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\T1/fvm/m/n/10 2.10 
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 [1

]
Chapter 1.
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[]\T1/fvm/m/n/10 The updated Entropy library works on all AVR based Arduino pla
tforms, and now has been
 []


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\T1/fvm/m/n/10 ported to the ARM based platforms, Teensy 3.x and the Due. On th
e Teensy, it is still using
 []


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\T1/fvm/m/n/10 clock jitter, though not the watch dog timer, and produces at ab
out twice the rate of the
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\T1/fvm/m/n/10 an AVR based Arduino. When the library is used with the Due, it 
makes use of the Atmel
 []


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\T1/fvm/m/n/10 SAM3X chips built in hardware random number generator. This allo
ws the library to produce
 []


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\T1/fvm/m/n/10 at a rate of XX unsigned longs per second, versus the 2 longs pe
r second on a standard Arduino. 
 []


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[]\T1/fvm/m/n/10 This updated version of the library also includes the option o
f producing floating point
 []


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\T1/fvm/m/n/10 random numbers. More detail on how to use this functionality is 
included with the documentation
 []


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\T1/fvm/m/n/10 for the randomf() method. Related to the inclusion of floating p
oint is another method
 []


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\T1/fvm/m/n/10 that will provide random numbers in a gaussian distribution (nor
mal, bell curve) with a
 []

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[]\T1/fvm/m/n/10 The Arduino currently lacks a means of obtaining true random n
umbers. One pre-existing
 []


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\T1/fvm/m/n/10 library exists, TrueRandom, but a review of the performance and 
code base confirms that
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\T1/fvm/m/n/10 the TrueRandom library does not make use of a truly random entro
py source (the unconnected
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\T1/fvm/m/n/10 analog pin) Kristinsson [2011] which is further biased by method
s which introduce additional
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\T1/fvm/m/n/10 biases into the results which it does return. When using the Ard
uino's pseudo-random number
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\T1/fvm/m/n/10 generator, random(), will produce a predictable sequence of numb
ers unless some random mechanism
 []


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\T1/fvm/m/n/10 is used to seed it. The manual recommends using the results from
 an unconnected analog
 []


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\T1/fvm/m/n/10 pin; however, there is ample evidence that this mechanism does n
ot introduce much randomness
 []


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[]\T1/fvm/m/n/10 The purpose of this library is to provide a mechanism to produ
ce a series of true random
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\T1/fvm/m/n/10 numbers based upon the entropy associated with the jitter of the
 AVR's watch dog timer,
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\T1/fvm/m/n/10 and the standard Timer 1. Pedersen [2006] Since this mechanism p
roduces entropy at a relatively
 []


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\T1/fvm/m/n/10 slow rate (approximately 8 bytes per second) its best use is as 
a seed value to the internal
 []


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\T1/fvm/m/n/10 pseudo-random number generator or for those demands that do not 
require large numbers of
 []


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\T1/fvm/m/n/10 random numbers, such as generating cryptographically secure pass
words. Hlavac et al. [2010] 
 []


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[]\T1/fvm/m/n/10 Preliminary testing indicates that this mechanism produces cry
ptographically secure random
 []


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\T1/fvm/m/n/10 numbers, but the mechanism is subject to potential biases introd
uced by alterations to the
 []


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\T1/fvm/m/n/10 host environment. Prior to deploying this library it is suggeste
d that the end-user perform
 []


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\T1/fvm/m/n/10 any testing required to establish that the specific implementati
on will meet the user's
 []


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[]\T1/fvm/m/n/10 The underlying mechanism that the library uses to generate tru
e random numbers were tested
 []


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\T1/fvm/m/n/10 on a number of different arduino devices; leonardo, uno, uno (sm
d), and the mega (R3), etc...
 []


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\T1/fvm/m/n/10 Details of this preliminary testing is available Multiple [2012]
 which was also the source
 []


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\T1/fvm/m/n/10 of the idea for the mechanism used by this library. The early te
sts performed on this library
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\T1/fvm/m/n/10 used methods published by John Walker. Walker [2011] The raw dat
a used in the testing of
 []

[1

]
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[]\T1/fvm/m/n/10 Since the basic method only produces about 2 long integer valu
es per second, the more
 []


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\T1/fvm/m/n/10 detailed testing of a single device is an ongoing process, which
 is estimated to take 1-2
 []


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\T1/fvm/m/n/10 years to collect enough data to perform more vigourous testing. 
The project's website should
 []

[2]
Chapter 2.

