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Cryptography

Algorithms that protect data and communication.

Cryptographic algorithms help encrypt data, exchange keys, verify integrity, and support secure systems.

CryptographyO(k^3)

RSA

Uses modular arithmetic with a public key and private key for encryption or signatures.

AdvancedFoundationFormula8 links
CryptographyPublic KeySecurity
CryptographyO(k^3)

Diffie-Hellman Key Exchange

Lets two parties derive a shared secret over an insecure channel.

AdvancedFoundationFormula8 links
CryptographyKey ExchangePublic KeySecurity
CryptographyO(n)

AES

Encrypts fixed-size blocks with a symmetric key using repeated substitution and permutation rounds.

AdvancedFoundationFormula11 links
CryptographySymmetric KeySecurity
CryptographyO(n)

SHA-256

Computes a fixed 256-bit cryptographic hash of an input message.

AdvancedFoundationFormula9 links
CryptographyHashingSecurity
CryptographyO(mt)

Argon2

Hashes passwords with tunable memory and time cost.

IntermediateCoreFormula4 links
CryptographyPassword HashingSecurity
CryptographyO(n)

ChaCha20

Encrypts data with a fast stream cipher built from add-rotate-xor rounds.

AdvancedCoreFormula3 links
CryptographyStream CipherSymmetric KeySecurity
CryptographyO(k^2)

EdDSA

Creates deterministic elliptic-curve signatures on Edwards curves.

AdvancedSpecializedFormula4 links
CryptographyElliptic CurveDigital SignatureSecurity
CryptographyO(k^2)

Elliptic Curve Diffie-Hellman

Establishes a shared secret using elliptic-curve key exchange.

AdvancedExtendedFormula4 links
CryptographyElliptic CurveKey ExchangeSecurity
CryptographyO(k^2)

Elliptic Curve Digital Signature Algorithm

Creates digital signatures with elliptic-curve keys.

AdvancedSpecializedFormula4 links
CryptographyElliptic CurveDigital SignatureSecurity
CryptographyO(n)

HMAC

Authenticates messages by combining a hash function with a shared secret key.

IntermediateCoreFormula7 links
CryptographyMessage AuthenticationHashingSecurity
CryptographyO(n)

BLAKE3

Computes a fast cryptographic hash using a tree structure that can run in parallel.

AdvancedExtendedFormula4 links
CryptographyHashingHash FunctionSecurity
CryptographyO(n)

HKDF

Derives strong key material from shared secrets using HMAC-based extract and expand steps.

IntermediateExtendedFormula5 links
CryptographyKey DerivationMessage AuthenticationSecurity
CryptographyO(t^2)

Shamir's Secret Sharing

Splits a secret into shares so only a threshold number of shares can reconstruct it.

AdvancedSpecializedFormula3 links
CryptographySecret SharingSecurityInterpolation
CryptographyO(iterations)

PBKDF2

Derives keys from passwords by iterating a pseudorandom function with a salt.

IntermediateCoreFormula6 links
CryptographyKey DerivationPassword HashingMessage Authentication
CryptographyO(N)

Scrypt

Derives password keys with intentionally high memory use to resist hardware guessing.

AdvancedCoreFormula4 links
CryptographyPassword HashingKey DerivationSecurity
CryptographyO(n)

SipHash

Computes a fast keyed hash for short messages and hash-table protection.

IntermediateExtendedNo formula3 links
CryptographyHash FunctionMessage AuthenticationSecurity
CryptographyO(rounds)

Feistel Network

Builds an invertible block cipher structure from repeated round functions.

IntermediateCoreFormula2 links
CryptographySymmetric KeySecurityClassic
CryptographyO(n)

Merkle-Damgard Construction

Builds a hash function by chaining a compression function over message blocks.

AdvancedCoreFormula3 links
CryptographyHash FunctionSecurityClassic
CryptographyO(n)

One-Time Pad

Encrypts a message by combining it with a truly random key used exactly once.

BeginnerCoreFormula1 links
CryptographySymmetric KeySecurityClassic
CryptographyO(rounds)

Zero-Knowledge Proof

Lets one party prove a statement without revealing the secret that makes it true.

AdvancedSpecializedFormula3 links
CryptographyZero KnowledgeSecurityProof
CryptographyO(log n)

Merkle Tree

Builds a tree of hashes so large datasets can be checked with small proofs.

IntermediateCoreFormula4 links
CryptographyHashingTreeSecurity
CryptographyO(n)

AES-GCM

AES-GCM encrypts data with a defined symmetric construction.

IntermediateCoreFormula1 links
CryptographySecuritySymmetric KeyMessage Authentication
CryptographyO(n)

AES-CTR Mode

AES-CTR Mode encrypts data with a defined symmetric construction.

IntermediateCoreFormula1 links
CryptographySecuritySymmetric Key
CryptographyO(n)

AES-CBC Mode

AES-CBC Mode encrypts data with a defined symmetric construction.

IntermediateCoreFormula1 links
CryptographySecuritySymmetric Key
CryptographyO(n)

AES-XTS Mode

AES-XTS Mode encrypts data with a defined symmetric construction.

IntermediateSpecializedFormula1 links
CryptographySecuritySymmetric Key
CryptographyO(n)

ChaCha20-Poly1305

ChaCha20-Poly1305 encrypts data with a defined symmetric construction.

