Linked from

The 18 pages that link to Elliptic-curve cryptography, each with the reason it gives.

• Prime numberRelated: Many implementations use finite fields whose size is prime or a prime power.

• Finite fieldRelated: Many implementations define their curve coordinates over finite fields.

• Number theoryRelated: It applies finite-field arithmetic and hard discrete-logarithm problems to cryptographic keys.

• CryptographyRelated: It offers key agreement and signatures with comparatively small keys.

• Algebraic geometryRelated: It uses the group structure of algebraic curves over finite fields.

• Field (mathematics)Related: Finite fields provide the setting for widely used elliptic-curve constructions.

• Elliptic curveBroader topic: Its security relies on the difficulty of recovering a scalar from point multiplication.

• Public-key cryptographyBroader topic: It achieves compact keys and signatures using a different mathematical structure from RSA.

• Diffie–Hellman key exchangeNarrower topic: Elliptic-curve Diffie–Hellman is one key-agreement construction within this broader family.

• RSA cryptosystemCompared with: It offers comparable security with smaller keys and often less computation than RSA.

• Post-quantum cryptographyCompared with: Its discrete-logarithm foundation is vulnerable to Shor's algorithm, unlike post-quantum assumptions.

• Shor's algorithmRelated: Shor's algorithm also solves the underlying elliptic-curve discrete logarithm problem efficiently.

• Discrete logarithmBroader topic: Its central hardness assumption is the elliptic-curve discrete logarithm problem.

• Modularity theoremRelated: It uses elliptic-curve arithmetic, though the modularity theorem is not its security foundation.

• Arithmetic geometryRelated: It applies the group structure of curve points over finite fields to cryptographic protocols.

• Mordell–Weil theoremRelated: Finite generation over number fields concerns a related group structure, though cryptography uses finite fields.

• Adi ShamirCompared with: It offers public-key security with different mathematics and typically smaller keys than RSA.

• Hasse's theorem on elliptic curvesRelated: Secure parameter choices depend on knowing or estimating the curve's group order.