Command Line Elliptic Curve Operations

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OpenSSL provides two powerful command line tools for working with keys suitable for Elliptic Curve (EC) algorithms:

openssl ecparam
openssl ec

The only Elliptic Curve algorithms that OpenSSL currently supports are Elliptic Curve Diffie Hellman (ECDH) for key agreement and Elliptic Curve Digital Signature Algorithm (ECDSA) for signing/verifying.

EC Private Key File Formats[edit]

By default OpenSSL will work with PEM files for storing EC private keys. These are text files containing base-64 encoded data. A typical traditional format private key file in PEM format will look something like the following, in a file with a ".pem" extension:

-----BEGIN EC PRIVATE KEY-----
MIIBIAIBAQQYd8yhaE899FaH3sw8aD4F/vtpMVBLfVqmoIHKMIHHAgEBMCQGByqG
SM49AQECGQD////////////////////+//////////8wSwQY////////////////
/////v/////////8BBgiEj3COVoFyqdCPa7MyUdgp9RiJWvVaRYDFQDEaWhENd6z
eMS2XKlZHipXYwWaLgQxBH0pd4EAxlodoXg3FliNziuLSu6OIo8YljipDyJjczcz
S0nctmptyPmXisp2SKlDsAIZAP///////////////3pi0DHIP0KU9kDsEwIBAaE0
AzIABBsl8ZSGJqcUpVoP8zekF92DGqDBMERcHhCXmgPXchP+ljybXbzYKINgxbp5
0g9/pw==
-----END EC PRIVATE KEY-----

Or, in an encrypted form like this:

-----BEGIN EC PRIVATE KEY-----
Proc-Type: 4,ENCRYPTED
DEK-Info: DES-EDE3-CBC,258248872DB25390

JIzhns0nRb+pj6RONAijJli8Rhu2bIrw8D+ruHEWL1IEH6Q5tvzqAI2PDYXbSzCn
24JPWx9khmTu6ijerANNYYk0p2Pjxr12MAYpqgtXbRrXLF4AIomzYWq16BH7Y63o
zvqWMBJO6tQ5RHPLM2FmweyPB/XSL7KvLTe+g6pz/W9wf52CyQ/VeK+yBXqEi7QF
0f9EKRlePRLAUcQPD4nkckcywX6Nz+TW/SOKt38YytM9MyQsAfcxu7u0nl/dLylk
n57qUm3nk0z0moYJbfLx59eP0/go8VjeP2fRKkgz1DOM7VkmtPrC7vnyRpKsnP2S
6n6uacerkNXTmUcz7mTCGGfrsBeACJeX1gwinDZVwkzDxNKhLXOlFFAMWE+SeiFp
kDny2v3D8sU=
-----END EC PRIVATE KEY-----

You may also encounter PKCS8 format private keys in PEM files. These look like this:

-----BEGIN PRIVATE KEY-----
MIIBMAIBADCB0wYHKoZIzj0CATCBxwIBATAkBgcqhkjOPQEBAhkA////////////
/////////v//////////MEsEGP////////////////////7//////////AQYIhI9
wjlaBcqnQj2uzMlHYKfUYiVr1WkWAxUAxGloRDXes3jEtlypWR4qV2MFmi4EMQR9
KXeBAMZaHaF4NxZYjc4ri0rujiKPGJY4qQ8iY3M3M0tJ3LZqbcj5l4rKdkipQ7AC
GQD///////////////96YtAxyD9ClPZA7BMCAQEEVTBTAgEBBBiKtwssqrxHY/gu
KDD4QgmyLDKaqBv2wEWhNAMyAAT5j6o+ojeB6jaFAfx4rtGf5hYbT1N6NnlAWiP1
+bEWtTJiEVqnpeZN0m0SLybIGZY=
-----END PRIVATE KEY-----

Or, in an encrypted form like this:

-----BEGIN ENCRYPTED PRIVATE KEY-----
MIIBWTAbBgkqhkiG9w0BBQMwDgQIGIcvnv17Q8oCAggABIIBOK+i1pk7em94F0Bn
+yKxU5p7e2+cnnW/8b2mjvga0Uj8JVxRHi5eR2/u+3fjHQItq0df+qzyVC0TTCPz
YZVrgHO9hPilgbGQKQQSpy9bpbGGiZ7I+aFpriEaJzugHUi8XTXY6XtnxgHAqTOX
nma2HHoGRic2wNgIGKQ+B1pULy2kFDMvQ/AwvYS13uH2Trfja9M9wRqYjM2MS0Ky
ii03OsNhJjZQcPmy2ALciR+umG4IQ7qszfrCA7L95F3qVXa7DgAPDZyUSdF3ucSh
IlrEvaP7FeLfJ1/ilUaXK6XC9EDYPDWMErUQJZJAywczQMqjY4/pdhb8Y+TpbN/r
q1I5j+JbRwfvvJV7CAHv1EEjvWiWvjHamlb7iqh3gneOYPbvSfjuaOyVd5YhwQ7P
nGOah+eEf9uyDSZabg==
-----END ENCRYPTED PRIVATE KEY-----

PKCS8 private key files, like the above, are capable of holding many different types of private key - not just EC keys.

