Cryptography Reference
In-Depth Information
List of Symbols
x⊕y
Bit-wise XOR of two (equilength) binary strings x and y
xy
Concatenation of two bitstrings x and y
f ◦g
Composition of two functions f and g
≫
Right shift operator
≪
Left shift operator
Right rotation operator
Left rotation operator
ROTL32(w,n)
Left rotate the 32-bit word w by n bits
ROTR32(w,n)
Right rotate the 32-bit word w by n bits
b
R
Byte b after right shifting by n bits
b
L
Byte b after left shifting by n bits
|x|
Length in bits of the integer x
bin
n
(x)
n-bit binary representation of the number x
w
(i)
i-th least significant byte of the word w
[w]
i
i-th least significant bit of the word w
+ =
Increment operator
=
Equality holds with probability p
w.h.p.
=
Equality holds with high probability (close to 1)
Z
N
The set {0,1,...,N −1} of integers modulo N
[a,b]
The set {a,a + 1,...,b} of integers from a to b
K[a...b]
The array K from index a to index b
K[a⊎b]
The sum K[a] + K[a + 1] + ... + K[b] for the array K
n
m
The binomial coe
cient
n
C
m
O (f(n))
Big Oh order notation
P(A) or Prob(A)
The probability of an event A
E(X)
The expectation of a random variable X
V (X)
The variance of a random variable X
σ(X)
The standard deviation of a random variable X
Ber(p)
The Bernoulli distribution with success probability p
B(n,p)
The Binomial distribution with the number of trials n
and a success probability p in each trial
N(,σ
2
)
The Normal distribution with mean and variance σ
2
Φ(.)
The standard normal cumulative distribution function
