I read chapters 2 and 3 and explored generating random bits. The chapter was clear that random bits generated using the Mersenne Twister algorithm, which is used in python, ruby and a bunch of others as the default generator, generates randomly distributed bytes that are not cryptographically secure because they are entirely deterministic. By doing some bitwise operations you can determine the next output given a certain number of outputs. This code code on github can predict the values after seeing 624 values from an MT algorithm:
https://gist.github.com/Rhomboid/b1a882c70b7a1901efa9
I tried graphing some functions using a jupyter notebook and matplotlib. The algorithm is good at producing evenly distributed points, so just graphing the output isn't very illuminating. I successfully generated a bunch of arrays of random numbers and plotted them in 2d graphs successively. I got hung up on an error trying to graph them in 3d space. This code created a valid graph:
ax = plt.axes(projection='3d')
# Data for three-dimensional scattered points
data = [random.random() for i in range(999)]
zdata = [random.random() for i in range(1000)]
xdata = [random.random() for i in range(1000)]
ydata = [random.random() for i in range(1000)]
ax.scatter3D(xdata, ydata, zdata, c=zdata, cmap='Blues');
but this code did not:
ax = plt.axes(projection='3d')
# Data for three-dimensional scattered points
data = [random.random() for i in range(999)]
zdata = [data for i in range(0, 999, 3)]
xdata = [data for i in range(1, 999, 3)]
ydata = [data for i in range(2, 999, 3)]
ax.scatter3D(xdata, ydata, zdata, c=zdata, cmap='Blues');
My error message was:
AttributeError: 'list' object has no attribute 'shape'
At first I was just hitting this error and tried making working code as close as possible to the code I wanted that created a valid graph. In both cases the data put into the graph are arrays of floats from 0 to 1. I don't think the second graph would be particularly more illuminating but it would be nice if it worked. Graphing something like the derivative between x and y in z-space might show a more useful pattern if the output can be determined from 624 successive example outputs, but I didn't get that far. Below are some screenshots.
In chapter 3 they talked about provably secure and insecure cryptographic schemes that often build off of perviously proven algorithms. I used ssl to generate a symmetric key like this:
>>openssl rand 16 -hex
95fe00b9be243fd3ae4242f0ab7907dd
The book also talked about how asymmetric keys were protected, how some were generated directly from passwords, and some were generated by a PRNG and then password protected locally, which can generally be considered more secure because they aren't as vulnerable to poor password strength. IE: if your information is encrypted based on a key generated from your password, if an attacker knows the algorithm they can try a number of common passwords to decrypt your message, where if your key is stored and protected locally by a password, it is harder for them to gain access to testing the password.
>> openssl genrsa -aes128 4096
Generating RSA private key, 4096 bit long modulus
............++
........................................................++
e is 65537 (0x10001)
Enter pass phrase:
Verifying - Enter pass phrase:
-----BEGIN RSA PRIVATE KEY-----
Proc-Type: 4,ENCRYPTED
DEK-Info: AES-128-CBC,07CFB3CBE8948D6154251E620AD974F5
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ebdj1g7UD2T+pWvKrs8I1ATt3MNxedx41fPEvPGX22IBrPoQC89YdlAztEAnraMD
-----END RSA PRIVATE KEY-----
![[paper clip]](/cours/static/images/paper_clip_tilt.png)
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