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Encryption noise

As explained in Real-World Cryptography

Encryption noise is an error component introduced or accumulated during homomorphic evaluation that can eventually prevent correct decryption.

Encryption noise is error carried by a ciphertext. In homomorphic encryption, additions and multiplications accumulate noise until decryption crosses a threshold and fails. section 15.2.3 section 15.2.2

A ciphertext reaches its limit

After several operations, a ciphertext may still decrypt correctly but have too much noise for further operations. Bootstrapping evaluates a decryption circuit on the ciphertext to reduce the noise, though that circuit introduces some error of its own. section 15.2.3

Noise appears in two useful cryptographic roles:

  • In LWE, adding a random small error makes secret recovery harder. section 14.3.2
  • In homomorphic encryption, accumulated error limits circuit depth unless bootstrapping refreshes the ciphertext. section 15.2.2

How Real-World Cryptography covers it

How deep it goes
Explains noise growth, failure thresholds, and bootstrapping, but stops short of construction-level mechanics.
Examples
Uses noisy linear equations, homomorphic additions and multiplications, and ciphertext refresh through bootstrapping.
What it assumes
Assumes basic encryption and decryption, while introducing homomorphic operations and public-key bootstrapping contextually.
What you can do after
Diagnose when accumulated ciphertext error will block further evaluation and understand why bootstrapping is needed.
How it connects
Connects homomorphic encryption, bootstrapping, LWE, and decryption circuits.
Cover of Real-World Cryptography
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Related concepts

This explainer was generated by Manning's knowledge graph from the text of Real-World Cryptography. The section links point to the parts of the book it draws on.