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The Quadratic Generator
Let ,
where
are primes
.
For each prime,
is a square if and only if
is not
a square (Lemma 22).
This implies that, if
and
,
there will be exactly one choice which makes
a square mod .
Hence, if
is a square mod ,
exactly one of its four square roots
will also be a square. This principal square root will be
denoted by .
The quadratic generator uses a randomly chosen square
(called the
seed) not divisible by
or
to generate a sequence of
0's and 1's (bits). The sequence is mod 2, where and
:
(from a practical point of view, it is simpler to generate the sequence
starting with the last number and squaring)
As a small example with
and ,
the sequence of
is
(note
that
,
not 3) which gives the sequence of bits 11010101.
Translated from LaTeX by Scott Sutherland
1998-03-15