EC Cryptography Tutorials - Herong's Tutorial Examples

∟Standard Elliptic Curves

∟What Are Standard Elliptic Curves

This section provides a list of standard elliptic curves selected and recommended by different organizations to generate secure EC private-pubic key pairs.

What Are Standard Elliptic Curves? Standard Elliptic Curves should actually be called standard sets of EC domain parameters. They are selected and recommended by different organizations to generated secure EC private-pubic key pairs.

The table below provides a summary of named elliptic curves (domain parameters) and their recommending organizations:

SECG       NIST   OID                    ANSI X9.62  Brainpool
---------  -----  ---------------------  ----------  ---------------
secp160k1
secp160r1
secp160r2
                  1.3.36.3.3.2.8.1.1.1               brainpoolP160r1
sect163k1  K-163
sect163r1
sect163r2  B-163
secp192k1
secp192r1  P-192  1.2.840.10045.3.1.1    prime192v1
                                         prime192v2
                                         prime192v2
                  1.3.36.3.3.2.8.1.1.3               brainpoolP192r1
sect193r1
sect193r2
secp224k1
secp224r1  P-224  1.3.132.0.33
                  1.3.36.3.3.2.8.1.1.5               brainpoolP224r1
sect233k1  K-233
sect233r1  B-233
sect239k1
                                         prime239v1
                                         prime239v2
                                         prime239v3
secp256k1
secp256r1  P-256  1.2.840.10045.3.1.7    prime256v1
                  1.3.36.3.3.2.8.1.1.7               brainpoolP256r1
sect283k1  K-283
sect283r1  B-283
                  1.3.36.3.3.2.8.1.1.9               brainpoolP320r1
secp384r1  P-384  1.3.132.0.34
                  1.3.36.3.3.2.8.1.1.11              brainpoolP384r1
sect409k1  K-409
sect409r1  B-409
                  1.3.36.3.3.2.8.1.1.13              brainpoolP512r1
secp521r1  P-521  1.3.132.0.35
sect571k1  K-571
sect571r1  B-571
---------  -----  ---------------------  ----------  ---------------
SECG       NIST   OID                    ANSI X9.62  Brainpool

Organization full names and Websites are list below:

• ANSI - American National Standards Institute at http://ansi.org.
• Brainpool - ECC Brainpool at http://www.ecc-brainpool.org.
• NIST - National Institute of Standards and Technology at https://www.nist.gov.
• OID - Object IDentifier developed ITU-T and ISO/IEC at http://oid-info.com.
• SECG - Standards for Efficient Cryptography Group at https://www.secg.org.

Detailed information of some standard curves will be in next sections.

Table of Contents

 About This Book

 Geometric Introduction to Elliptic Curves

 Algebraic Introduction to Elliptic Curves

 Abelian Group and Elliptic Curves

 Discrete Logarithm Problem (DLP)

 Finite Fields

 Generators and Cyclic Subgroups

 Reduced Elliptic Curve Groups

 Elliptic Curve Subgroups

 tinyec - Python Library for ECC

 EC (Elliptic Curve) Key Pair

 ECDH (Elliptic Curve Diffie-Hellman) Key Exchange

 ECDSA (Elliptic Curve Digital Signature Algorithm)

 ECES (Elliptic Curve Encryption Scheme)

 EC Cryptography in Java

►Standard Elliptic Curves

►What Are Standard Elliptic Curves

 "openssl ecparam -list_curves" - Curves Supported by OpenSSL

 "secp256r1" - For 256-Bit ECC Keys

 "secp256k1" - For 256-Bit ECC Keys

 "sect283r1" - For 256-Bit ECC Keys

 "brainpoolP256r1"“ - For 256-Bit ECC Keys

 "brainpoolP256t1"“ - For 256-Bit ECC Keys

 Terminology

 References

 Full Version in PDF/EPUB

What Are Standard Elliptic Curves - Updated in 2024, by Herong Yang