ECC

ECC (Elliptic Curve Cryptography) is a modern and efficient type of public key cryptography. Its security is based on the difficulty to solve discrete logarithms on the field defined by specific equations computed over a curve.

ECC can be used to create digital signatures or to perform a key exchange.

Compared to traditional algorithms like RSA, an ECC key is significantly smaller at the same security level. For instance, a 3072-bit RSA key takes 768 bytes whereas the equally strong NIST P-256 private key only takes 32 bytes (that is, 256 bits).

With this module you can generate new ECC keys:

>>> from Crypto.PublicKey import ECC
>>>
>>> mykey = ECC.generate(curve='p256')

export an ECC private key and protect it with a password, so that it is resistant to brute force attacks:

>>> pwd = b'secret'
>>> with open("myprivatekey.pem", "wt") as f:
>>>     data = mykey.export_key(format='PEM'
                                passphrase=pwd,
                                protection='PBKDF2WithHMAC-SHA512AndAES256-CBC',
                                prot_params={'iteration_count':131072})
>>>     f.write(data)

and reimport it later:

>>> pwd = b'secret'
>>> with open("myprivatekey.pem", "rt") as f:
>>>     data = f.read()
>>>     mykey = ECC.import_key(data, pwd)

You can also export the public key, which is not sensitive:

>>> with open("mypublickey.pem", "wbt) as f:
>>>     data = mykey.public_key().export_key()

Curve	Strings accepted for the curve API parameter
NIST P-192	'NIST P-192', 'p192', 'P-192', 'prime192v1', 'secp192r1'
NIST P-224	'NIST P-224', 'p224', 'P-224', 'prime224v1', 'secp224r1'
NIST P-256	'NIST P-256', 'p256', 'P-256', 'prime256v1', 'secp256r1'
NIST P-384	'NIST P-384', 'p384', 'P-384', 'prime384v1', 'secp384r1'
NIST P-521	'NIST P-521', 'p521', 'P-521', 'prime521v1', 'secp521r1'
Ed25519	'ed25519', 'Ed25519'
Ed448	'ed448', 'Ed448'

For more information about each NIST curve see FIPS 186-4, Section D.1.2.

The Ed25519 and the Ed448 curves are defined in RFC8032.

The ECC key can be used to perform or verify signatures, using the modules Crypto.Signature.DSS (ECDSA; NIST curves only) or Crypto.Signature.eddsa (EdDSA; Ed25519 and Ed448 curve only).

class Crypto.PublicKey.ECC.EccKey(**kwargs)

Class defining an ECC key. Do not instantiate directly. Use generate(), construct() or import_key() instead.

Variables:

• curve (string) – The name of the curve as defined in the ECC table.

• pointQ (EccPoint) – an ECC point representating the public component.

• d (integer) – A scalar that represents the private component in NIST P curves. It is smaller than the order of the generator point.

• seed (bytes) – A seed that representats the private component in EdDSA curves (Ed25519, 32 bytes; Ed448, 57 bytes).

export_key(**kwargs)

Export this ECC key.

Parameters:

• format (string) –

  The output format:

  • 'DER'. The key will be encoded in ASN.1 DER format (binary). For a public key, the ASN.1 subjectPublicKeyInfo structure defined in RFC5480 will be used. For a private key, the ASN.1 ECPrivateKey structure defined in RFC5915 is used instead (possibly within a PKCS#8 envelope, see the use_pkcs8 flag below).

  • 'PEM'. The key will be encoded in a PEM envelope (ASCII).

  • 'OpenSSH'. The key will be encoded in the OpenSSH format (ASCII, public keys only).

  • 'SEC1'. The public key (i.e., the EC point) will be encoded into bytes according to Section 2.3.3 of SEC1 (which is a subset of the older X9.62 ITU standard). Only for NIST P-curves.

  • 'raw'. The public key will be encoded as bytes, without any metadata.

    • For NIST P-curves: equivalent to 'SEC1'.

    • For EdDSA curves: bytes in the format defined in RFC8032.

• passphrase (bytes or string) – (Private keys only) The passphrase to protect the private key.

• use_pkcs8 (boolean) –

  (Private keys only) If True (default and recommended), the PKCS#8 representation will be used. It must be True for EdDSA curves.

  If False and a passphrase is present, the obsolete PEM encryption will be used.

• protection (string) – When a private key is exported with password-protection and PKCS#8 (both DER and PEM formats), this parameter MUST be present, For all possible protection schemes, refer to the encryption parameters of PKCS#8. It is recommended to use 'PBKDF2WithHMAC-SHA5126AndAES128-CBC'.

• compress (boolean) –

  If True, the method returns a more compact representation of the public key, with the X-coordinate only.

  If False (default), the method returns the full public key.

  This parameter is ignored for EdDSA curves, as compression is mandatory.

