Understanding Frequency Analysis in Classical Cryptography

What Frequency Analysis Actually Measures

Frequency analysis is the art of counting how often each letter appears in a piece of text, then comparing that pattern to what you would expect from normal language. In English, some letters are workhorses: E is the most common, followed closely by T and A. Others, like Z, Q, and X, are rare. When you encrypt a message with a simple substitution cipher — where each letter is consistently replaced by another — those frequencies do not disappear. They are merely disguised. If the original message had lots of E's, the ciphertext will have lots of whatever letter replaced E. That is the crack in the armour.

The Classic Letter Frequencies of English

Before you can break anything, you need a rough mental map of English letter frequencies. For everyday prose, a reliable guide is:

• E — around 12.7%
• T — around 9.1%
• A — around 8.2%
• O — around 7.5%
• I — around 7.0%
• N — around 6.7%
• S — around 6.3%
• H — around 6.1%
• R — around 6.0%
• D — around 4.3%
• L — around 4.0%
• U — around 2.8%

These percentages shift slightly depending on the text. A short message about quizzes might be full of Z's and Q's; a passage from a thriller might have more action words. But for a paragraph or more of ordinary English, these figures are a dependable starting point. You will also want to note common pairs (digraphs) like TH, HE, IN, ER, AN, and RE, and common triplets such as THE, AND, ING.

Counting Letters by Hand

You do not need fancy software. Grab a pencil and a sheet of paper. Write out the ciphertext in groups of five letters (this makes counting easier and avoids mistakes). Then create a tally table for A to Z. Go through the text one letter at a time, marking a stroke for each occurrence. When you have finished, total the tallies. You can also count digraphs: look for repeated two-letter combinations and note them down. If you prefer, a simple spreadsheet works, but the physical act of tallying builds intuition. You will start to feel which letters are unusually common. As a beginner, aim for at least 100–150 letters of ciphertext before trusting the counts. Shorter messages are noisier and harder to break.

From Counts to Cribs: Spotting Patterns

Once you have your frequency table, compare it to the English one. The most frequent ciphertext letter is a strong candidate for E. The next few might be T, A, or O. But do not stop there. Look at the structure. A single-letter word in the ciphertext is almost certainly A or I (or O in older poetry). A three-letter word that appears often is likely THE or AND. If you see a repeated pattern like XYYX, it might be THAT, SEES, or ELLE in French. This is where puzzle solving becomes a detective game. You form a hypothesis, test it against the ciphertext, and revise. The technique is called using cribs — guessed words or phrases that give you a foothold.

A Worked Example: Breaking a Simple Substitution

Suppose you intercept this ciphertext: WKLV LV D WHVW PHVVDJH. First, count the letters. V appears four times, L three times, W twice, and H twice. The most frequent letter is V. If V is E, then the cipher might be a Caesar shift. Look at the word WKLV. If V is E, then the shift is three places backwards? Let us check: W→T, K→H, L→I, V→S. That gives THIS. Yes! The next word LV becomes IS. D becomes A. WHVW becomes TEST. PHVVDJH becomes MESSAGE. The plaintext is "THIS IS A TEST MESSAGE". You have just used frequency analysis (plus a little Caesar logic) to crack a message. For a general substitution cipher, where letters are not shifted uniformly, you would rely more heavily on digraphs and cribs, but the principle is identical.

Common Pitfalls and How to Sharpen Your Eye

Frequency analysis is powerful, but it is not magic. Here are a few traps for new codebreakers:

• Short texts lie. A 20-letter ciphertext might have Z as the most common letter, simply by chance. Always work with as much text as you can.
• Spaces and punctuation matter. If the ciphertext retains spaces, use them. Word lengths are clues. If spaces are removed, you must reconstruct word boundaries, which is harder.
• Not all ciphers are vulnerable. The Vigenère cipher, for example, uses a repeating keyword to shift letters differently, which flattens the frequency distribution. Breaking it requires finding the key length first (using the Kasiski examination or index of coincidence), then applying frequency analysis to each column separately.
• Language varies. A message about physics will not match the frequencies of a shopping list. If you suspect a specific topic, adjust your expected frequencies accordingly.

The best way to improve is to practise. Start with Caesar ciphers, then move to simple substitution. You will soon find that your eye catches odd patterns automatically. Frequency analysis is not just a historical curiosity — it is a foundation for understanding why modern cryptography needs to be so much more complex. But for a curious beginner, there is no better place to start than counting letters and letting the patterns speak.