Index Of Coincidence

In [2]:

ioc("the quick brown fox jumps over the lazy dog") * 26
ioc(os.urandom(2 ** 15)) * 256

Index of coincidence is a metric that can be used to measure how evenly-distributed (or “random”) the letters of a given text is.

Algorithm

The metric calculates how likely you are to pick the same character if you pick two random characters from the text. An easy way to calculate this is to pick two random characters and count how many of them are identical.

Example

In [3]:

lipsum = """
Lorem ipsum dolor sit amet, consectetur
adipiscing elit. Nulla tempus convallis
accumsan. Suspendisse ac euismod lectus.
Class aptent taciti sociosqu ad litora
torquent per conubia nostra, per inceptos
himenaeos. Aliquam sit amet urna accumsan,
porttitor sem id, aliquam sapien. Morbi
ullamcorper erat eget auctor viverra.
Nam rutrum eget justo id fermentum. Proin
accumsan condimentum dolor, non bibendum
lorem placerat quis. Sed ultrices, nisl
non varius feugiat, purus eros faucibus
quam, vel laoreet quam turpis laoreet nibh.
Etiam tincidunt massa volutpat ligula
pharetra faucibus. Curabitur malesuada erat
orci, ac aliquet nibh vestibulum tincidunt.
Nulla gravida erat neque, tristique aliquet
erat egestas at. Vivamus tristique tristique
nisl, convallis faucibus nisi dignissim sed.
Cras id erat sed sapien rutrum imperdiet.
Maecenas vestibulum mi libero, non iaculis
nunc viverra sed. Donec massa felis, tincidunt
at ligula ut, ultrices pulvinar libero. Aenean
lectus ipsum, porta sit amet sapien quis, fermentum non.""".replace("\n", "")

In [4]:

same = 0
total = 0

for _ in range(5_000_000):
    c1 = random.choice(lipsum)
    c2 = random.choice(lipsum)
    
    if c1 == c2:
        same += 1
    total += 1

In [5]:

same / total

In [6]:

same / total * 26

Out [6]:

1.6683212000000003

In [7]:

rand_bytes = list(os.urandom(2 ** 14))

rand_bytes[:10]

Out [7]:

[250, 198, 255, 162, 148, 14, 127, 254, 85, 202]

In [8]:

same = 0
total = 0

for _ in range(5_000_000):
    c1 = random.choice(rand_bytes)
    c2 = random.choice(rand_bytes)
    
    if c1 == c2:
        same += 1
    total += 1

Index Of Coincidence

Algorithm

Example

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