## Shifts in time: cryptography and randomness

**Date:** 12 April 2003.

**Presenter:** Sven Dietrich, Carnegie Mellon University.

In 1917, Gilbert Vernam developed the Vernam cipher, also
commonly
known as the *one-time pad*, a polyalphabetic substitution
cryptosystem
intended to thwart any adversary. J. Mauborgne, inspired by
Vernam's work,
extended the idea by replacing the repeated keystream ($2^5$
keys) with a
non-repeating keystream sequence to create a *one-time
system*. This
one-time system requires a good source of random number
sequences to be
theoretically unbreakable, many of which were produced
differently over time,
e.g. by linear congruential generators of the form $x_i =
(a{x}_{i-1} + b) mod
n$, linear feedback shift registers, the Blum-Blum-Shub
pseudo-random number
generator, and even lava lamps. We observe the progress in the
mathematics of
producing these sequences throughout the 20th century and in the
early 21st
century.

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Last modified: 15 April 2003