Cryptography Reference
In-Depth Information
Appendix B
Mathematical Notation
∀
quantifier “for all”
∃
quantifier “there exists”
≡
congruence relation
:=
definition
sum
product
end of proof
∞
infinity
O
point at infinity
S
set
|
S
|
cardinality of
S
(i.e., number of elements)
2
S
power set of
S
(i.e., set of all subsets of
S
)
∅
empty set (i.e.,
|∅|
=0)
set of all permutations on
S
(i.e.,
Perm
S→S
P
(
S
)
)
x
∈
S
x
is an element of
S
x/
∈
S
x
is not an element of
S
x
∈
R
S
x
is a random (i.e., randomly chosen) element of
S
x
∈
(
a, b
)
x
is an element from the open interval (
a, b
)
x
∈
[
a, b
]
x
is an element from the closed interval [
a, b
]
A
∪
B
union of sets
A
and
B
A
∩
B
intersection of sets
A
and
B
A
\
B
difference of sets
A
and
B
A
⊆
B
set
A
is a subset of set
B
(or
B
is a superset of
A
)
N
natural numbers
+
+
:=
N
positive natural numbers (i.e.,
N
N
\{
0
}
Z
integer numbers (i.e., integers)
