The Cayley PRNG, named after the mathematician Arthur Cayley (1821–1895) pictured above, uses a pair of generators of a symmetric group to generate pseudorandom permutations which are then converted to pseudorandom numbers. Cayley's Theorem states that every group is isomorphic to a subgroup of the symmetric group acting on the group, which implies that symmetric groups have a rich structure. The Cayley PRNG exploits this rich structure as a source of pseudorandomness.

Compiling the Code

Windows and Visual Studio

A Visual Studio solution file PRNG.sln has been provided in the root folder. It has been tested with Visual Studio 2019 Community under Windows 10.

Unix and g++

A make file has been placed in the Code directory. Type "make generator" to create the executable file generate.exe. It has been tested with g++ 7.4 on the Ubuntu 18.04.1 subsystem under Windows 10.

Running the Code

Running generator.exe will perform a time-test on Cayley32 versus the Mersenne Twister with a preset seed. Optional switches are as follows:

Switch	Description
-h	Display help.
-g	Generate an infinite number of pseudorandom bits from Cayley32 to stdout.
-ge	Generate an infinite number of pseudorandom bits from Cayley32e to stdout.
-gm	Generate an infinite number of pseudorandom bits from the Mersenne Twister to stdout.
-s \(n\)	Seed value \(n\), a hexidecimal number.

The following screenshot shows how to use the -h, -g, and -s switches.