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README.md
Pure-Python ECDSA
This is an easy-to-use implementation of ECDSA cryptography (Elliptic Curve Digital Signature Algorithm), implemented purely in Python, released under the MIT license. With this library, you can quickly create keypairs (signing key and verifying key), sign messages, and verify the signatures. The keys and signatures are very short, making them easy to handle and incorporate into other protocols.
Features
This library provides key generation, signing, and verifying, for five
popular NIST "Suite B" GF(p) (prime field) curves, with key lengths of 192,
224, 256, 384, and 521 bits. The "short names" for these curves, as known by
the OpenSSL tool (openssl ecparam -list_curves), are: prime192v1,
secp224r1, prime256v1, secp384r1, and secp521r1. It includes the
256-bit curve secp256k1 used by Bitcoin. There is also support for the
regular (non-twisted) variants of Brainpool curves from 160 to 512 bits. The
"short names" of those curves are: brainpoolP160r1, brainpoolP192r1,
brainpoolP224r1, brainpoolP256r1, brainpoolP320r1, brainpoolP384r1,
brainpoolP512r1.
No other curves are included, but it is not too hard to add support for more
curves over prime fields.
Dependencies
This library uses only Python and the 'six' package. It is compatible with Python 2.6, 2.7 and 3.3+. It also supports execution on the alternative implementations like pypy and pypy3.
If gmpy2 or gmpy is installed, they will be used for faster arithmetic.
Either of them can be installed after this library is installed,
python-ecdsa will detect their presence on start-up and use them
automatically.
To run the OpenSSL compatibility tests, the 'openssl' tool must be in your
PATH. This release has been tested successfully against OpenSSL 0.9.8o,
1.0.0a, 1.0.2f and 1.1.1d (among others).
Installation
This library is available on PyPI, it's recommended to install it using pip:
pip install ecdsa
In case higher performance is wanted and using native code is not a problem,
it's possible to specify installation together with gmpy2:
pip install ecdsa[gmpy2]
or (slower, legacy option):
pip install ecdsa[gmpy]
Speed
The following table shows how long this library takes to generate keypairs
(keygen), to sign data (sign), and to verify those signatures (verify).
All those values are in seconds.
For convenience, the inverses of those values are also provided:
how many keys per second can be generated (keygen/s), how many signatures
can be made per second (sign/s) and how many signatures can be verified
per second (verify/s). The size of raw signature (generally the smallest
way a signature can be encoded) is also provided in the siglen column.
Use tox -e speed to generate this table on your own computer.
On an Intel Core i7 4790K @ 4.0GHz I'm getting the following performance:
siglen keygen keygen/s sign sign/s verify verify/s
NIST192p: 48 0.00035s 2893.02 0.00038s 2620.53 0.00069s 1458.92
NIST224p: 56 0.00043s 2307.11 0.00048s 2092.00 0.00088s 1131.33
NIST256p: 64 0.00056s 1793.70 0.00061s 1639.87 0.00113s 883.79
NIST384p: 96 0.00116s 864.33 0.00124s 806.29 0.00233s 429.87
NIST521p: 132 0.00221s 452.16 0.00234s 427.31 0.00460s 217.19
SECP256k1: 64 0.00056s 1772.65 0.00061s 1628.73 0.00110s 912.13
BRAINPOOLP160r1: 40 0.00026s 3801.86 0.00029s 3401.11 0.00052s 1930.47
BRAINPOOLP192r1: 48 0.00034s 2925.73 0.00038s 2634.34 0.00070s 1438.06
BRAINPOOLP224r1: 56 0.00044s 2287.98 0.00048s 2083.87 0.00088s 1137.52
BRAINPOOLP256r1: 64 0.00056s 1774.11 0.00061s 1628.25 0.00112s 890.71
BRAINPOOLP320r1: 80 0.00081s 1238.18 0.00087s 1146.71 0.00151s 661.95
BRAINPOOLP384r1: 96 0.00117s 855.47 0.00124s 804.56 0.00241s 414.83
BRAINPOOLP512r1: 128 0.00223s 447.99 0.00234s 427.49 0.00437s 229.09
ecdh ecdh/s
NIST192p: 0.00110s 910.70
NIST224p: 0.00143s 701.17
NIST256p: 0.00178s 560.44
NIST384p: 0.00383s 261.03
NIST521p: 0.00745s 134.23
SECP256k1: 0.00168s 596.23
BRAINPOOLP160r1: 0.00085s 1174.02
BRAINPOOLP192r1: 0.00113s 883.47
BRAINPOOLP224r1: 0.00145s 687.82
BRAINPOOLP256r1: 0.00195s 514.03
BRAINPOOLP320r1: 0.00277s 360.80
BRAINPOOLP384r1: 0.00412s 242.58
BRAINPOOLP512r1: 0.00787s 127.12
To test performance with gmpy2 loaded, use tox -e speedgmpy2.
