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------- Strong random data generation on a Macintosh (pre - OS X) ------
-- GENERAL: We aim to generate unpredictable bits without explicit
user interaction. A general review of the problem may be found
in RFC 1750, "Randomness Recommendations for Security", and some
more discussion, of general and Mac-specific issues has appeared
in "Using and Creating Cryptographic- Quality Random Numbers" by
Jon Callas (
The data and entropy estimates provided below are based on my
limited experimentation and estimates, rather than by any
rigorous study, and the entropy estimates tend to be optimistic.
They should not be considered absolute.
Some of the information being collected may be correlated in
subtle ways. That includes mouse positions, timings, and disk
size measurements. Some obvious correlations will be eliminated
by the programmer, but other, weaker ones may remain. The
reliability of the code depends on such correlations being
poorly understood, both by us and by potential interceptors.
This package has been planned to be used with OpenSSL, v. 0.9.5.
It requires the OpenSSL function RAND_add.
-- OTHER WORK: Some source code and other details have been
published elsewhere, but I haven't found any to be satisfactory
for the Mac per se:
* The Linux random number generator (by Theodore Ts'o, in
drivers/char/random.c), is a carefully designed open-source
crypto random number package. It collects data from a variety
of sources, including mouse, keyboard and other interrupts.
One nice feature is that it explicitly estimates the entropy
of the data it collects. Some of its features (e.g. interrupt
timing) cannot be reliably exported to the Mac without using
undocumented APIs.
* Truerand by Don P. Mitchell and Matt Blaze uses variations
between different timing mechanisms on the same system. This
has not been tested on the Mac, but requires preemptive
multitasking, and is hardware-dependent, and can't be relied
on to work well if only one oscillator is present.
* Cryptlib's RNG for the Mac (RNDMAC.C by Peter Gutmann),
gathers a lot of information about the machine and system
environment. Unfortunately, much of it is constant from one
startup to the next. In other words, the random seed could be
the same from one day to the next. Some of the APIs are
hardware-dependent, and not all are compatible with Carbon (OS
X). Incidentally, the EGD library is based on the UNIX entropy
gathering methods in cryptlib, and isn't suitable for MacOS
* Mozilla (and perhaps earlier versions of Netscape) uses the
time of day (in seconds) and an uninitialized local variable
to seed the random number generator. The time of day is known
to an outside interceptor (to within the accuracy of the
system clock). The uninitialized variable could easily be
identical between subsequent launches of an application, if it
is reached through the same path.
* OpenSSL provides the function RAND_screen(), by G. van
Oosten, which hashes the contents of the screen to generate a
seed. This is not useful for an extension or for an
application which launches at startup time, since the screen
is likely to look identical from one launch to the next. This
method is also rather slow.
* Using variations in disk drive seek times has been proposed
(Davis, Ihaka and Fenstermacher,;
Jakobsson, Shriver, Hillyer and Juels, These variations
appear to be due to air turbulence inside the disk drive
mechanism, and are very strongly unpredictable. Unfortunately
this technique is slow, and some implementations of it may be
patented (see Shriver's page above.) It of course cannot be
used with a RAM disk.
-- TIMING: On the 601 PowerPC the time base register is guaranteed
to change at least once every 10 addi instructions, i.e. 10
cycles. On a 60 MHz machine (slowest PowerPC) this translates to
a resolution of 1/6 usec. Newer machines seem to be using a 10
cycle resolution as well.
For 68K Macs, the Microseconds() call may be used. See Develop
issue 29 on the Apple developer site
for information on its accuracy and resolution. The code below
has been tested only on PowerPC based machines.
The time from machine startup to the launch of an application in
the startup folder has a variance of about 1.6 msec on a new G4
machine with a defragmented and optimized disk, most extensions
off and no icons on the desktop. This can be reasonably taken as
a lower bound on the variance. Most of this variation is likely
due to disk seek time variability. The distribution of startup
times is probably not entirely even or uncorrelated. This needs
to be investigated, but I am guessing that it not a majpor
problem. Entropy = log2 (1600/0.166) ~= 13 bits on a 60 MHz
machine, ~16 bits for a 450 MHz machine.
