Cryptography Reference
In-Depth Information
+
Z
positive integers
Z
−
negative integers
Z
n
integers modulo
n
Z
n
multiplicative group of integers modulo
n
(
x
|
p
)
Legendre symbol of
x
modulo
p
(
x
|
n
)
Jacobi symbol of
x
modulo
p
Z
n
with Jacobi symbol 1
J
n
elements of
QR
n
set of quadratic residues modulo
n
QNR
n
set of quadratic nonresidues modulo
n
QR
n
set of pseudosquares modulo
n
Q
rational numbers
R
real numbers
+
R
positive real numbers
R
−
negative real numbers
π
transcendental number that expresses the ratio of the circumference
of a perfect circle to its diameter (
π
=3
.
14159
...
)
e
transcendental number that represents the base of the natural
logarithm (
e
=2
.
71828
...
)
C
complex numbers
√
−
i
1
F
finite field
F
q
finite field with
q
elements (i.e.,
|
F
q
|
=
q
)
E
(
F
q
)
elliptic curve over
F
q
P
set of all primes
∗
binary operation
+
addition
−
subtraction
·
multiplication
/
division
x
←
X
value assignment (i.e.,
x
is assigned a value from
X
)
u
←
x
X
value assignment according to the uniform distribution
¬
X
bitwise negation of the Boolean variable
X
(NOT)
X
∧
Y
bitwise and of the Boolean variables
X
and
Y
(AND)
X
∨
Y
bitwise or of the Boolean variables
X
and
Y
(OR)
X
⊕
Y
bitwise exclusive of the Boolean variables
X
and
Y
(XOR)
X
←
s
circular left shift of Boolean variable
X
by
s
positions
X
→
s
circular right shift of Boolean variable
X
by
s
positions
a
=
b
a
is equal to
b
a<b
a
is smaller than
b
a
b
a
is much smaller than
b
