Cryptography Reference
In-Depth Information
2
, ...,
Proposition 39.
If
g
is a generator modulo
p
, then the sequence of integers
g
,
g
g
p
1
is a permutation of 1, 2, . . . ,
p
1.
If |
b
|
p
=
t
and
u
is a positive integer, then |
b
u
|
p
=
t
/(
t
,
u
).
Proposition 40.
Proposition 41.
Let
r
be the number of positive integers not exceeding
p
1 that are
relatively prime to
p
1. Then, if the prime
p
has a generator, it has
r
of them.
Proposition 42.
Every prime has a generator.
Proposition 43.
Let
p
be prime, and let
g
be a generator modulo
p
. Suppose
a
and
b
are positive integers not divisible by
p
. Then we have all of the following:
a.
log1
0 (mod
p
1)
b.
log(
ab
)
log
a
+ log
b
(mod
p
1)
c.
log(
a
k
)
k
log
a
(mod
p
1)
where all logarithms are taken to the base
g
modulo
p
.
Search WWH ::
Custom Search