User-launched application startup times will have a variance of
a second or more relative to machine startup time. Entropy >~22
Machine startup time is available with a 1-second resolution. It
is predictable to no better a minute or two, in the case of
people who show up punctually to work at the same time and
immediately start their computer. Using the scheduled startup
feature (when available) will cause the machine to start up at
the same time every day, making the value predictable. Entropy
>~7 bits, or 0 bits with scheduled startup.
The time of day is of course known to an outsider and thus has 0
entropy if the system clock is regularly calibrated.
-- KEY TIMING: A very fast typist (120 wpm) will have a typical
inter-key timing interval of 100 msec. We can assume a variance
of no less than 2 msec -- maybe. Do good typists have a constant
rhythm, like drummers? Since what we measure is not the
key-generated interrupt but the time at which the key event was
taken off the event queue, our resolution is roughly the time
between process switches, at best 1 tick (17 msec). I therefore
consider this technique questionable and not very useful for
obtaining high entropy data on the Mac.
-- MOUSE POSITION AND TIMING: The high bits of the mouse position
are far from arbitrary, since the mouse tends to stay in a few
limited areas of the screen. I am guessing that the position of
the mouse is arbitrary within a 6 pixel square. Since the mouse
stays still for long periods of time, it should be sampled only
after it was moved, to avoid correlated data. This gives an
entropy of log2(6*6) ~= 5 bits per measurement.
The time during which the mouse stays still can vary from zero
to, say, 5 seconds (occasionally longer). If the still time is
measured by sampling the mouse during null events, and null
events are received once per tick, its resolution is 1/60th of a
second, giving an entropy of log2 (60*5) ~= 8 bits per
measurement. Since the distribution of still times is uneven,
this estimate is on the high side.
For simplicity and compatibility across system versions, the
mouse is to be sampled explicitly (e.g. in the event loop),
rather than in a time manager task.
-- STARTUP DISK TOTAL FILE SIZE: Varies typically by at least 20k
from one startup to the next, with 'minimal' computer use. Won't
vary at all if machine is started again immediately after
startup (unless virtual memory is on), but any application which
uses the web and caches information to disk is likely to cause
this much variation or more. The variation is probably not
random, but I don't know in what way. File sizes tend to be
divisible by 4 bytes since file format fields are often
long-aligned. Entropy > log2 (20000/4) ~= 12 bits.
gets fragmented this could be anywhere in principle. In a
perfectly unfragmented volume this will be strongly correlated
with the total file size on the disk. With more fragmentation
comes less certainty. I took the variation in this value to be
1/8 of the total file size on the volume.
-- SYSTEM REQUIREMENTS: The code here requires System 7.0 and above
(for Gestalt and Microseconds calls). All the calls used are
/*------------------------------ Includes ----------------------------*/
#include "Randomizer.h"
// Mac OS API
#include <Files.h>
#include <Folders.h>
#include <Events.h>
#include <Processes.h>
#include <Gestalt.h>
#include <Resources.h>
#include <LowMem.h>
// Standard C library
#include <stdlib.h>
#include <math.h>
/*---------------------- Function declarations -----------------------*/
// declared in OpenSSL/crypto/rand/rand.h
extern "C" void RAND_add (const void *buf, int num, double entropy);
unsigned long GetPPCTimer (bool is601); // Make it global if needed
// elsewhere
/*---------------------------- Constants -----------------------------*/
#define kMouseResolution 6 // Mouse position has to differ
// from the last one by this
// much to be entered
#define kMousePositionEntropy 5.16 // log2 (kMouseResolution**2)
#define kTypicalMouseIdleTicks 300.0 // I am guessing that a typical
// amount of time between mouse
// moves is 5 seconds
#define kVolumeBytesEntropy 12.0 // about log2 (20000/4),
// assuming a variation of 20K
// in total file size and
// long-aligned file formats.