IntermediateCoreNo formula1 links
CryptographySecurityStream CipherMessage Authentication
CryptographyO(n)

CMAC

CMAC protects secrecy, integrity, or authenticity with a named cryptographic primitive.

IntermediateCoreFormula1 links
CryptographySecurityMessage AuthenticationSymmetric Key
CryptographyO(n)

Poly1305-AES

Poly1305-AES encrypts data with a defined symmetric construction.

IntermediateExtendedNo formula1 links
CryptographySecurity
CryptographyO(n)

Bcrypt

Bcrypt protects secrecy, integrity, or authenticity with a named cryptographic primitive.

IntermediateCoreFormula1 links
CryptographySecurityPassword HashingKey Derivation
CryptographyO(n)

PSS Signature Padding

PSS Signature Padding proves message authenticity with public-key verification.

IntermediateCoreNo formula1 links
CryptographySecurityDigital SignaturePublic Key
CryptographyO(n)

OAEP Padding

OAEP Padding adapts public-key encryption or signatures to safer randomized encodings.

IntermediateCoreNo formula1 links
CryptographySecurityPublic Key
CryptographyO(n)

ElGamal Encryption

ElGamal Encryption protects secrecy, integrity, or authenticity with a named cryptographic primitive.

IntermediateCoreFormula1 links
CryptographySecurityPublic Key
CryptographyO(n)

Schnorr Signature

Schnorr Signature proves message authenticity with public-key verification.

IntermediateCoreFormula6 links
CryptographySecurityDigital SignaturePublic Key
CryptographyO(n)

Pedersen Commitment

Pedersen Commitment binds a value while hiding it until it is opened.

IntermediateCoreFormula1 links
CryptographySecurityProofZero Knowledge
CryptographyO(n)

Commit-Reveal Scheme

Commit-Reveal Scheme binds a value while hiding it until it is opened.

IntermediateCoreNo formula1 links
CryptographySecurityHash FunctionProof
CryptographyO(n)

Threshold Signature Scheme

Threshold Signature Scheme proves message authenticity with public-key verification.

IntermediateSpecializedNo formula2 links
CryptographySecurityDigital SignatureSecret Sharing
CryptographyO(n)

BLS Signature

BLS Signature proves message authenticity with public-key verification.

IntermediateSpecializedNo formula1 links
CryptographySecurityDigital SignaturePublic Key
CryptographyO(k^2)

Miller-Rabin Primality Test

Tests whether an integer is probably prime by looking for modular witnesses of compositeness.

IntermediateCoreFormula8 links
CryptographyRandomness
CryptographyO(k^2)

Pollard's Rho Factorization

Finds a nontrivial factor by searching for cycles in a pseudorandom modular sequence.

IntermediateCoreNo formula2 links
CryptographyRandomness
CryptographyO(k^2)

AKS Primality Test

AKS Primality Test addresses deterministic primality testing by checking polynomial congruences that characterize prime numbers.

AdvancedSpecializedNo formula2 links
Cryptography
CryptographyO(k^2)

Fermat Primality Test

Checks probable primality using Fermat's congruence for selected bases.

IntermediateCoreNo formula4 links
Cryptography
CryptographyO(k^2)

Montgomery Multiplication

Multiplies numbers modulo n without trial division by working in Montgomery form.

IntermediateCoreFormula5 links
Cryptography
CryptographyO(k^2)

Barrett Reduction

Reduces large integers modulo a fixed n using a precomputed reciprocal approximation.

IntermediateCoreFormula5 links
Cryptography
CryptographyO(log e * M(k))

Modular Exponentiation

Computes large powers modulo an integer without constructing the full power.

BeginnerFoundationNo formula10 links
Cryptography
CryptographyO((V + E) log V)

HMAC-DRBG

Generates deterministic random bits by updating HMAC-based internal state.

IntermediateCoreNo formula5 links
CryptographyRandomnessGraph
CryptographyO((V + E) log V)

CTR-DRBG

Generates deterministic random bits with a block-cipher counter construction.

IntermediateCoreNo formula4 links
CryptographyRandomnessGraph
CryptographyO((V + E) log V)

Hash-DRBG

Generates deterministic random bits by iterating a cryptographic hash over internal state.

IntermediateCoreNo formula2 links
CryptographyRandomnessHashingGraph
CryptographyO((V + E) log V)

Fortuna PRNG

Fortuna PRNG addresses cryptographic random generation by collecting entropy pools and reseeding a generator conservatively.

IntermediateExtendedNo formula2 links
CryptographyRandomnessGraph
CryptographyO(n log n)

Fiat-Shamir Transform

Turns some interactive public-coin proofs into noninteractive proofs by hashing the transcript.

IntermediateCoreNo formula2 links
CryptographyHashing
CryptographyO(k^2)

Lamport One-Time Signature

Signs one message by revealing selected one-time secret values for its digest bits.

IntermediateCoreNo formula3 links
Cryptography
CryptographyO(log n)

Merkle Signature Scheme

Merkle Signature Scheme addresses hash-based signatures by authenticating many one-time public keys with a Merkle tree.

IntermediateExtendedNo formula2 links
CryptographyHashing
CryptographyO(k^2)

DSA

Signs message digests with modular arithmetic over a subgroup and a per-signature nonce.

IntermediateCoreNo formula3 links
Cryptography
CryptographyO(k^2)

ElGamal Signature

Signs messages with a discrete-log construction using a fresh random nonce.

IntermediateCoreNo formula2 links
CryptographyRandomness