## One Time PadsJune 12, 2013 There's a notable Dilbert cartoon, published on October 25, 2001. In this cartoon, our geek protagonist, Dilbert, is touring the Land of the Accounting Trolls. He's introduced to their random number generator, a troll who repeatedly says, "nine." Dilbert questions whether this is truly random. His troll tour guide says, "That's the problem with randomness - You can never be sure."[1] As the Dilbert cartoon illustrates, true randomness is hard to quantify. Every programming language has a random number function, but the idea that an algorithm can give you something random is flawed at a fundamental level. There's a famous quotation by computer pioneer, John von Neumann, that"Any one who considers arithmetical methods of producing random digits is, of course, in a state of sin. For, as has been pointed out several times, there is no such thing as a random number — there are only methods to produce random numbers, and a strict arithmetic procedure of course is not such a method."Since random numbers are important in computer simulations, such as the Monte Carlo method, von Neumann went against his own advice and developed a simple pseudorandom number generator, called the middle-square method, which was useful in the early days of computing. Unknown to von Neumann, but known to the present readers of Wikipedia, this simple method of generating pseudorandom numbers was invented by Brother Edvin, a Franciscan friar, circa 1245. There are two problems with this method, but they're fortunately very apparent when they happen. The first is when the middle digits become all zeros. After that point, the generator output is always zero. The other problem is that the generator can enter a mode in which it outputs the same short sequence, over and over.
This generator gives a long list of pseudorandom numbers when proper values are selected for a, c and m. Computer scientist, Donald Knuth, prefers to use
a=6364136223846793005, c=1442695040888963407, and m = 2The choice of a power of two for m simplifies the modulus operation.
These are just two examples of many simple pseudorandom number generators proven to be useful in the early days of computing when processors were slow and memory was small. Since we now have fast computers, we can be more creative with our pseudorandom number generators. One example of a more elaborate generator is the Mersenne twister; which, as its name implies, involves the Mersenne primes. Aside from that fact, it's somewhat hard to describe, but it's used as the random number generator in Python, PHP, and some other programming languages.
Most random number generators are suitable for computer simulations if we're careful to select those with sufficiently large periods. Cryptographic randomness is another case entirely, since the common pseudorandom number algorithms we might use in our cipher will be known also to our adversaries. Certain regularities in the output of such algorithms offer a signature of what method we might be using.
Physical random number generation is an alternative to algorithmic generation. The simplest of these is casting dice, but this method is slow and tedious.
## References:- This cartoon may have been inspired by the Beatles composition, Revolution 9, which appeared on their white album. This experimental music track has a male voice repeatedly saying, "number nine."
- Landon Curt Noll, Robert G. Mende and Sanjeev Sisodiya, "Method for seeding a pseudo-random number generator with a cryptographic hash of a digitization of a chaotic system," US Patent No. 5,732,138, March 24, 1998.
- Roarke Horstmeyer, Benjamin Judkewitz, Ivo Vellekoop and Changhuei Yang, "Physical key-protected one-time pad," arXiv Preprint Server, May 16, 2013.
- One-Time Pad Reinvented to Make Electronic Copying Impossible, Physics arXiv Blog, Technology Review, May 20, 2013.
- Tony Warnock, "Random-Number Generators," Los Alamos Science (Monte Carlo Special Issue, 1987), pp. 137-141 (PDF file).
- Laszlo Hars, "Random Topics," SummerCon (June 11-13, 2004, Pittsburgh, PA).
Linked Keywords: Dilbert cartoon, published on October 25, 2001; cartoon; geek; Dilbert; Accounting Troll; random number generator; troll; randomness; random; programming language; algorithm; John von Neumann famous quotation; John von Neumann; computer simulation; Monte Carlo method; pseudorandomness; pseudorandom number generator; middle-square method; history of computing hardware; early days of computing; Wikipedia; generating pseudorandom numbers; Franciscan friar; sequence; seed; square; numerical digit; Inkscape; linear congruential generator; recurrence relation; recursive relation; Derrick Henry Lehmer; D.H. Lehmer; computer scientist; Donald Knuth; power of two; modulus operation; central processing unit; CPU; memory; Mersenne twister; Mersenne prime; Python; PHP; programming language; random number generator attack; cryptographic randomness; cipher; physical random number generation; dice; decimal representation; decimal place; electronic; white noise; analog electronics; natural environment; environmental; noise; Geiger counters; radio receiver; Intel; voltage; transistor; integrated circuit; research; researcher; Max Planck Institute for the Physics of Light; Erlangen, Germany; quantum foam; vacuum state; Lavarand; Silicon Graphics; art; lava lamp; US Patent; Google Patents; one-time pad; binary number; exclusive-or; XOR; computer file; digital file; scientist; engineer; California Institute of Technology (Pasadena); University of Twente (Enschede, the Netherlands); scattering of light; material; experiment; spatial light modulator; opal; diffusion filter; gigabit; arXiv; terabit; cubic millimeter; annealing; microstructure; eavesdropper; public key cryptography; key; cryptanalysis; quantum computer; Internet; Revolution 9; white album; Landon Curt Noll, Robert G. Mende and Sanjeev Sisodiya, "Method for seeding a pseudo-random number generator with a cryptographic hash of a digitization of a chaotic system," US Patent No. 5,732,138, March 24, 1998. |
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