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Cryptographic theory

As explained in Hacking Cryptography

The mathematical foundations and security analyses underlying cryptographic algorithms and protocols.

Cryptographic theory supplies the mathematical ideas behind algorithms and protocols that protect confidentiality and integrity. It becomes security only through software or hardware implementations designed to meet concrete system goals. section 1.5

The mathematics may be carefully developed and debated, yet practical failures usually arise in engineering: bugs, defective randomness, unsafe component interactions, or observable computation. Small implementation mistakes can expose critical keys even when the underlying theory remains sound. section 1.3 section 1.5

The PlayStation 3 failure

A faulty random-number process in a key cryptographic operation allowed Sony’s private key to be calculated and published, undermining the console’s goal of running only approved software. section 1.3

Apply cryptographic theory defensively:

  • Use well-established implementations rather than writing production cryptography from scratch. section 1.5
  • Treat interactions between cryptographic components as potential sources of subtle weaknesses. section 1.5
  • If custom cryptographic code is unavoidable, obtain review from as many qualified experts as possible. section 1.5

How Hacking Cryptography covers it

How deep it goes
Distinguishes mathematical theory from engineering attacks and implementation failures, but stops short of deriving algorithms or formal security proofs.
Examples
Uses the PlayStation 3 key-recovery failure and power-consumption analysis to illustrate implementation vulnerabilities.
What you can do after
Operate/configure cryptographic systems by selecting established implementations and arranging expert review for custom code.
How it connects
Connects cryptographic algorithms with cryptographic implementations, security goals, randomness, and implementation attacks.
Cover of Hacking Cryptography
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Related concepts

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