  In the cryptanalysis of stream ciphers and pseudorandom sequences, the
notions of linear, jump, and 2-adic complexity arise naturally to measure the
(non)randomness of a given string. We define an isometry K on F_q^\infty that
is the precise equivalent to Euclid's algorithm over the reals to calculate the
continued fraction expansion of a formal power series. The continued fraction
expansion allows to deduce the linear and jump complexity profiles of the input
sequence. Since K is an isometry, the resulting F_q^\infty-sequence is i.i.d.
for i.i.d. input. Hence the linear and jump complexity profiles may be modelled
via Bernoulli experiments (for F_2: coin tossing), and we can apply the very
precise bounds as collected by Revesz, among others the Law of the Iterated
Logarithm.
  The second topic is the 2-adic span and complexity, as defined by Goresky and
Klapper. We derive again an isometry, this time on the dyadic integers Z_2
which induces an isometry A on F_2}^\infty. The corresponding jump complexity
behaves on average exactly like coin tossing.
  Index terms:
  Formal power series, isometry, linear complexity, jump complexity, 2-adic
complexity, 2-adic span, law of the iterated logarithm, Levy classes, stream
ciphers, pseudorandom sequences