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[]\T1/fvm/m/n/10 The library directory should be placed in your libraries sub-f
older where your Arduino
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\T1/fvm/m/n/10 IDE is configured to keep your sketches. When you first place th
is library, you will need
 []


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[]\T1/fvm/m/n/10 To use the library, you will need to include the libraries hea
der file, Entropy.h in
 []


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\T1/fvm/m/n/10 your sketch. Prior to calling any of the entropy retrieval metho
ds, you need to initialize
 []


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[]\T1/fvm/m/n/10 The library only produces uniformly distributed integers (byte
s, ints, and longs) and
 []


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\T1/fvm/m/n/10 single precision floats. Since they are so useful for certain ap
plications the library
 []


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\T1/fvm/m/n/10 will also produce gaussian distributed floats with a specified m
ean and standard deviation.
 []


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\T1/fvm/m/n/10 If other distributions are needed it is recommended that the use
r consult an appropriate
 []


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\T1/fvm/m/n/10 reference Matloff [2006] on generating different distributions. 
One of the examples provided
 []


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\T1/fvm/m/n/10 with the library demonstrates how to convert the random long int
eger returned by this library
 []


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[]\T1/fvm/m/n/10 This method configures the chip's timers and set-ups the inter
nal structures nescessary
 []


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\T1/fvm/m/n/10 to convert the hardware timer's jitter into an unbiased stream o
f entropy. On the Due it
 []


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\T1/fvm/m/n/10 configures the chips hardware random number generator. This meth
od should only be called
 []


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\T1/fvm/m/n/10 once, in the setup function of your sketch. After this method is
 executed, it will take
 []


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\T1/fvm/m/n/10 the Arduino approximately five hundred milli-seconds before the 
first unsigned long (32-bit)
 []


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[]\T1/fvm/m/n/10 For this reason, the call to the initialize method should occu
r fairly early in the set-up
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\T1/fvm/m/n/10 function, allowing ample time to perform other set-up activities
, before requesting any
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[]\T1/fvm/m/n/10 This method returns an unsigned char value that represents the
 number of unsigned long
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\T1/fvm/m/n/10 integers in the entropy pool. Since the entropy retrieval method
s (random) will block any
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\T1/fvm/m/n/10 further program execution until at least one value exists in the
 entropy pool, this function
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[3

] (./available_example.ino)
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[]\T1/fvm/m/n/10 The random method is the mechanism to retrieve the generated e
ntropy. It comes in three
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\T1/fvm/m/n/10 flavors, of which, this one returns a single unsigned long (32-b
it) integer value in the
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\T1/fvm/m/n/10 range of 0 to 0xFFFFFFFF. Since this method will prevent any fur
ther program execution until
 []


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\T1/fvm/m/n/10 a value is available to return, it can take up to a maximum of 5
00 milliseconds to execute.
 []


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\T1/fvm/m/n/10 If the delay is not desirable, the available method can be used 
to test if entropy is available
 []


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\T1/fvm/m/n/10 prior to calling this method. If desired the returned value can 
be cast from unsigned to
 []


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[]\T1/fvm/m/n/10 The library does not produce floating point random values but 
if those are wanted, it
 []


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\T1/fvm/m/n/10 is a simple matter to use the value returned by this method to p
roduce a random floating
 []

(./available_example.ino)
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[]\T1/fvm/m/n/10 The random method is the mechanism to retrieve the generated e
ntropy. It comes in three
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\T1/fvm/m/n/10 flavors, of which, this one returns a single unsigned long (32-b
it) integer value in the
 []


