January 15, 2002
Practical Aspects of Modern Cryptography
•
The Binomial Theorem
•
(
x
+
y
)
p
=
x
p
+
(
)
x
p
-1
y
+ … +
(
)
xy
p
-1
+
y
p
•
•
If
p
is prime, then
(
)
mod
p
= 0
for
0 <
i
<
p
.
•
•
Thus,
(
x
+
y
)
p
mod
p
= (
x
p
+
y
p
) mod
p
.
p
1
Proof of Fermat’s Little Theorem
p
p
-1
p
i