#define kApplicationUpTimeEntropy 6.0 // Variance > 1 second, uptime
// in ticks
#define kSysStartupEntropy 7.0 // Entropy for machine startup
// time
/*------------------------ Function definitions ----------------------*/
CRandomizer::CRandomizer (void)
long result;
mSupportsLargeVolumes =
(Gestalt(gestaltFSAttr, &result) == noErr) &&
((result & (1L << gestaltFSSupports2TBVols)) != 0);
if (Gestalt (gestaltNativeCPUtype, &result) != noErr)
mIsPowerPC = false;
mIs601 = false;
mIs601 = (result == gestaltCPU601);
mIsPowerPC = (result >= gestaltCPU601);
mLastMouse.h = mLastMouse.v = -10; // First mouse will
// always be recorded
mLastPeriodicTicks = TickCount();
GetTimeBaseResolution ();
// Add initial entropy
AddTimeSinceMachineStartup ();
AddAbsoluteSystemStartupTime ();
AddStartupVolumeInfo ();
AddFiller ();
void CRandomizer::PeriodicAction (void)
AddCurrentMouse ();
AddNow (0.0); // Should have a better entropy estimate here
mLastPeriodicTicks = TickCount();
/*------------------------- Private Methods --------------------------*/
void CRandomizer::AddCurrentMouse (void)
Point mouseLoc;
unsigned long lastCheck; // Ticks since mouse was last
// sampled
GetGlobalMouse (&mouseLoc);
mouseLoc = LMGetMouseLocation();
if (labs (mLastMouse.h - mouseLoc.h) > kMouseResolution/2 &&
labs (mLastMouse.v - mouseLoc.v) > kMouseResolution/2)
AddBytes (&mouseLoc, sizeof (mouseLoc),
if (mLastMouse.h == mouseLoc.h && mLastMouse.v == mouseLoc.v)
mMouseStill ++;
double entropy;
// Mouse has moved. Add the number of measurements for
// which it's been still. If the resolution is too
// coarse, assume the entropy is 0.
lastCheck = TickCount() - mLastPeriodicTicks;
if (lastCheck <= 0)
lastCheck = 1;
entropy = log2l
if (entropy < 0.0)
entropy = 0.0;
AddBytes (&mMouseStill, sizeof (mMouseStill), entropy);
mMouseStill = 0;
mLastMouse = mouseLoc;
void CRandomizer::AddAbsoluteSystemStartupTime (void)
unsigned long now; // Time in seconds since
// 1/1/1904
GetDateTime (&now);
now -= TickCount() / 60; // Time in ticks since machine
// startup
AddBytes (&now, sizeof (now), kSysStartupEntropy);
void CRandomizer::AddTimeSinceMachineStartup (void)
AddNow (1.5); // Uncertainty in app startup
// time is > 1.5 msec (for
// automated app startup).
void CRandomizer::AddAppRunningTime (void)
ProcessSerialNumber PSN;
ProcessInfoRec ProcessInfo;
ProcessInfo.processInfoLength = sizeof (ProcessInfoRec);
ProcessInfo.processName = nil;
ProcessInfo.processAppSpec = nil;
GetCurrentProcess (&PSN);
GetProcessInformation (&PSN, &ProcessInfo);
// Now add the amount of time in ticks that the current process
// has been active
AddBytes (&ProcessInfo, sizeof (ProcessInfoRec),
void CRandomizer::AddStartupVolumeInfo (void)
short vRefNum;
long dirID;
XVolumeParam pb;
OSErr err;
if (!mSupportsLargeVolumes)
FindFolder (kOnSystemDisk, kSystemFolderType, kDontCreateFolder,
&vRefNum, &dirID);
pb.ioVRefNum = vRefNum;
pb.ioCompletion = 0;
pb.ioNamePtr = 0;
pb.ioVolIndex = 0;
err = PBXGetVolInfoSync (&pb);
if (err != noErr)
// Base the entropy on the amount of space used on the disk and
// on the next available allocation block. A lot else might be
// unpredictable, so might as well toss the whole block in. See
// comments for entropy estimate justifications.
