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A monoalphabetic substitution cipher that maps letters via an affine function in modular arithmetic.
DESCRIPTION
The affine cipher encrypts each letter by mapping it to a numeric value and applying E(x)=ax+b mod m, then converting back to a letter. It generalizes Caesar (a=1) and relies on a and m being coprime for invertibility. Like other monoalphabetic ciphers, it is vulnerable to frequency analysis and provides no modern security. It is primarily used for education and illustrating modular arithmetic in cryptography.
ALTERNATIVE DEFINITIONS
Wikipedia
In classical cryptography, the affine cipher is a type of monoalphabetic substitution cipher, wherein each letter in an alphabet is mapped to its numeric equivalent, encrypted using a simple mathematical function, and converted back to a letter.
Emphasizes numeric mapping and affine transformation in modular arithmetic.
Wolfram MathWorld
The affine cipher replaces each letter x by ax + b (mod m), where a and m are coprime, and then maps back to a letter.
Formal definition highlighting invertibility conditions and function form.
RELATED TERMS
Substitution Monoalphabetic Substitution Caesar Cipher Atbash Cipher Frequency Analysis Modular Arithmetic Plaintext Ciphertext Classical Cryptography
COMPETING TERMS
RELATIONS
- Broader: Classical Cryptography Monoalphabetic Substitution Substitution
- Narrower: Atbash Cipher
KNOWLEDGE AREAS
TARGET AUDIENCE
Cybersecurity Engineer Security Architect Software Developer Data Scientist
EXTERNAL SOURCES
- Wikipedia - Affine cipher
- Crypto Corner - Interactive affine cipher tutorial
- Practical Cryptography - Explanation and attacks
TOP QUESTIONS
How does the Affine Cipher work?
Letters are mapped to numbers, transformed by E(x)=ax+b mod m, then mapped back, using an invertible a with respect to m.
Category: Example
Is the Affine Cipher secure?
No. Like other monoalphabetic ciphers, it’s easily broken by frequency analysis and known-plaintext attacks.
Category: Risks
How does the Affine Cipher relate to the Caesar Cipher?
Caesar is a special case with a=1; the affine cipher generalizes shifts with both a multiplier and offset.
Category: Misunderstanding
What’s a common mistake with the Affine Cipher?
Choosing a non-coprime a yields a non-invertible mapping, making decryption impossible or ambiguous.
Category: Mistakes
How is the Affine Cipher broken?
Frequency analysis and solving simple linear equations mod m recover a and b from ciphertext samples.
Category: Testing
Where is the Affine Cipher used today?
In education and demonstrations of modular arithmetic and classical cryptography concepts.
Category: Relevancy
What is the role of modular arithmetic in the Affine Cipher?
It ensures wrap-around within the alphabet and defines invertibility conditions for decryption.
Category: Example
What are appropriate alphabets for the Affine Cipher?
Any finite alphabet; typically 26 letters, but it can extend to custom symbol sets with modulus m.
Category: Opinion
How to practice implementing the Affine Cipher?
Start with a simple alphabet, write encrypt/decrypt functions, and test on sample texts and known keys.
Category: Getting Started