Elliptic-curve cryptography
Elliptic-curve cryptography is public-key cryptography based on algebraic operations over elliptic curves, typically defined over finite fields.
Software Security for Developers
Elliptic-curve cryptography is public-key cryptography based on the algebraic structure of elliptic curves over finite fields.
- How it is used
- Applies public-key cryptography to encryption, key agreement, signatures, TLS, and security-sensitive application development.
- How deep it goes
- Explains security intuition, curve selection, Java workflows, ECDH, and ECDSA while deferring mathematical equations and proofs.
- Examples
- Uses Curve25519, named-curve choices, TLS key agreement, and Java ECIES encryption of a refunds JSON file.
- What you can do after
- Apply ECC via Java security APIs, approved curves, ECIES, ECDH, ECDSA, and TLS configuration without implementing the underlying mathematics.
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Real-World Cryptography
Elliptic curve cryptography is public-key cryptography based on the algebraic structure of elliptic curves over finite fields.
- How it is used
- Implements Diffie-Hellman key exchange with substantially smaller parameters than traditional finite-field Diffie-Hellman.
- How deep it goes
- Explains curve equations, additive groups, geometric point addition, modular coordinates, and standard curves without implementation details.
- Examples
- Uses geometric point-addition diagrams and identifies P-256 and Curve25519 as widely used curves.
- What you can do after
- Evaluate/understand how ECDH derives from elliptic-curve groups and why it achieves smaller parameters.
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Elliptic Curve Cryptography for Developers
Elliptic curve cryptography is public-key cryptography based on algebraic operations over elliptic curves.
- How it is used
- Deploys public-key mathematics for key sharing, authentication, signatures, proofs, and selected blockchain applications.
- How deep it goes
- Defines finite-field curves and security motivation, while deferring detailed field-size, dimension, and pairing computations.
- Examples
- Uses SSL/TLS handshakes, web certificates, HIPAA documents, EMVCo transactions, blockchains, and finite-field point diagrams.
- What you can do after
- Evaluate ECC’s security rationale, resource advantages, and cryptographic applications relative to RSA and other methods.
Read how Elliptic Curve Cryptography for Developers explains elliptic-curve cryptography →
Related concepts
- elliptic curveuses · An elliptic curve is a nonsingular algebraic curve defined by a cubic equation whose points, including a point at infinity, support a group operation.
- finite fielduses · A finite field is a field containing finitely many elements, with addition, subtraction, multiplication, and division by nonzero elements defined within it.
- discrete logarithmuses · A discrete logarithm is an exponent or scalar that relates a specified group element to a base or generator under the group operation.
- RSAalternative to · RSA is a public-key cryptosystem based on the computational difficulty of factoring large composite integers and supporting encryption and digital signatures.
- ECDSAused by · ECDSA is a public-key digital signature algorithm that uses elliptic-curve arithmetic to generate and verify signatures.
- cryptographic keyproduces · A cryptographic key is a value supplied to a cryptographic algorithm to control operations such as encryption, decryption, signing, authentication, or verification.
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