You can convert between these formats if you like. All of the conversion commands can read either the encrypted or unencrypted forms of the files however you must specify whether you want the output to be encrypted or not. To convert a PKCS8 file to a traditional encrypted EC format use:

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

You can replace the first argument "aes-128-cbc" with any other valid openssl cipher name (see Manual:enc(1) for a list of valid cipher names). To convert a PKCS8 file to a traditional unencrypted EC format, just drop the first argument:

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

Or to convert from a traditional EC format to an encrypted PKCS8 format use:

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

Or to a non-encrypted PKCS8 format use:

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

Note that by default in the above traditional format EC Private Key files are not encrypted (you have to explicitly state that the file should be encrypted, and what cipher to use), whilst for PKCS8 files the opposite is true. The default is to encrypt - you have to explicitly state that you do not want encryption applied if appropriate using the "-nocrypt" option.

As well as PEM format all of the above types of key file can also be stored in DER format. This is a binary format and so is not directly human readable - unlike a PEM file. A PEM file is essentially just DER data encoded using base 64 encoding rules with a header and footer added. Often it is more convenient to work with PEM files for this reason.

The openssl commands typically have options "-inform DER" or "-outform DER" to specify that the input or output file is DER respectively. So for example the command to convert a PKCS8 file to a traditional encrypted EC format in DER is the same as above, but with the addition of "-outform DER":

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

Note that you cannot encrypt a traditional format EC Private Key in DER format (and in fact if you attempt to do so the argument is silently ignored!). The same is not true for PKCS8 files - these can still be encrypted even in DER format. So for example the following will convert a traditional format key file to an ecrypted PKCS8 format DER encoded key:

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

EC Public Key File Formats[edit]

EC Public Keys are also stored in PEM files. A typical EC public key looks as follows:

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

This format is used to store all types of public keys in OpenSSL not just EC keys.

It is possible to create a public key file from a private key file (although obviously not the other way around!):

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

As above a DER encoded version can be created using "-outform DER":

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

Generating EC Keys and Parameters[edit]

An EC Parameters file contains all of the information necessary to define an Elliptic Curve that can then be used for cryptographic operations (for OpenSSL this means ECDH and ECDSA). OpenSSL contains a large set of pre-defined curves that can be used. The full list of built-in curves can be obtained through the following command:

openssl ecparam -list_curves

An EC parameters file can then be generated for any of the built-in named curves as follows:

openssl ecparam -name secp256k1 -out secp256k1.pem

Replace secp256k1 in the above with whichever curve you are interested in.

Keys can be generated from the ecparam command, either through a pre-existing parameters file or directly by selecting the name of the curve. To generate a private/public key pair from a pre-eixsting parameters file use the following:

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

Or to do the equivalent operation without a parameters file use the following:

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

Information on the parameters that have been used to generate the key are embedded in the key file itself.

By default, when creating a parameters file, or generating a key, openssl will only store the name of the curve in the generated parameters or key file, not the full set of explicit parameters associated with that name. For example:

openssl ecparam -in secp256k1.pem -text -noout

This will simply confirm the name of the curve in the parameters file by printing out the following:

ASN1 OID: secp256k1

If you wish to examine the specific details of the parameters associated with a particular named curve then this can be achieved as follows:

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

The above command shows the details for a built-in named curve from a file, but this can also be done directly using the "-name" argument instead of "-in". The output will look similar to the following:

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)

The meaning of each of these parameters is discussed further on this page.

Parameters and key files can be generated to include the full explicit parameters instead of just the name of the curve if desired. This might be important if, for example, not all the target systems know the details of the named curve. In OpenSSL version 1.0.2 new named curves have been added such as brainpool512t1. Attempting to use a parameters file or key file in versions of OpenSSL less than 1.0.2 with this curve will result in an 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:

This problem can be avoided if explicit parameters are used instead. So under OpenSSL 1.0.2 you could create a parameters file like this:

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

Looking at the parameters file you will notice that it is now much longer:

-----BEGIN EC PARAMETERS-----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-----END EC PARAMETERS-----

The full parameters are included rather than just the name. This can now be processed by versions of OpenSSL less than 1.0.2. So under 1.0.1:

openssl ecparam -in brainpoolP512t1.pem -text -noout

This will correctly display the parameters, even though this version of OpenSSL does not know about this curve.

The same is true of key files. So to generate a key with explicit parameters:

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

This key file can now be processed by versions of openssl that do not know about the brainpool curve.

It should be noted however that once the parameters have been converted from the curve name format into explicit parameters it is not possible to change them back again, i.e. there is no utility to take a set of explicit parameters and work out which named curve they are associated with.

See also[edit]