KISS (algorithm) explained

KISS (algorithm) should not be confused with Kiss (cryptanalysis).

KISS (Keep it Simple Stupid) is a family of pseudorandom number generators introduced by George Marsaglia.^{[1] [2] [3]} Starting from 1998 Marsaglia posted on various newsgroups including sci.math, comp.lang.c, comp.lang.fortran and sci.stat.math several versions of the generators. All KISS generators combine three or four independent random number generators with a view to improving the quality of randomness. KISS generators produce 32-bit or 64-bit random integers, from which random floating-point numbers can be constructed if desired. The original 1993 generator is based on the combination of a linear congruential generator and of two linear feedback shift-register generators. It has a period 2⁹⁵, good speed and good statistical properties; however, it fails the LinearComplexity test in the Crush and BigCrush tests of the TestU01 suite.^[4] A newer version from 1999 is based on a linear congruential generator, a 3-shift linear feedback shift-register and two multiply-with-carry generators. It is 10–20% slower than the 1993 version but has a larger period 2¹²³ and passes all tests in TestU01. In 2009 Marsaglia presented a version based on 64-bit integers (appropriate for 64-bit processors) which combines a multiply-with-carry generator, a Xorshift generator and a linear congruential generator.^[5] It has a period of around 2²⁵⁰ (around 10⁷⁵).

Further reading

• Book: Bucklew, James . Introduction to Rare Event Simulation . https://books.google.com/books?id=AfXiBwAAQBAJ&pg=PA1 . 2013 . Springer . 978-1-4757-4078-3 . 1–8 . 1.1 Uniform Generators .
• Book: Robert . Christian . George Casella . Monte Carlo Statistical Methods . https://books.google.com/books?id=lrvfBwAAQBAJ&pg=PR39 . 2013 . Springer . 978-1-4757-3071-5. 39–43 . 2.1.2 The Kiss Generator.
• Rose . Gregory G. . KISS: A bit too simple. Cryptography and Communications . 10 . 123–137 . 2017 . 1936-2447 . 10.1007/s12095-017-0225-x. free .

Notes and References

1. Marsaglia. George. Zaman. Arif. 1993. The KISS generator. Technical Report, Department of Statistics, Florida State University, Tallahassee, FL, USA.
2. Rose. Greg. 2018. KISS: A Bit Too Simple. Cryptography and Communications. 10. 123–137. 10.1007/s12095-017-0225-x. free.
3. Book: Kneusel, Ronald T.. Random Numbers and Computers. Springer. 2018. 978-3-319-77696-5.
4. L'Ecuyer. Pierre. Simard. Richard. 2007. TestU01: A C Library for Empirical Testing of Random Number Generators. ACM Transactions on Mathematical Software. 33. 4. 22–es. 10.1145/1268776.1268777. 273446 .
5. Web site: 64-bit KISS RNGs. Feb 28, 2009.