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Cryptography
Explore arithmetic and security models; encryption and authentication; groups, signatures and hashes. Concepts and connections are available independently of video coverage.
Prerequisites and connections
Groups
A group has an associative operation, an identity and an inverse for every element.
Video explanations to be added
Arithmetic and security models
Modular arithmetic
Congruence identifies integers with the same remainder modulo a positive integer.
Video explanations to be addedModular inverses
An integer has an inverse modulo n exactly when it is coprime to n.
Video explanations to be addedChinese remainder theorem
Pairwise coprime moduli give a unique combined congruence class modulo their product.
Video explanations to be addedCryptographic security models
Security depends on defined adversary capabilities, assumptions and failure probability.
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Encryption and authentication
Symmetric encryption
A shared secret key supports encryption and decryption under a specified scheme.
Video explanations to be addedPublic-key encryption
Public encryption keys and private decryption keys have different roles.
Video explanations to be addedRSA
RSA uses modular exponentiation with related exponents; secure encryption requires appropriate padding and parameters.
Video explanations to be addedDiffie–Hellman key agreement
Parties derive a shared secret through group exponentiation; authentication is needed against interception.
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Groups, signatures and hashes
Elliptic curve cryptography
Finite-field elliptic curve groups support cryptography based on hard discrete logarithms.
Video explanations to be addedDigital signatures
A private signing key and public verification key authenticate messages under security assumptions.
Video explanations to be addedCryptographic hashes
Cryptographic hashes aim at preimage and collision resistance; hashing alone is not encryption.
Video explanations to be addedZero-knowledge proofs
A proof can establish a statement without revealing extra witness information in a formal security model.
Video explanations to be added