On the same machine I'm getting the following performance with gmpy2:
siglen keygen keygen/s sign sign/s verify verify/s
NIST192p: 48 0.00017s 5945.50 0.00018s 5544.66 0.00033s 3002.54
NIST224p: 56 0.00021s 4742.14 0.00022s 4463.52 0.00044s 2248.59
NIST256p: 64 0.00024s 4155.73 0.00025s 3994.28 0.00047s 2105.34
NIST384p: 96 0.00041s 2415.06 0.00043s 2316.41 0.00085s 1177.18
NIST521p: 132 0.00072s 1391.14 0.00074s 1359.63 0.00140s 716.31
SECP256k1: 64 0.00024s 4216.50 0.00025s 3994.52 0.00047s 2120.57
BRAINPOOLP160r1: 40 0.00014s 7038.99 0.00015s 6501.55 0.00029s 3397.79
BRAINPOOLP192r1: 48 0.00017s 5983.18 0.00018s 5626.08 0.00035s 2843.62
BRAINPOOLP224r1: 56 0.00021s 4727.54 0.00022s 4464.86 0.00043s 2326.84
BRAINPOOLP256r1: 64 0.00024s 4221.00 0.00025s 4010.26 0.00049s 2046.40
BRAINPOOLP320r1: 80 0.00032s 3142.14 0.00033s 3009.15 0.00061s 1652.88
BRAINPOOLP384r1: 96 0.00041s 2415.98 0.00043s 2340.35 0.00083s 1198.77
BRAINPOOLP512r1: 128 0.00064s 1567.27 0.00066s 1526.33 0.00127s 788.51
ecdh ecdh/s
NIST192p: 0.00051s 1960.26
NIST224p: 0.00067s 1502.97
NIST256p: 0.00073s 1376.12
NIST384p: 0.00132s 758.68
NIST521p: 0.00231s 433.23
SECP256k1: 0.00072s 1387.18
BRAINPOOLP160r1: 0.00042s 2366.60
BRAINPOOLP192r1: 0.00049s 2026.80
BRAINPOOLP224r1: 0.00067s 1486.52
BRAINPOOLP256r1: 0.00076s 1310.31
BRAINPOOLP320r1: 0.00101s 986.16
BRAINPOOLP384r1: 0.00131s 761.35
BRAINPOOLP512r1: 0.00211s 473.30
(there's also gmpy version, execute it using tox -e speedgmpy)
For comparison, a highly optimised implementation (including curve-specific
assembly for some curves), like the one in OpenSSL 1.1.1d, provides following
performance numbers on the same machine.
Run openssl speed ecdsa and openssl speed ecdh to reproduce it:
sign verify sign/s verify/s
192 bits ecdsa (nistp192) 0.0002s 0.0002s 4785.6 5380.7
224 bits ecdsa (nistp224) 0.0000s 0.0001s 22475.6 9822.0
256 bits ecdsa (nistp256) 0.0000s 0.0001s 45069.6 14166.6
384 bits ecdsa (nistp384) 0.0008s 0.0006s 1265.6 1648.1
521 bits ecdsa (nistp521) 0.0003s 0.0005s 3753.1 1819.5
256 bits ecdsa (brainpoolP256r1) 0.0003s 0.0003s 2983.5 3333.2
384 bits ecdsa (brainpoolP384r1) 0.0008s 0.0007s 1258.8 1528.1
512 bits ecdsa (brainpoolP512r1) 0.0015s 0.0012s 675.1 860.1
op op/s
192 bits ecdh (nistp192) 0.0002s 4853.4
224 bits ecdh (nistp224) 0.0001s 15252.1
256 bits ecdh (nistp256) 0.0001s 18436.3
384 bits ecdh (nistp384) 0.0008s 1292.7
521 bits ecdh (nistp521) 0.0003s 2884.7
256 bits ecdh (brainpoolP256r1) 0.0003s 3066.5
384 bits ecdh (brainpoolP384r1) 0.0008s 1298.0
512 bits ecdh (brainpoolP512r1) 0.0014s 694.8
Keys and signature can be serialized in different ways (see Usage, below). For a NIST192p key, the three basic representations require strings of the following lengths (in bytes):
to_string: signkey= 24, verifykey= 48, signature=48
compressed: signkey=n/a, verifykey= 25, signature=n/a
DER: signkey=106, verifykey= 80, signature=55
PEM: signkey=278, verifykey=162, (no support for PEM signatures)
History
In 2006, Peter Pearson announced his pure-python implementation of ECDSA in a message to sci.crypt, available from his download site. In 2010, Brian Warner wrote a wrapper around this code, to make it a bit easier and safer to use. Hubert Kario then included an implementation of elliptic curve cryptography that uses Jacobian coordinates internally, improving performance about 20-fold. You are looking at the README for this wrapper.
