Prime Numbers

9.5 Large-integer multiplication 497
This is because the representation
x =
D−1
j=0
xj2 qj/D ,
and similarly for y (where the digits in base B are generally irrational also),
leads to the equivalence, without carry, of (xy) modp and x × y. But now the
signal lengths are powers of two, and the digits, although not integers, are
some convenient word size. It turns out to be possible to mimic this irrational
base expansion, by using a certain variable-base representation according to
the following theorem:
Theorem 9.5.18 (Crandall). For p =2 q − 1 (p not necessarily prime) and
integers 0 ≤ x, y < p, choose signal length 1