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Creating Elliptic Curve Keys using OpenSSL

Recently, I have been using OpenSSL to generate private keys and X509 certificates for Elliptic Curve Cryptography (ECC) and then using them in ASP.NET Core for token signing.

In this article, I’m going to show you how to use OpenSSL to generate private and public keys on the curve of your choice. Check out my other article for how to do the same for RSA keys.

tl;dr - OpenSSL ECDSA Cheat Sheet

find your curve

openssl ecparam -list_curves

generate a private key for a curve

openssl ecparam -name prime256v1 -genkey -noout -out private-key.pem

generate corresponding public key

openssl ec -in private-key.pem -pubout -out public-key.pem

optional: create a self-signed certificate

openssl req -new -x509 -key private-key.pem -out cert.pem -days 360

optional: convert pem to pfx

openssl pkcs12 -export -inkey private-key.pem -in cert.pem -out cert.pfx

Generating an Elliptic Curve Private Key Using OpenSSL To start, you will need to choose the curve you will be working with. You can use the following command to see a list of supported curve names and descriptions.

openssl ecparam -list_curves In this example, I am using prime256v1 (secp256r1), which is suitable for JWT signing; this is the curve used for JOSE’s ES256.

You can now generate a private key:

openssl ecparam -name prime256v1 -genkey -noout -out private-key.pem This should give you a PEM file containing your EC private key, which looks something like the following:

openssl ec -in private-key.pem -pubout -out public-key.pem This should give you another PEM file, containing the public key:

-----BEGIN PUBLIC KEY----- MFkwEwYHKoZIzj0CAQYIKoZIzj0DAQcDQgAEOr6rMmRRNKuZuwws/hWwFTM6ECEE aJGGARCJUO4UfoURl8b4JThGt8VDFKeR2i+ZxE+xh/wTBaJ/zvtSqZiNnQ== -----END PUBLIC KEY----- Creating an EC Self-Signed Certificate Using OpenSSL Now that you have a private key, you could use it to generate a self-signed certificate. This is not required, but it allows you to use the key for server/client authentication, or gain X509 specific functionality in technologies such as JWT and SAML.

openssl req -new -x509 -key private-key.pem -out cert.pem -days 360 This will again generate another PEM file, this time containing the certificate created by your private key:

You could leave things there, but if you are working on Windows, you may prefer a PFX file that contains both the certificate and the private key for you to export and use.

You can do this using OpenSSL’s pkcs12 command:

openssl pkcs12 -export -inkey private-key.pem -in cert.pem -out cert.pfx OpenSSL will ask you to create a password for the PFX file. Feel free to leave this blank.

This should leave you with a certificate that Windows can both install and export the EC private key from.

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ec NAME openssl-ec, ec - EC key processing

SYNOPSIS openssl ec [-inform PEM|DER] [-outform PEM|DER] [-in filename] [-passin arg] [-out filename] [-passout arg] [-des] [-des3] [-idea] [-text] [-noout] [-param_out] [-pubin] [-pubout] [-conv_form arg] [-param_enc arg] [-engine id]

DESCRIPTION The ec command processes EC keys. They can be converted between various forms and their components printed out. Note OpenSSL uses the private key format specified in 'SEC 1: Elliptic Curve Cryptography' (http://www.secg.org/). To convert a OpenSSL EC private key into the PKCS#8 private key format use the pkcs8 command.

COMMAND OPTIONS -inform DER|PEM This specifies the input format. The DER option with a private key uses an ASN.1 DER encoded SEC1 private key. When used with a public key it uses the SubjectPublicKeyInfo structure as specified in RFC 3280. The PEM form is the default format: it consists of the DER format base64 encoded with additional header and footer lines. In the case of a private key PKCS#8 format is also accepted.

-outform DER|PEM This specifies the output format, the options have the same meaning as the -inform option.

-in filename This specifies the input filename to read a key from or standard input if this option is not specified. If the key is encrypted a pass phrase will be prompted for.

-passin arg the input file password source. For more information about the format of arg see the PASS PHRASE ARGUMENTS section in openssl(1).

-out filename This specifies the output filename to write a key to or standard output by is not specified. If any encryption options are set then a pass phrase will be prompted for. The output filename should not be the same as the input filename.

-passout arg the output file password source. For more information about the format of arg see the PASS PHRASE ARGUMENTS section in openssl(1).

-des|-des3|-idea These options encrypt the private key with the DES, triple DES, IDEA or any other cipher supported by OpenSSL before outputting it. A pass phrase is prompted for. If none of these options is specified the key is written in plain text. This means that using the ec utility to read in an encrypted key with no encryption option can be used to remove the pass phrase from a key, or by setting the encryption options it can be use to add or change the pass phrase. These options can only be used with PEM format output files.

-text prints out the public, private key components and parameters.

-noout this option prevents output of the encoded version of the key.

-modulus this option prints out the value of the public key component of the key.

-pubin by default a private key is read from the input file: with this option a public key is read instead.

-pubout by default a private key is output. With this option a public key will be output instead. This option is automatically set if the input is a public key.

-conv_form This specifies how the points on the elliptic curve are converted into octet strings. Possible values are: compressed (the default value), uncompressed and hybrid. For more information regarding the point conversion forms please read the X9.62 standard. Note Due to patent issues the compressed option is disabled by default for binary curves and can be enabled by defining the preprocessor macro OPENSSL_EC_BIN_PT_COMP at compile time.

-param_enc arg This specifies how the elliptic curve parameters are encoded. Possible value are: named_curve, i.e. the ec parameters are specified by a OID, or explicit where the ec parameters are explicitly given (see RFC 3279 for the definition of the EC parameters structures). The default value is named_curve. Note the implicitlyCA alternative ,as specified in RFC 3279, is currently not implemented in OpenSSL.

-engine id specifying an engine (by its unique id string) will cause ec to attempt to obtain a functional reference to the specified engine, thus initialising it if needed. The engine will then be set as the default for all available algorithms.

NOTES The PEM private key format uses the header and footer lines:

-----BEGIN EC PRIVATE KEY----- -----END EC PRIVATE KEY----- The PEM public key format uses the header and footer lines:

-----BEGIN PUBLIC KEY----- -----END PUBLIC KEY----- EXAMPLES To encrypt a private key using triple DES:

openssl ec -in key.pem -des3 -out keyout.pem To convert a private key from PEM to DER format:

openssl ec -in key.pem -outform DER -out keyout.der To print out the components of a private key to standard output:

openssl ec -in key.pem -text -noout To just output the public part of a private key:

openssl ec -in key.pem -pubout -out pubkey.pem To change the parameters encoding to explicit:

openssl ec -in key.pem -param_enc explicit -out keyout.pem To change the point conversion form to compressed:

openssl ec -in key.pem -conv_form compressed -out keyout.pem SEE ALSO ecparam(1), dsa(1), rsa(1)

HISTORY The ec command was first introduced in OpenSSL 0.9.8.

AUTHOR Nils Larsch for the OpenSSL project (http://www.openssl.org).