AddBytes (&pb, sizeof (pb),
kVolumeBytesEntropy +
log2l (((pb.ioVTotalBytes.hi - pb.ioVFreeBytes.hi)
* 4294967296.0D +
(pb.ioVTotalBytes.lo - pb.ioVFreeBytes.lo))
/ pb.ioVAlBlkSiz - 3.0));
On a typical startup CRandomizer will come up with about 60
bits of good, unpredictable data. Assuming no more input will
be available, we'll need some more lower-quality data to give
OpenSSL the 128 bits of entropy it desires. AddFiller adds some
relatively predictable data into the soup.
void CRandomizer::AddFiller (void)
ProcessSerialNumber psn; // Front process serial
// number
RGBColor hiliteRGBValue; // User-selected
// highlight color
long processCount; // Number of active
// processes
long cpuSpeed; // Processor speed
long totalMemory; // Total logical memory
// (incl. virtual one)
long systemVersion; // OS version
short resFile; // Current resource file
} data;
GetNextProcess ((ProcessSerialNumber*) kNoProcess);
while (GetNextProcess (&data.psn) == noErr)
GetFrontProcess (&data.psn);
LMGetHiliteRGB (&data.hiliteRGBValue);
Gestalt (gestaltProcClkSpeed, &data.cpuSpeed);
Gestalt (gestaltLogicalRAMSize, &data.totalMemory);
Gestalt (gestaltSystemVersion, &data.systemVersion);
data.resFile = CurResFile ();
// Here we pretend to feed the PRNG completely random data. This
// is of course false, as much of the above data is predictable
// by an outsider. At this point we don't have any more
// randomness to add, but with OpenSSL we must have a 128 bit
// seed before we can start. We just add what we can, without a
// real entropy estimate, and hope for the best.
AddBytes (&data, sizeof(data), 8.0 * sizeof(data));
AddCurrentMouse ();
AddNow (1.0);
//------------------- LOW LEVEL ---------------------
void CRandomizer::AddBytes (void *data, long size, double entropy)
RAND_add (data, size, entropy * 0.125); // Convert entropy bits
// to bytes
void CRandomizer::AddNow (double millisecondUncertainty)
long time = SysTimer();
AddBytes (&time, sizeof (time), log2l (millisecondUncertainty *
//----------------- TIMING SUPPORT ------------------
void CRandomizer::GetTimeBaseResolution (void)
#ifdef __powerc
long speed;
// gestaltProcClkSpeed available on System 7.5.2 and above
if (Gestalt (gestaltProcClkSpeed, &speed) != noErr)
// Only PowerPCs running pre-7.5.2 are 60-80 MHz
// machines.
mTimebaseTicksPerMillisec = 6000.0D;
// Assume 10 cycles per clock update, as in 601 spec. Seems true
// for later chips as well.
mTimebaseTicksPerMillisec = speed / 1.0e4D;
// 68K VIA-based machines (see Develop Magazine no. 29)
mTimebaseTicksPerMillisec = 783.360D;
unsigned long CRandomizer::SysTimer (void) // returns the lower 32
// bit of the chip timer
#ifdef __powerc
return GetPPCTimer (mIs601);
UnsignedWide usec;
Microseconds (&usec);
return usec.lo;
#ifdef __powerc
// The timebase is available through mfspr on 601, mftb on later chips.
// Motorola recommends that an 601 implementation map mftb to mfspr
// through an exception, but I haven't tested to see if MacOS actually
// does this. We only sample the lower 32 bits of the timer (i.e. a
// few minutes of resolution)
asm unsigned long GetPPCTimer (register bool is601)
cmplwi is601, 0 // Check if 601
bne _601 // if non-zero goto _601
mftb r3 // Available on 603 and later.
blr // return with result in r3
mfspr r3, spr5 // Available on 601 only.
// blr inserted automatically