Implementing-cryptography-using-python

Chapter 4 ■ Cryptographic Math and Frequency Analysis 115
Pseudorandomness
You will now examine pseudorandom number generation (PRNG) and why it
is insecure for use in cryptography. The goal of PRNG is to have a reproducible
sequence of random-feeling numbers. PRNG offers benefits when running
simulations that need to be consistent between each execution. Some examples
of simulation that benefit from the consistency of a PRNG generator include
testing stock market predictions, testing scientific experiments, rolling dice in
games, and generating symmetric-key encryption.
In the early days of computing, when applications needed to simulate nuclear
reactions but also needed to be reproducible in the case of an error in the program,
John von Neumann generated one of the first pseudorandom generators using
the middle-square method. The method generates a sequence of n-digit numbers
based on the digits in the middle of the number and then squares them. For
example, if you have a seed number of 682117, you square it to get 465283601689.
The middle numbers are 283601. Square this number and repeat. So while the
number appears random, you can reproduce the generated numbers as long as
you start with the same seed.
Take a look at how this can be done using Python:
n = int(input("Please enter a six-digit number: "))
for i in range(1,10):
n = int(str(n * n).zfill(12)[3:9])
print(n)
Please enter a six-digit number: 682117
283601
429527
493443
485994
190168
163868
852721
133103
716408
PRNG in encryption needs to have two properties that ensure its security.
When the properties exist, the PRNG is known as a cryptographically secure
pseudorandom number generator (CSPRNG). A CSPRNG must have the following
properties:
■■
Next-bit test: You should not be able to guess the next bit with no better
than 50% probability. This means given S i + 1 , S i + 2 , S i + 3 , . . . , S i + n you
should not be able to guess S i + n + 1 .
■ ■ State compromised extension: You should not be able to calculate
S i , S i − 1 , . . . , given S i + 1 , . . . , S i + n .