Caloogy Blog
Cryptography
Shamir's Secret Sharing: Split a Private Key into n Shares, Recover It from Any k
Oct 20, 2026 · 4 min
Post-Quantum Cryptography Explained
Oct 19, 2026 · 21 min
How Mathematicians Broke Enigma: Permutation Groups and Conjugation
Oct 9, 2026 · 5 min
The One-Time Pad and Shannon: The Only Cipher Proven "Absolutely Secure"
Sep 27, 2026 · 4 min
Schnorr Signatures and Σ-Protocols: The Simplest Zero-Knowledge Proof
Jul 31, 2026 · 4 min
The Birthday Paradox and Hash Collisions: Why SHA-256 Has Only 128-Bit Collision Resistance
Apr 24, 2026 · 4 min
Homomorphic Encryption Explained
Apr 9, 2026 · 19 min
Isogeny Cryptography and the Death of SIKE: A Laptop Breaks a NIST Candidate in an Hour
Feb 21, 2026 · 5 min
Bilinear Pairings and BLS Signatures: Compressing Ten Thousand Signatures into One
Feb 4, 2026 · 4 min
Diffie–Hellman and the Discrete Logarithm: Why Prime-Order Subgroups
Dec 8, 2025 · 5 min
Where Primes Come From: The Fermat Test, Carmichael Numbers and Miller–Rabin
Nov 18, 2025 · 5 min
The Chinese Remainder Theorem: One Theorem Holding Up Half of Cryptography
Nov 11, 2025 · 4 min
The Finite Field Inside AES: The S-box Is Really an Inverse in F28
Oct 29, 2025 · 4 min
LLL Lattice Reduction: How the Knapsack Cryptosystem Fell
Sep 29, 2025 · 6 min
Why RSA Decrypts Correctly: Euler's Theorem and the Chinese Remainder Theorem
Jun 9, 2025 · 5 min
Linear Feedback Shift Registers: Primitive Polynomials over F2[x] and Stream Ciphers
May 5, 2025 · 5 min
Casting Out Nines and Check Digits
May 4, 2025 · 15 min
Elliptic Curves: Why Points on a Curve Can Be "Added"
Apr 25, 2025 · 5 min