Public key crytography and data integrity

Public Key Cryptography

Shared symmetric keys: A common secret value used by two parties for symmetric encryption.
One-way function: A function that is easy to compute but hard to reverse.
Trapdoor function: A one-way function that is easy to invert only with special secret knowledge.
Public-key algorithm: A cryptographic algorithm that uses paired public and private keys.
Asymmetric cryptography: Another term for public key cryptography.
Public key: The openly shared key used for encryption or signature verification.
Private key: The secret key used for decryption or signing.
Factoring: The problem of finding the prime factors of a composite number; basis of RSA.
Discrete logarithms: The problem of finding the exponent in modular arithmetic; basis of Diffie–Hellman and ECC.
RSA: A public key system based on factoring, used for encryption and digital signatures. Larger key sizes are needed as computing power grows.
ECC: Elliptic-curve cryptography, based on discrete logarithms over elliptic curves.

Diffie–Hellman Key Exchange: A protocol that allows two parties to establish a shared secret over an insecure channel.
Hybrid cryptosystem: Combines public key methods for key exchange with symmetric ciphers for encrypting data.
Forward secrecy: Ensures past session keys remain secure even if long-term keys are later compromised. Usually provided by ephemeral Diffie-Hellman key exchange (ephemeral = D-H public/private keys are generated fresh for each session)
Long-term key: A cryptographic key pair intended for extended use (months or years), typically bound to an identity and used for tasks like authentication or signing.
Ephemeral key: A short-lived asymmetric key generated for a single protocol run (e.g., in Diffie–Hellman). It is discarded afterward to provide forward secrecy.
Session key: A temporary symmetric key derived during a protocol run, used to encrypt and authenticate traffic in one communication session.

Cryptographic hash function: Maps input data to a fixed-length digest in a way that is hard to reverse.
Message digest: The fixed-size output of a hash function; sometimes we just call it a hash.
Preimage resistance: Hard to find an input that hashes to a given output.
Second preimage resistance: Hard to find a different input that produces the same hash as a specific given input.
Collision resistance: Hard to find two different inputs that produce the same hash.
Avalanche effect: A small change in input causes a large, unpredictable change in the hash output.
Uniformity: Property outputs are evenly distributed across the entire output space.
Pigeonhole principle: Explains why collisions must exist since many inputs map to fewer outputs.
Birthday paradox: Shows collisions are easier to find than expected; probability rises quickly with more inputs.
Recognize SHA-1, SHA-2 (SHA-256, SHA-512), SHA-3: Major standardized cryptographic hash functions.

Message authentication code (MAC): A keyed hash value used to ensure message integrity.
HMAC: A MAC constructed from a hash function and a secret key.
CBC-MAC / CMAC: MACs built from block cipher modes.
Digital signature: A value computed with a private key that proves the origin and integrity of data.
Signing: Creating a digital signature with a private key.
Verification (Validation): Checking a digital signature using the corresponding public key.
Non-repudiation: Assurance that a signer cannot later deny creating a valid digital signature.

Digital certificates (X.509): Certificates that bind a public key to an identity such as a domain name.
Certification Authority (CA): A trusted entity that issues and signs digital certificates.
Trust store: A system-maintained collection of trusted root certificates.
Certificate chain: A sequence of certificates from the server’s certificate up to a trusted root CA, used to validate authenticity.

Quantum computing threat: The possibility that future quantum computers could break today’s public key systems.
Shor’s algorithm: A quantum algorithm that efficiently solves factoring and discrete logarithm problems.
Grover’s algorithm: A quantum algorithm that speeds up brute-force search, reducing effective key sizes.
Post-quantum cryptography (PQC): New classical cryptosystems designed to resist both classical and quantum attacks.

TLS (Transport Layer Security): A protocol that provides secure communication over the internet using authentication, encryption, and integrity checks.
TLS Handshake: The process by which client and server agree on protocol versions, negotiate cryptographic algorithms, authenticate the server (and optionally client), and establish shared session keys.
Handshake transcript: The record of all handshake messages exchanged; used in signature and MAC calculations to prevent tampering.
ServerHello / ClientHello: Initial handshake messages where both sides advertise supported versions, cipher suites, and options.
Cipher suite: A named set of algorithms specifying key exchange, encryption, and authentication methods used in a TLS session.
HKDF (HMAC-based Key Derivation Function): A standardized function that uses HMAC to derive multiple cryptographic keys from a shared secret, widely used in TLS to expand ephemeral secrets into session keys.
AEAD (Authenticated Encryption with Associated Data): An encryption mode (e.g., AES-GCM, ChaCha20-Poly1305) that ensures both confidentiality and integrity while also authenticating associated unencrypted data like headers.
Authentication tag: A short value (MAC) included with each encrypted TLS record to confirm data integrity and authenticity.