Command-line Elliptic Curve operations

OpenSSL® provides the following command-line tools to work with keys suitable for Elliptic Curve (EC) Cryptography algorithms:

openssl ecparam
openssl ec

Currently, OpenSSL supports the following EC algorithms:

Elliptic Curve Diffie Hellman (ECDH) for key agreement
Elliptic Curve Digital Signature Algorithm (ECDSA) for signing and verifying

ecparams and ec do not support the x25519, ed25519, and ed448 curves. See
the genpkey subcommand for information about those curves.

EC private key file formats

OpenSSL uses Privacy Enhanced Mail (PEM) files to store EC private keys by
default. These files contain base-64 encoded data and use the .pem
extension. The following example shows a private key file in PEM format.

The following example shows an encrypted private key file in PEM format.

The following example shows a private key file that uses the Public
Key Cryptography Standard 8 (PKCS8) in PEM format.

The following example shows an encrypted PKCS8 private key file in PEM format:

PKCS8 private key files support different private keys types, apart from the EC keys.
You can convert the files to use different private key types and set them as encrypted
or unencrypted.

Use the following command to convert a PKCS8 file to a traditional encrypted EC key file:

openssl ec -aes-128-cbc -in p8file.pem -out tradfile.pem

Replace argument -aes-128-cbc with any other valid OpenSSL cipher name. (See the
OpenSSL documentation
for a list of valid cipher names.)

Use the following command to convert a PKCS8 file to a traditional unencrypted EC key file:

openssl ec -in p8file.pem -out tradfile.pem

Use the following command to convert an EC key file to encrypted PKCS8 format:

openssl pkcs8 -topk8 -in tradfile.pem -out p8file.pem

Use the following command to convert an EC key file to unencrypted PKCS8 format:

openssl pkcs8 -topk8 -nocrypt -in tradfile.pem -out p8file.pem

Note: The EC private key files are not encrypted by default. You must
explicitly set the file to encrypted and specify the cipher algorithm. The
PKCS8 files are encrypted by default. Use the -nocrypt option to set the
file to unencrypted.

A PEM file is DER data encoded by using base 64 encoding rules, with a header
and footer. PEM files are human-readable, so they are more convenient to use.
However, you can store all the files shown above in DER format. DER format
is a binary format, and unlike a PEM file, it is not human-readable.

Most openssl commands have options -inform DER and -outform DER.
-inform DER specifies that the input file is DER, and -outform DER
specifies that the output file is DER.

Use the following command to convert the PKCS8 format to a traditional
encrypted EC key in DER format.

openssl ec -in p8file.pem -outform DER -out tradfile.der

You cannot encrypt a traditional EC private key file in DER format. If
you attempt to do so, the command silently ignores the argument. However,
you can encrypt PKS8 files in DER format.

Use the following command to convert a traditional EC key file to encrypted PKCS8 in DER format:

openssl pkcs8 -topk8 -in tradfile.pem -outform DER -out p8file.der

EC public key file formats

PEM format supports several types of public keys in OpenSSL. The following
file shows EC public keys in PEM format.

-----BEGIN PUBLIC KEY-----
MEkwEwYHKoZIzj0CAQYIKoZIzj0DAQMDMgAE+Y+qPqI3geo2hQH8eK7Rn+YWG09T
ejZ5QFoj9fmxFrUyYhFap6XmTdJtEi8myBmW
-----END PUBLIC KEY-----

Use the following command to create a public key file from a private key file
in PEM format. Note that it is not possible to create a private key file from
a public key file.

openssl ec -in ecprivkey.pem -pubout -out ecpubkey.pem

Use the following command to create a public key file from a private key file in DER format:

openssl ec -in ecprivkey.pem -pubout -outform DER -out ecpubkey.der

Generating EC keys and parameters

The EC parameters file contains all the information necessary to define an
elliptic curve for cryptographic operations. OpenSSL uses ECDH and ECDSA
algorithms. Use the following command to obtain a list of built-in curves:

openssl ecparam -list_curves

Use the following command to generate an EC parameters file of curve secp256k1:

openssl ecparam -name secp256k1 -out secp256k1.pem

Replace secp256k1 with any other name obtained from the openssl ecparam -list_curves command.

