Cryptanalysis - How Weak Math Breaks Strong Systems

Cryptanalysis is the art and science of breaking cryptographic systems. When encryption is poorly designed - because of weak math, short keys, or predictable patterns - attackers can exploit those weaknesses to read secret messages.

What Makes a System "Weak"?

Too few keys: brute-force attacks can test them all
Simple math: like using modulo 26 for letters
Pattern leakage: repeated letters or structures
Reused keys: especially dangerous in stream ciphers

Example: Caesar Cipher

The Caesar cipher shifts each letter by a fixed number (e.g., +3). It only has 25 possible keys - easy for a computer (or even a human) to break.

Try It: Caesar Brute Force Cracker

Encrypted message (uppercase, no punctuation):

Frequency Analysis

Languages have patterns. In English, the most common letter is E. If a cipher always replaces the same letter the same way (like Caesar or monoalphabetic), frequency analysis can reveal the code.

Try It: Letter Frequency Counter

Enter a ciphertext:

Cracking RSA with Small Numbers

RSA is strong when large prime numbers are used. But if the primes are small, it becomes easy to factor n and discover the private key \( d \).

Try It: Small RSA Cracker

Enter public key (e, n) and ciphertext C:
e:
n:
C:

Summary

Cryptanalysis exposes weak systems
Short keys and simple math = easy targets
Patterns in plaintext can leak into ciphertext
Strong encryption uses randomness and big prime numbers