Vigenère Cipher

The Vigenère Cipher is a method of encrypting alphabetic text using a series of Caesar ciphers based on the letters of a keyword. It is a polyalphabetic substitution cipher, meaning the same plaintext letter can be encoded to different ciphertext letters depending on its position.

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Introduction to Vigenère Cipher

The Vigenère Cipher is a method of encrypting alphabetic text using a series of Caesar ciphers based on the letters of a keyword. It is a polyalphabetic substitution cipher, meaning the same plaintext letter can be encoded to different ciphertext letters depending on its position.

Prerequisites

Caesar cipher concept Keyword repetition Vigenère square (tabula recta) Modular arithmetic
Why This Matters: Vigenère Cipher problems appear in 1-2 questions in advanced exams like CAT and Banking PO mains. They test understanding of polyalphabetic substitution.

How to Solve Vigenère Cipher Problems

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Step 1: Write the keyword repeatedly above the plaintext (or ciphertext for decoding)

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Step 2: Convert each plaintext letter and key letter to positions (A=0 to Z=25)

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Step 3: For encoding: cipher_position = (plain_position + key_position) mod 26

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Step 4: For decoding: plain_position = (cipher_position - key_position) mod 26

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Step 5: Convert resulting positions back to letters

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Step 6: The Vigenère square (tabula recta) can be used as an alternative to arithmetic

Pro Strategy: Use the Vigenère square for visual reference. The keyword determines the row, and the plaintext letter determines the column (for encoding). For decoding, find the ciphertext letter in the keyword row, then read the column header.

Example Problem

Example: Decode 'LXFOPVEFRNHR' using keyword 'LEMON'. Solution: Step 1: Keyword repeated: LEMONLEMONLE (ciphertext length 12) Step 2: Convert: L(11),E(4),M(12),O(14),N(13),L(11),E(4),M(12),O(14),N(13),L(11),E(4) Step 3: Ciphertext: L(11),X(23),F(5),O(14),P(15),V(21),E(4),F(5),R(17),N(13),H(7),R(17) Step 4: Plain_position = (cipher - key) mod 26: (11-11)=0→A, (23-4)=19→T, (5-12)=-7+26=19→T, (14-14)=0→A, (15-13)=2→C, (21-11)=10→K, (4-4)=0→A, (5-12)=-7+26=19→T, (17-14)=3→D, (13-13)=0→A, (7-11)=-4+26=22→W, (17-4)=13→N Step 5: Decoded: ATTACKATDAWN Answer: ATTACKATDAWN

Pro Tips & Tricks

  • The keyword determines the shift for each position (A=0 shift, B=1 shift, ..., Z=25 shift)
  • Vigenère square: rows = key letters, columns = plaintext letters, intersection = ciphertext
  • To decode, find ciphertext letter in the key letter's row, column header is plaintext
  • Keyword length is the period of the cipher
  • Longer keywords make the cipher more secure
  • A keyword of length 1 is equivalent to a Caesar cipher

Shortcut Methods to Solve Faster

Encoding: C = (P + K) mod 26
Decoding: P = (C - K) mod 26
Use A=0, B=1, ..., Z=25 for easier modulo arithmetic
Tabula recta: create a 26x26 table for quick lookup

Common Mistakes to Avoid

Using A=1 instead of A=0 (off by one errors)
Forgetting to wrap around using modulo 26
Mismatching keyword length with message length
Applying the wrong operation (addition vs subtraction) for encoding vs decoding

Exam Importance

Vigenère Cipher is an important topic for various competitive exams. Here's how frequently it appears:

SSC CGL
1-2 questions
BANKING PO
1-2 questions
RAILWAYS RRB
1-2 questions
CAT
2-3 questions
INSURANCE
1-2 questions

Ready to Master Vigenère Cipher?

Start with Worksheet 1 and work your way up to expert level! Each worksheet includes:

20 practice questions
Detailed solutions
Step-by-step explanations
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