Frequency Analysis is an awesome tool for anyone into cryptography or puzzles. It is all about counting how often letters or groups of letters appear in text. This can really helpful when you are trying to break substitution ciphers. Let me show you how it works!
What is Frequency Analysis?
Frequency Analysis is when you study how often letters or groups of letters show up in some text. In cryptography, it helps to break substitution ciphers by looking at which letters come up the most in the cipher text. I remember the first time I used Frequency Analysis. It was a puzzle in a local newspaper, and I spent hours trying to figure it out. When I finally did, it felt like unlocking a secret code!
Why Frequency Analysis Matters
Every language has its own pattern of letter frequencies. For example, in English, letters like E, T, A, and O are used a lot, while Z, Q, and X are rare. By counting how often each letter appears in a cipher text, you can guess which letters they might be.
How Frequency Analysis Works
Here’s how you can use Frequency Analysis:
- Single Letters (Unigram):
- Count how often each letter appears in the cipher text.
- Compare these counts with how often letters usually appear in English.
- Groups of Letters (Polygram):
- Two-letter groups (Bigrams): Look for common pairs like ‘TH’, ‘HE’, ‘IN’.
- Three-letter groups (Trigrams): Find frequent trigrams like ‘THE’, ‘AND’, ‘ING’.
- Step Size and Offset:
- Step Size: This tells you how many positions between the starts of the codes. For example, with a step size of 1, bigrams would be AB, BC, CD, etc.
- Offset: This is where you start your analysis. With an offset of 1, bigrams would be BC, DE, FG, etc.
Let’s Try an Example
Here’s an example to see how Frequency Analysis works:
Ciphertext: “IE SKXY BEO WXT, SAYK SKXY BEO’HU CEY, SKUPU BEO XPU. – YUIIB PEEZUHUMY”
- Count Letter Frequencies:
- E: 6 times
- S: 5 times
- K: 5 times
- (Keep counting for all letters)
- Compare with English Letter Frequencies:
- E is the most common letter in English, about 12% of the time.
- This suggests that the frequent ‘E’ in the cipher text might be ‘E’ in the plaintext.
- Make Guesses and Decode:
- Based on the frequency, start making guesses and look for patterns or words.
- Keep refining your guesses until the cipher text is decoded.
Example Frequency Chart
Here’s a chart showing how often letters appear in English. This can help you figure out the cipher text:
| Letter | Frequency (%) |
|---|---|
| E | 12.7 |
| T | 9.1 |
| A | 8.2 |
| O | 7.5 |
| I | 7.0 |
| N | 6.7 |
| S | 6.3 |
| H | 6.1 |
| R | 6.0 |
| D | 4.3 |
| L | 4.0 |
| C | 2.8 |
| U | 2.8 |
| M | 2.4 |
| W | 2.4 |
| F | 2.2 |
| G | 2.0 |
| Y | 2.0 |
| P | 1.9 |
| B | 1.5 |
| V | 1.0 |
| K | 0.8 |
| J | 0.2 |
| X | 0.2 |
| Q | 0.1 |
| Z | 0.1 |
Boosting Your Skills
Frequency Analysis is powerful, but mixing it with other methods can make you even better at solving ciphers. When I solve puzzles like Cryptoquip and Cryptoquote, using frequency analysis with context clues and pattern recognition really helps.
