- Modulus (mod)
- The number you “wrap around” at in modular arithmetic.
17 mod 12 = 5, like a clock. See Modular Arithmetic. - Congruence
- Two numbers are congruent mod n if they leave the same remainder. Written
a ≡ b (mod n). - Prime number
- A whole number > 1 divisible only by 1 and itself. The “atoms” of multiplication and the basis of RSA.
- Coprime
- Two numbers whose greatest common divisor is 1. Key to choosing RSA exponents.
- One-way function
- Easy to compute, hard to reverse. The heart of every cipher — e.g. multiplying two primes vs. factoring the product.
- Modular exponentiation
- Computing
a^b mod nefficiently by squaring. Worked example on the learning path. - RSA
- A public-key system whose security rests on the difficulty of factoring large semiprimes. See Primes & RSA.
- Discrete logarithm
- Given
g^x = y (mod p), findingxis believed hard. Basis of Diffie–Hellman. See Discrete Logs. - Diffie–Hellman
- A protocol letting two parties agree a shared secret over a public channel using the discrete-log problem.
- Elliptic curve (ECC)
- A curve of the form
y² = x³ + ax + bwhose points form a group; gives strong security with small keys. See ECDSA. - ECDSA
- The elliptic-curve signature scheme that signs Bitcoin and Ethereum transactions.
- Hash function
- A one-way fingerprint of data (e.g. SHA-256). Explore it in the Simulator.
- Shor's algorithm
- A quantum algorithm that would break RSA and ECC by factoring / solving discrete logs efficiently. See Quantum.
- Lattice cryptography
- Post-quantum schemes whose security rests on hard lattice problems; basis of several NIST standards.
- Post-quantum cryptography
- Cryptography designed to resist quantum attacks. See Post-Quantum.
- Symmetric cryptography
- Encryption where the same secret key both encrypts and decrypts. Fast, so it protects most real data. See Symmetric Cryptography.
- AES
- The Advanced Encryption Standard — the worldwide symmetric block cipher (128-bit blocks, 128/256-bit keys).
- Block cipher
- A symmetric cipher that encrypts fixed-size blocks of data; a mode (CBC, CTR, GCM) extends it to long messages.
- One-time pad
- XOR with a truly random key as long as the message and never reused — provably unbreakable but impractical to key.
- MAC / HMAC
- A keyed tag proving a message wasn’t altered and came from a key holder — integrity and authentication. See Protocols.
- TLS
- Transport Layer Security — the protocol behind the HTTPS padlock, combining key exchange, certificates and symmetric encryption.
- Cryptographic protocol
- A sequence of steps combining crypto tools (key exchange, authentication, encryption) to reach a goal over an untrusted network.
- Zero-knowledge proof
- A protocol that proves a statement is true while revealing nothing else about the secret behind it.
- Kerckhoffs’s principle
- A system must stay secure even if the attacker knows everything except the key — no “security through obscurity.” See Security Definitions.
- Semantic security (IND-CPA)
- A formal definition: the ciphertext leaks essentially nothing about the plaintext, even against chosen-plaintext attacks.
- Provable security
- A proof (a “reduction”) that breaking a scheme would also solve a problem believed hard, like factoring.
- Cryptanalysis
- The science of breaking ciphers and measuring their strength. See Cryptanalysis.
- Frequency analysis
- Counting how often symbols appear to break substitution ciphers; the first known cryptanalysis (Al-Kindi, 9th c.).
- Birthday attack
- Finds a hash collision in only about 2n/2 work for an n-bit hash — why secure hashes need 256+ bits.
- Side-channel attack
- Recovering a key by measuring a device’s timing, power use or emissions instead of attacking the math.