Cryptography
Explore arithmetic and security models; encryption and authentication; groups, signatures and hashes. Concepts and connections are available independently of video coverage.
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Modular arithmetic
Congruence identifies integers with the same remainder modulo a positive integer.
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Cryptographic security models
Security depends on defined adversary capabilities, assumptions and failure probability.
Euclidean algorithm
The Euclidean algorithm computes a greatest common divisor by repeated division with remainder. Replacing (a,b) by (b,r) preserves the common divisors, and the strictly smaller nonnegative remainders force termination.
Fermat and Euler theorems
Coprime residues satisfy power congruences controlled by prime moduli or Euler's totient.
Groups
A group has an associative operation, an identity and an inverse for every element.
Modular inverses
An integer has an inverse modulo n exactly when it is coprime to n.
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- Modular inverses · Related · Map context
- Cryptographic security models · Related · Map context
- Groups · Related · Map context
- Symmetric encryption · Related · Map context
- Modular inverses · Next concept · Map context
- Prime factorization · Related · Map context
- Fermat and Euler theorems · Related · Map context
- Fermat and Euler theorems · Next concept · Map context
- Euclidean algorithm · Related · Map context
- Modular inverses · Related · Map context
- Quadratic residues · Next concept · Map context
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Discrete Mathematics: Counting and Number Theory
Connect functions and counting with elementary number theory, graph structures and algorithmic reasoning. Shared concepts and reviewed map connections organize the path; video explanations are added as resources pass review.
Number Theory
Explore divisibility and congruences; arithmetic functions and equations; prime distribution and advanced connections. Concepts and connections are available independently of video coverage.