You can generate keys by using the ecparam command, either by using a
pre-existing parameters file or by using the name of the curve. Use the
following command to generate a private/public key pair from a parameters file:

openssl ecparam -in secp256k1.pem -genkey -noout -out secp256k1-key.pem

Use the following command to generate a private/public key pair from the name of the curve:

openssl ecparam -name secp256k1 -genkey -noout -out secp256k1-key.pem

The key file has the information of the parameters used to generate the key
embedded. OpenSSL stores the name of the curve in the parameters file or the
key file. It does not explicitly store the full set of parameters associated
with the name by default. Use the following command to confirm the name of
the curve in the parameters file:

openssl ecparam -in secp256k1.pem -text -noout

Example output:

ASN1 OID: secp256k1

Use the following command to list parameter details from a parameters file:

openssl ecparam -in secp256k1.pem -text -param_enc explicit -noout

Use the following command to list parameter details from the name of a curve,
substituting the name of the curve accordingly:

openssl ecparam -name secp256k1 -text -param_enc explicit -noout

Example output:

Field Type: prime-field
Prime:
    00:ff:ff:ff:ff:ff:ff:ff:ff:ff:ff:ff:ff:ff:ff:
    ff:ff:ff:ff:ff:ff:ff:ff:ff:ff:ff:ff:ff:fe:ff:
    ff:fc:2f
A:    0
B:    7 (0x7)
Generator (uncompressed):
    04:79:be:66:7e:f9:dc:bb:ac:55:a0:62:95:ce:87:
    0b:07:02:9b:fc:db:2d:ce:28:d9:59:f2:81:5b:16:
    f8:17:98:48:3a:da:77:26:a3:c4:65:5d:a4:fb:fc:
    0e:11:08:a8:fd:17:b4:48:a6:85:54:19:9c:47:d0:
    8f:fb:10:d4:b8
Order:
    00:ff:ff:ff:ff:ff:ff:ff:ff:ff:ff:ff:ff:ff:ff:
    ff:fe:ba:ae:dc:e6:af:48:a0:3b:bf:d2:5e:8c:d0:
    36:41:41
Cofactor:  1 (0x1)

You can generate parameter files and key files that explicitly include the
full set of parameters instead of just the name of the curve. This is important
when some target systems don't know the details of the curve. OpenSSL version
1.0.2 added new curves, such as brainpool512t1. Earlier versions of OpenSSL
that use a parameter file or key file configured with brainpool512t1 result
in the following error:

bash$ openssl ecparam -in brainpoolP512t1.pem -text -noout
unable to load elliptic curve parameters
140138321110720:error:1009E077:elliptic curve routines:EC_ASN1_PKPARAMETERS2GROUP:ec group new by name failure:ec_asn1.c:1035:
140138321110720:error:1009107F:elliptic curve routines:d2i_ECPKParameters:pkparameters2group failure:ec_asn1.c:1080:
140138321110720:error:0906700D:PEM routines:PEM_ASN1_read_bio:ASN1 lib:pem_oth.c:83:

Use explicit parameters to avoid this problem, as shown in the following
command with OpenSSL 1.0.2:

openssl ecparam -name brainpoolP512t1 -out brainpoolP512t1.pem -param_enc explicit

The command yields a longer parameters file with all the parameters.

Earlier versions of OpenSSL can process the parameters file. Use the
following command in OpenSSL version 1.0.1:

openssl ecparam -in brainpoolP512t1.pem -text -noout

OpenSSL version 1.0.1. displays the parameters even if it doesn't know
the curve.

Use the following command to generate a key file with explicit parameters:

openssl ecparam -name brainpoolP512t1 -genkey -noout -out brainpoolP512t1-key.pem -param_enc explicit

Earlier versions of OpenSSL can process the key file you obtain.

Note: After the parameters change to explicit parameters, don't
revert the changes. There is no utility to find which explicit parameters
correspond to a curve.

References

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