https://khayliang.github.io/Writings, portfolio, resume 2026-08-29T08:06:27+00:00 Khayliang Tan https://khayliang.github.io/ Jekyll © 2026 Khayliang Tan /assets/img/favicons/favicon.ico /assets/img/favicons/favicon-96x96.png 2026-08-29T00:00:00+00:00 2026-08-29T00:00:00+00:00 https://khayliang.github.io/posts/tarjans-algo/ Khayliang Tan

Tarjan’s algorithm is a modification of the Bridge Finding Algorithm except for directed graphs. We maintain a stack, with the following invariant: Let $S$ be a stack with vertices $v_1, \dots, v_k$. For a vertex $v_{k + 1}$ to be added onto the stack, there must exist a path from vertex $v_{k+1}$ to some previous vertex existing in the stack, $v_1,\dots,v_k$. We define a recursive functi...

2026-08-29T00:00:00+00:00 2026-08-29T00:00:00+00:00 https://khayliang.github.io/posts/rsa/ Khayliang Tan

Background Definitions The Euler’s totient function, represented as $\phi(n)$, gives us the number of positive integers up to $n$, that are relatively prime to $n$. For example, $\phi(9) = 6$ since the numbers $1,2,4,5,7,8$ are relatively prime. Lemmas Lemma 1: If $k$ is relatively prime to $n$, then there exists a multiplicative inverse $k^{-1}$ such that [k\cdot k^{-1} \equiv 1 \mod n] Pro...

2026-08-29T00:00:00+00:00 2026-08-29T00:00:00+00:00 https://khayliang.github.io/posts/kademlia-dht/ Khayliang Tan

Kademlia is a distributed hash table where the platform enables the distributed storage of key-value pairs with redundancy. Kademlia is composed of distributed processors connected together which we call nodes. Each node in the system gets a unique ID, and all IDs in Kademlia are of fixed binary length, including the keys that will be stored. Next, we can logically compute a distance between e...