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\T1/fvm/m/n/10 range of [0,max). Note that the returned value will always be le
ss than max. The returned
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\T1/fvm/m/n/10 value can be cast to any integer type that will contain the resu
lt. In other words, if
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\T1/fvm/m/n/10 max is 256 or less the returned value can be stored in a char va
riable or an unsigned char
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\T1/fvm/m/n/10 variable, depending upon whether negative values are required. S
imiliarly, if max is 65536
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\T1/fvm/m/n/10 or less the returned value can be stored in a int or unsigned in
t, again depending upon
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[4]
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[]\T1/fvm/m/n/10 Like the previous implementation of this method described, thi
s method will prevent any
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\T1/fvm/m/n/10 further program execution until a value is available to return. 
This method behaves differently
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\T1/fvm/m/n/10 from the previous if max is less than 256 or max is less than 65
536. In the first case
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\T1/fvm/m/n/10 the 32-bit unsigned integer in the entropy pool is broken into f
our byte sized integers.
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\T1/fvm/m/n/10 Consequently four byte sized values are returned for every 32-bi
t integer in the entropy
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\T1/fvm/m/n/10 pool. In a similar way, values less than 65536 but greater than 
or equal to 256 will return
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\T1/fvm/m/n/10 two 16-bit integer values for every 32-bit integer in the entrop
y pool. Note that the latter
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\T1/fvm/m/n/10 means that the method will need to use two bytes of the entropy 
to provide a uniformly distributed
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\T1/fvm/m/n/10 random byte (max = 256). This is nescessary to allow the functio
n to maintain uniform distribution
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\T1/fvm/m/n/10 of returned values for other values of max... More detail is ava
ilable as comments in the
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[]\T1/fvm/m/n/10 The random method is the mechanism to retrieve the generated e
ntropy. It comes in three
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\T1/fvm/m/n/10 flavors, of which, this one returns a single unsigned long (32-b
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\T1/fvm/m/n/10 range of [min,max). Note that the returned value will always be 
greater than or equal to
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\T1/fvm/m/n/10 min and less than max. The returned value can be cast to any int
eger type that will contain
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\T1/fvm/m/n/10 the result. In other words, if max is 256 or less the returned v
alue can be stored in a
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\T1/fvm/m/n/10 char variable or an unsigned char variable, depending upon wheth
er negative values are required.
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\T1/fvm/m/n/10 Similiarly, if max is 65536 or less the returned value can be st
ored in a int or unsigned
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[]\T1/fvm/m/n/10 This function is useful for simulating the role of dice, or th
e drawing of cards, etc..
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\T1/fvm/m/n/10 Like the previous implementation of this method described, this 
method will prevent any
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\T1/fvm/m/n/10 further program execution until a value is available to return. 
This method behaves differently
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\T1/fvm/m/n/10 from the previous if (max-min) is less than 256 or (max-min) is 
less than 65536. In the
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\T1/fvm/m/n/10 first case the 32-bit unsigned integer in the entropy pool is br
oken into four byte sized
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\T1/fvm/m/n/10 integers. Consequently four byte sized values are returned for e
very 32-bit integer in
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\T1/fvm/m/n/10 the entropy pool. In a similar way, value differences less than 
65536 but greater than
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\T1/fvm/m/n/10 or equal to 256 will return two 16-bit integer values for every 
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[5] (./random_minmax_example.ino)
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tioned when attempting
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\T1/fvm/m/n/10 to retrieve a full byte of entropy using the random(256) method.
 Since that method will
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 a single byte of entropy
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\T1/fvm/m/n/10 than two. In all other ways it behaves in a manner consistent wi
th the random() method. 
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\T1/fvm/m/n/10 to retrieve a full word (16-bit integer) of entropy using the ra
ndom(65536) method. Since
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\T1/fvm/m/n/10 that method will need to consume four bytes from the entropy str
eam to return only two bytes,
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\T1/fvm/m/n/10 this method was included for the special case where a single int
eger is needed. This allows
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\T1/fvm/m/n/10 two such integers to be returned from each entropy value, rather
 than only one. In all
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[]\T1/fvm/m/n/10 This method will produce a uniformly distributed random float 
in the range of [0 - max). 
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[]\T1/fvm/m/n/10 This method will produce a uniformly distributed random float 
in the range of [min -
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[6] (./randomf_example.ino)
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[]\T1/fvm/m/n/10 This method will produce a gaussian distributed (normal, bell 
curve) random float with
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[7]
Chapter 3.
(../Entropy.h [8

]) (../Entropy.cpp [9]
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[10]
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[11] [12] [13]) (../keywords.txt [14]) (../gpl.txt [15] [16] [17] [18] [19]
[20] [21] [22] [23] [24]) (./manual.bbl [25]
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[]\T1/fvm/m/n/10 Josef Hlavac, Robert Lorencz, and Martin Hadacek.  True random
 number generation on an
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\T1/fvm/m/n/10 atmelavr microcontrolle.  \T1/fvm/m/sl/10 2010 2nd International
 Conference on Computer Engineering
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[]\T1/fvm/m/n/10 Benedikt Kristinsson.  Ardrand: The arduino as a hardware rand
om number generator,
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\T1/fvm/m/n/10 December 2011.  URL line-breaking $http : / / reykjavik . academ
ia . edu / BenediktKristinsson /
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[]\T1/fvm/m/n/10 Norm Matloff.  Random number generation, 2006.  URL $http : / 
/ heather . cs . ucdavis . edu /
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[]\T1/fvm/m/n/10 Multiple.  Random numbers and random seeds, May 2012.  URL $ht
tp : / / arduino . cc / forum /
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[]\T1/fvm/m/n/10 Kasper Pedersen.  Entropy gathering for cryptographic applicat
ions in avr -
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