Implementing-cryptography-using-python

116 Chapter 4 ■ Cryptographic Math and Frequency Analysis
Breaking C’s rand() Function
In the C programming language, and most other software languages, the
compiler implements pseudorandom number generators. Almost all module
functions depend on the basic function random(), which generates a random
float uniformly in the semi-open range [0.0, 1.0). Python uses the Mersenne
Twister algorithm as the core generator. It produces 53-bit precision floats and
has a period of 2**19937 − 1. The underlying implementation in C, the rand()
function, is both fast and thread safe. The Mersenne Twister is one of the most
extensively tested random number generators in existence. However, being
completely deterministic, it is not suitable for all purposes and is completely
unsuitable for cryptographic purposes. The random module also provides the
SystemRandom class, which uses the system function os.urandom() to generate
random numbers from sources provided by the operating system:
def crand(seed):
r=[]
r.append(seed)
for i in range(30):
r.append((16807*r[-1]) % 2147483647)
if r[-1] < 0:
r[-1] += 2147483647
for i in range(31, 34):
r.append(r[len(r)-31])
for i in range(34, 344):
r.append((r[len(r)-31] + r[len(r)-3]) % 2**32)
while True:
next = r[len(r)-31]+r[len(r)-3] % 2**32
r.append(next)
yield (next >> 1 if next < 2**32 else (next % 2**32) >> 1)
my_generator = crand(123)
for i in range(5):
print (next(my_generator))
The output for the program will match the “random” numbers produced
here. If the numbers are predictable, then they are not random:
128959393
1692901013
436085873
748533630
776550279