Blog posts

Shamir secret sharing with a single share: finding the root of a degree-$3^9$ polynomial $P$ via $\gcd(P(x), x^p - x)$.

Crypto writeups for 0xL4ugh CTF (December 2024), including an AES-CTR nonce-reuse attack.

My favorite theorem in extremal graph theory: Zarankiewicz problems and an application to communication complexity.

Do the unit vectors always span a vector space? Why not, and what a Schauder basis is instead, with examples and the role of separability.

RSA with a leaky hint $K = (Ap^2 - Cp + D)d$: approximating $p$ from $K$, then recovering it exactly.

A b01lersCTF 2022 challenge built on the Goldreich–Levin hardcore predicate, solved with a noisy inner-product oracle.

Floating-point $a\cos(x) + b\sin(x)$ turned into integers: recovering $a$ and $b$ with LLL.

Trying OSINT for the first time: writeups for three DownUnderCTF challenges, solved for b01lers.

Carmichael numbers in place of primes: getting past the server's Fermat checks, then recovering $k$ from $a$ and $a^k \bmod n$.

Which integers can be written as $x^2 + 2y^2$? An olympiad number theory problem, solved with Legendre symbols.

Author's writeups for my first CTF challenges, including an attack on Shamir secret sharing with badly chosen evaluation points.

Factoring $N = pq$ when $p$ and $q$ use only the digits $2$ and $7$, recovering them one digit at a time from the bottom.

Factoring $N = pq$ with a square-root oracle: a nontrivial square root of $1$ modulo $N$ leaks a prime factor.

A batch of RSA variants, from tiny $e$ to ambiguous moduli, solved in a CTF I played solo.

A solo run of Pointer Overflow CTF: writeups for its crypto, web and forensics challenges.

Crypto, web, pwn and misc writeups from b01lers Bootcamp CTF, the beginner CTF where I got started.

Crypto (Cherry Leak) and forensics (brokenimg) writeups from my first CTF as a member of b01lers.