已经被一个更复杂的算法所取代：https://sourceware.org/git/?p=glibc.git;a=blob_plain;f=stdlib/random_r.c;hb=HEAD

如果链接断开，谷歌搜索"glibc rand_r“

Answer 2

我曾经为离散数学的一门课程写过一篇关于CRNG的报告。为此，我在msvcrt.dll中反汇编了rand()：

msvcrt.dll:77C271D8 mov     ecx, [eax+14h]
msvcrt.dll:77C271DB imul    ecx, 343FDh
msvcrt.dll:77C271E1 add     ecx, 269EC3h
msvcrt.dll:77C271E7 mov     [eax+14h], ecx
msvcrt.dll:77C271EA mov     eax, ecx
msvcrt.dll:77C271EC shr     eax, 10h
msvcrt.dll:77C271EF and     eax, 7FFFh

所以它是一个LCG类似于(未测试的)..。

int ms_rand(int& seed)
{
  seed = seed*0x343fd+0x269EC3;  // a=214013, b=2531011
  return (seed >> 0x10) & 0x7FFF;
}

Answer 3

伪随机数发生器(PRNG)的领域是相当广阔的。

首先，您必须了解，如果没有外部输入(通常是物理输入)，您就无法获得真正的随机数源。这就是为什么这些算法被称为伪随机:它们通常使用种子来初始化非常长的序列中的位置，这看起来是随机的，但它根本不是随机的。

最简单的算法之一是线性同余生成器 (LCG)，它有一些约束来保证长序列，而且它根本不安全。

另一个有趣的(至少在名字上)是Blum Blum Shub Generator (BBS)，这对于普通的PRNG来说是不寻常的，因为它依赖于模算术中的求幂，在打破序列方面提供了与RSA和El Gamal等其他算法相当的安全性(如果我也不确定它的证明)