Cryptography Reference
In-Depth Information
a>b
a
is greater than
b
a
b
a
is much greater than
b
x
greatest integer less than or equal to
x
(i.e., floor of
x
)
x
smallest integer greater than or equal to
x
(i.e., ceiling of
x
)
div
integer division
mod
modulo operator
a
|
b
integer
a
divides integer
b
a
b
integer
a
does not divide integer
b
gcd
(
a
1
,...,a
k
) greatest common divisor of integers
a
1
,...,a
k
lcm
(
a
1
,...,a
k
) least common multiple of integers
a
1
,...,a
k
n
!
factorial of integer
n
(with 0! = 1)
π
(
n
)
prime counting function of integer
n
φ
(
n
)
Euler's totient function of integer
n
L
formal language
Σ
alphabet
Σ
in
input alphabet
Σ
out
output alphabet
{
0
,
1
}
binary alphabet
w
word (i.e., string over an alphabet)
|
w
|
length of
w
ε
empty word
Σ
n
setofallwordsoflength
n
over alphabet Σ
Σ
∗
set of all words over alphabet Σ
◦
or
string concatenation
f
function
X
→
Y
mapping from domain
X
to codomain
Y
f
(
X
)
⊆
Y
range of
f
f
−
1
inverse function
F
function family
f
k
instance of function family
F
Rand
X→Y
family of all functions of
X
to
Y
Perm
X→X
family of all permutations on
X
h
hash function
H
hash function family
p
(
n
)
polynomial in
n
deg
(
p
(
n
))
degree of polynomial
p
(
n
)
L
n
[
a, c
]
running time function
ord
(
x
)
order of group element
x
ord
n
(
x
)
order of
x
modulo
n
Ω
sample space (i.e., finite or countably infinite set)
