1. Random Number Generation
Paul Downing and Tyler Sullivan

2. What is an RNG?
Random Number Generators are devices - algorithmic or otherwise - used to generate random integers, and then use them in some function or another.
Two types: True and Pseudo
Pseudorandom is the more commonly used of the two
True is more random, but more time costly

3. PRNG #1: Middle Squares This algorithm follows a three-step process.
Take in a seed.
Square the seed.
Take the center three numerals from that
Concatenate onto a numeral string.
Square the squared numeral.
Repeat steps 3-5 until your numeral string is long enough for you.

4. Middle Squares Example
Seed: 123
512
886
15129
123
And so on...

5. Implementation of Middle Squares
for (int i = 0; i < samplesToProduce; ++i) { //select the middle three digits for the next seed //the seed has been selected newseed = (x / 1000) % ; storageArray[i] = newseed; //The sequence will almost always go to zero, so an improvement //to the algorithm would be reseeding with the time as seen below. /* if (newseed < threshHold){ newseed = time(NULL); } */ x = newseed * newseed; }

6. PRNG #2: Blum Blum Shub Most Hilarious Name for a PRNG Award 2014
M is an integer made of two multiplied large primes
M = pq
p and q need to be congruent to 3 % 4
VERY SLOW, not technically useful in computer science
Difficult to decrypt back to the seed and p or q, with high numbers

7. Example of Blum Blum Shub
p= 11, q = 19, seed = 3
The sequence “begins” at item -1, which is equal to the seed, but goes unlisted.
Each term in the sequence is the previous term squared mod M
9, 81, 82, 36, 42, 92,

8. PRNG #3: Linear Congruential Generator
X is the term in the sequence
a is a multiplier on that term, 0<a<m
c is an incrementer, 0<c<m
m is the modulus.
Starting from a seed, this generates a pseudorandom number sequence.
Example: Seed = 5, a = 8, c = 3, m = 16
11, 0, 3, 11…
Not that good of an algorithm, forms sequences very easily with small numbers

9. Implementation of LCG (C++)
class mRND {
public:
void seed( unsigned int s ) { _seed = s; }
protected:
mRND() : _seed( 0 ), _a( 0 ), _c( 0 ), _m( ) {}
int rnd() { return( _seed = ( _a * _seed + _c ) % _m ); }
int _a, _c;
unsigned int _m, _seed; };

10. Implementation of LCG (C++)
class BSD_RND : public mRND {
public:
BSD_RND() { _a = ; _c = 12345; }
int rnd() { return mRND::rnd(); } };
int main( int argc, char* argv[] ) {
BSD_RND bsd_rnd;
cout << endl << "BSD RAND:" << endl << "=========" << endl;
for( int x = 0; x < 10; x++ )
cout << bsd_rnd.rnd() << endl;
cout << endl << endl;
system( "pause" );
return 0; }

11. C++ Output BSD RAND: ========= 12345 1406932606 654583775 1449466924

12. TRNG True Random Number Generators RANDOM.ORG Hardware-based TRNG
Quantum RNG

13. RANDOM.ORG Website simulates truly random real-world events Dice rolls
Card drawing
Coin flips
Normal, integer-creating TRNGs can be found on the site, as well.

14. How does that work?
To quote the website, “atmospheric noise” is processed as commands are input.
This noise is obtained through radio receivers, in several places across the world
The website has actually been rated by several organizations very highly in the quality of its randomness.

15. Hardware Based TRNG More general description of what RANDOM.ORG does
Uses physical random phenomena to create random numbers.
Physical -> Transducer -> Amplifier -> Analog to Digital -> Number

16. Thermal Noise HBTRNG
An electric resistor makes random noise through thermal agitation
This noise is then amplified by some method
The amplified stream of noise is converted into binary strings
These binary strings are then easily converted to integers

17. A simple TNHBTRNG

18. Quantum TRNG Nuclear Decay can be used as a randomness source
The decay of nuclear things is considered extremely random
Until a literally unreachable cold temperature. (0 K)

19. Nuclear Decay -> Numbers
The decay of a nuclear substance is measured by a Geiger counter
Geiger counter data is sent to a computer
The time interval between decay instances is measured
This is used to create a 0 or 1 bit
A string of binary is then easily converted into a random number.

20. Thanks for listening!

21. Works Cited “How Machines Generate Random Numbers With Time
Rosetta Code’s C++ example on LCGs.
random.org f