• prot_params (dict) – When a private key is exported with password-protection and PKCS#8 (both DER and PEM formats), this dictionary contains the parameters to use to derive the encryption key from the passphrase. For all possible values, refer to the encryption parameters of PKCS#8. The recommendation is to use {'iteration_count':21000} for PBKDF2, and {'iteration_count':131072} for scrypt.

Warning

If you don’t provide a passphrase, the private key will be exported in the clear!

Note

When exporting a private key with password-protection and PKCS#8 (both DER and PEM formats), any extra parameters to export_key() will be passed to Crypto.IO.PKCS8.

Returns:

A multi-line string (for 'PEM' and 'OpenSSH') or bytes (for 'DER', 'SEC1', and 'raw') with the encoded key.

has_private()

True if this key can be used for making signatures or decrypting data.

public_key()

A matching ECC public key.

Returns:

a new EccKey object

class Crypto.PublicKey.ECC.EccPoint(x, y, curve='p256')

A class to model a point on an Elliptic Curve.

The class supports operators for:

• Adding two points: R = S + T

• In-place addition: S += T

• Negating a point: R = -T

• Comparing two points: if S == T: ... or if S != T: ...

• Multiplying a point by a scalar: R = S*k

• In-place multiplication by a scalar: T *= k

Variables:

• x (integer) – The affine X-coordinate of the ECC point

• y (integer) – The affine Y-coordinate of the ECC point

• xy – The tuple with affine X- and Y- coordinates

copy()

Return a copy of this point.

double()

Double this point (in-place operation).

Returns:

This same object (to enable chaining).

is_point_at_infinity()

True if this is the point-at-infinity.

point_at_infinity()

Return the point-at-infinity for the curve.

size_in_bits()

Size of each coordinate, in bits.

size_in_bytes()

Size of each coordinate, in bytes.

exception Crypto.PublicKey.ECC.UnsupportedEccFeature

Crypto.PublicKey.ECC.construct(**kwargs)

Build a new ECC key (private or public) starting from some base components.

In most cases, you will already have an existing key which you can read in with import_key() instead of this function.

Parameters:

• curve (string) – Mandatory. The name of the elliptic curve, as defined in the ECC table.

• d (integer) – Mandatory for a private key and a NIST P-curve (e.g., P-256): the integer in the range [1..order-1] that represents the key.

• seed (bytes) – Mandatory for a private key and an EdDSA curve. It must be 32 bytes for Ed25519, and 57 bytes for Ed448.

• point_x (integer) – Mandatory for a public key: the X coordinate (affine) of the ECC point.

• point_y (integer) – Mandatory for a public key: the Y coordinate (affine) of the ECC point.

Returns:

a new ECC key object

Return type:

EccKey

Crypto.PublicKey.ECC.generate(**kwargs)

Generate a new private key on the given curve.

Parameters:

• curve (string) – Mandatory. It must be a curve name defined in the ECC table.

• randfunc (callable) – Optional. The RNG to read randomness from. If None, Crypto.Random.get_random_bytes() is used.

Crypto.PublicKey.ECC.import_key(encoded, passphrase=None, curve_name=None)

Import an ECC key (public or private).

Parameters:

• encoded (bytes or multi-line string) –

  The ECC key to import. The function will try to automatically detect the right format.

  Supported formats for an ECC public key:

  • X.509 certificate: binary (DER) or ASCII (PEM).

  • X.509 subjectPublicKeyInfo: binary (DER) or ASCII (PEM).

  • SEC1 (or X9.62), as bytes. NIST P curves only. You must also provide the curve_name (with a value from the ECC table)

  • OpenSSH line, defined in RFC5656 and RFC8709 (ASCII). This is normally the content of files like ~/.ssh/id_ecdsa.pub.

  Supported formats for an ECC private key:

  • A binary ECPrivateKey structure, as defined in RFC5915 (DER). NIST P curves only.

  • A PKCS#8 structure (or the more recent Asymmetric Key Package, RFC5958): binary (DER) or ASCII (PEM).

  • OpenSSH 6.5 and newer versions (ASCII).

  Private keys can be in the clear or password-protected.

  For details about the PEM encoding, see RFC1421/RFC1423.

• passphrase (byte string) – The passphrase to use for decrypting a private key. Encryption may be applied protected at the PEM level (not recommended) or at the PKCS#8 level (recommended). This parameter is ignored if the key in input is not encrypted.

• curve_name (string) – For a SEC1 encoding only. This is the name of the curve, as defined in the ECC table.

Note

To import EdDSA private and public keys, when encoded as raw bytes, use:

• Crypto.Signature.eddsa.import_public_key(), or

• Crypto.Signature.eddsa.import_private_key().

Returns:

a new ECC key object

Return type:

EccKey

Raises:

ValueError – when the given key cannot be parsed (possibly because the pass phrase is wrong).