The Birthday Problem

Now that we have learned about the birthday problem, what significance does it have in the real world? One category of applications of this problem are hash functions in computer science. "A hash function is a mathematical function that converts any digital data into an output string with a fixed number of characters" (Loo, 2023). It converts data (like a message or password) into a fixed output (the hash). "Hashing is useful to ensure the authenticity of a piece of data and that it has not been tampered with...and hash functions are the basic tools of modern cryptography that are used in information security" for authentication (Loo, 2023). An issue that can arise with hashing is two different inputs resulting in the same hash, called "a hash collision." This "problem in computer science generalizes the birthday problem to other scenarios" as we can calculate the probability of two or more inputs having the same hash similarly to calculating the probability of two or more people having the same birthday (Tesler, 2020). This probability is significant because if this event occurs, the hash created by a hacker's input would be the same as the hash for your password, allowing their (even incorrect) input to qualify as verification to access your account. Thankfully, there's "no need to worry about random collisions compromising your password strength [because though] there is a chance that your strong password shares a hash with a very weak password, that chance is much smaller than the chance of the attacker brute-forcing the entire sample space of the hashing function" (Bellore, 2021). Although random collisions are not likely to have an effect on password strength, this knowledge remains useful because password security is an important topic in our modern society and it is interesting to see how the calculations used to solve the birthday problem apply here.