(3.X) Cloudflare

Your Final Interview Question: What does this picture mean? (If you know you know) §

Random Number Generation

Encryption algorithms require randomness, and computers suck at generating random numbers.

Cloudflare is a DNS provider, which provides security to millions of websites. Predictable systems are vulnerable to attack, so they need a good way to achieve True Random Number Generation.

Lava lamps are inherently chaotic, so a camera takes photos at regular intervals and converts the pixels in the image into a string that can be then used as a seed to generate secure encryption keys.

---

What are some good reasons for needing to generate random numbers in the field of data science and machine learning? §

1. Initializing Parameters: in ML and DL, algorithms are often initialized with random weights, biases and parameters.
2. Monte Carlo Simulation: need to generate observations on various probability distributions
3. Random Sampling: either simulated random sampling, or generating random numbers to aid real random sampling (e.g I will sample from the $n$th floor where $n$ is a randomly generated number.)
4. Stochastic Optimization: Many optimization algorithms used in ML, such as Stochastic Gradient Descent (SGD), rely on randomness.
5. Exploration in Reinforcement Learning: can be used to help the model explore random strategies/states/actions, resulting in more robust learning.
6. Regularization: Such as ‘dropout’ when training neural networks.
7. Simulating Random Processes: related to Monte Carlo Simulation.
8. Ensuring Reproducibility: By setting a ‘seed’, we can debug and compare the performance of ML algorithms.

---

What are the different types of random number generation? §

True Random Number Generation (TRNG)

This involves using truly random natural phenomenon

True Random Number Generation (TRNG)

This involves using truly random natural phenomenon

---

How does random.randint work behind the scenes? §

The randint function, commonly found in programming languages like Python, is an implementation of a Pseudo-Random Number Generator (PRNG). Let’s take a closer look at how it typically works behind the scenes, using Python’s randint as an example:

1. Seed Initialization:

   • PRNGs start with an initial value known as a seed. In Python, if you don’t explicitly set a seed, the system time or another source of randomness is used to generate the seed. This seed is the starting point for generating a sequence of numbers that appears random.

2. Algorithm for Generating Numbers:

   • Once the seed is set, randint uses a specific algorithm to generate a sequence of numbers. Python’s random module, which includes randint, historically used the Mersenne Twister algorithm, a widely used and well-regarded PRNG. The Mersenne Twister produces numbers that pass many tests for statistical randomness.
   • These algorithms involve a series of mathematical operations (like multiplication, division, addition, modulo, bitwise operations) on the seed or the last generated number to produce the next number in the sequence.

3. Generating a Specific Range:

   • randint(a, b) in Python generates a random integer N such that a <= N <= b. The underlying PRNG algorithm generates a random number, which is then scaled or transformed to fall within the specified range [a, b].
   • This transformation is done in a way that tries to maintain uniform distribution, meaning each number in the range [a, b] has an equal probability of being selected.

4. Handling the State:

   • Each call to randint updates the state of the PRNG. This means that the output of one call to randint affects the next call. This sequence is deterministic; given the same initial seed and the same sequence of calls, randint will produce the same sequence of numbers.

5. Considerations of Randomness:

   • It’s important to note that the numbers generated by randint are pseudo-random. They are not truly random because they are generated by a deterministic process. However, for many applications, pseudo-random numbers are sufficient.
   • For cryptographic purposes or applications where true randomness is required, a Cryptographically Secure Pseudo-Random Number Generator (CSPRNG) or a True Random Number Generator (TRNG) should be used instead.

In summary, randint works by using a deterministic algorithm (like the Mersenne Twister) to generate a sequence of numbers that appear random, starting from an initial seed. The algorithm ensures that these numbers are uniformly distributed across the specified range.

---

How do computers typically generate observations on different probability distributions? §

$F^{-1}(U)=X$