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Elliptic-curve cryptography

Elliptic-curve cryptography (ECC) is an approach to public-key cryptography based on the algebraic structure of elliptic curves over finite fields. ECC allows smaller keys to provide equivalent security, compared to cryptosystems based on modular exponentiation in finite fields, such as the RSA cryptosystem and ElGamal cryptosystem.

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History

Elliptic curve theory

Implementation

Security

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Elliptic-curve cryptography

Nodes114
Edges113
Triples9
Avg. degree1.98
Density0.017544
Components1

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Important terminology

curve elliptic curves displaystyle key security cryptography nist use rsa also ecc field mathbb based used quantum domain parameters nsa

Entity relationships Subject–Predicate–Object triples

SubjectPredicateObjectConfidenceSrc
Montgomery or Edwards forminstance ofand curves used in other representations0.80text
are written differently.This set of pointsinstance ofand curves used in other representations0.80text
together with the group operation of elliptic curvesinstance ofand curves used in other representations0.80text
is an abelian groupinstance ofand curves used in other representations0.80text
with the point at infinity as an identity elementinstance ofand curves used in other representations0.80text
ECDH rely on related Diffieinstance ofKey-agreement protocols0.80text
RSA is a smaller key sizeinstance ofdetermine the difficulty of the problem.The primary benefit promised by elliptic curve cryptography over alternatives0.80text
reducing storageinstance ofdetermine the difficulty of the problem.The primary benefit promised by elliptic curve cryptography over alternatives0.80text
transmission requirementsinstance ofdetermine the difficulty of the problem.The primary benefit promised by elliptic curve cryptography over alternatives0.80text

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