Testing
To run the full test suite, do this:
tox -e coverage
On an Intel Core i7 4790K @ 4.0GHz, the tests take about 16 seconds to execute.
The test suite uses
hypothesis so there is some
inherent variability in the test suite execution time.
One part of test_pyecdsa.py checks compatibility with OpenSSL, by
running the "openssl" CLI tool, make sure it's in your PATH if you want
to test compatibility with it.
Security
This library was not designed with security in mind. If you are processing data that needs to be protected we suggest you use a quality wrapper around OpenSSL. pyca/cryptography is one example of such a wrapper. The primary use-case of this library is as a portable library for interoperability testing and as a teaching tool.
This library does not protect against side channel attacks.
Do not allow attackers to measure how long it takes you to generate a keypair or sign a message. Do not allow attackers to run code on the same physical machine when keypair generation or signing is taking place (this includes virtual machines). Do not allow attackers to measure how much power your computer uses while generating the keypair or signing a message. Do not allow attackers to measure RF interference coming from your computer while generating a keypair or signing a message. Note: just loading the private key will cause keypair generation. Other operations or attack vectors may also be vulnerable to attacks. For a sophisticated attacker observing just one operation with a private key will be sufficient to completely reconstruct the private key.
Please also note that any Pure-python cryptographic library will be vulnerable
to the same side channel attacks. This is because Python does not provide
side-channel secure primitives (with the exception of
hmac.compare_digest()), making side-channel secure programming
impossible.
This library depends upon a strong source of random numbers. Do not use it on
a system where os.urandom() does not provide cryptographically secure
random numbers.
Usage
You start by creating a SigningKey. You can use this to sign data, by passing
in data as a byte string and getting back the signature (also a byte string).
You can also ask a SigningKey to give you the corresponding VerifyingKey.
The VerifyingKey can be used to verify a signature, by passing it both the
data string and the signature byte string: it either returns True or raises
BadSignatureError.
from ecdsa import SigningKey
sk = SigningKey.generate() # uses NIST192p
vk = sk.verifying_key
signature = sk.sign(b"message")
assert vk.verify(signature, b"message")
Each SigningKey/VerifyingKey is associated with a specific curve, like
NIST192p (the default one). Longer curves are more secure, but take longer to
use, and result in longer keys and signatures.
from ecdsa import SigningKey, NIST384p
sk = SigningKey.generate(curve=NIST384p)
vk = sk.verifying_key
signature = sk.sign(b"message")
assert vk.verify(signature, b"message")
The SigningKey can be serialized into several different formats: the shortest
is to call s=sk.to_string(), and then re-create it with
SigningKey.from_string(s, curve) . This short form does not record the
curve, so you must be sure to pass to from_string() the same curve you used
for the original key. The short form of a NIST192p-based signing key is just 24
bytes long. If a point encoding is invalid or it does not lie on the specified
curve, from_string() will raise MalformedPointError.
from ecdsa import SigningKey, NIST384p
sk = SigningKey.generate(curve=NIST384p)
sk_string = sk.to_string()
sk2 = SigningKey.from_string(sk_string, curve=NIST384p)
print(sk_string.hex())
print(sk2.to_string().hex())
Note: while the methods are called to_string() the type they return is
actually bytes, the "string" part is leftover from Python 2.
sk.to_pem() and sk.to_der() will serialize the signing key into the same
formats that OpenSSL uses. The PEM file looks like the familiar ASCII-armored
"-----BEGIN EC PRIVATE KEY-----" base64-encoded format, and the DER format
is a shorter binary form of the same data.
SigningKey.from_pem()/.from_der() will undo this serialization. These
formats include the curve name, so you do not need to pass in a curve
identifier to the deserializer. In case the file is malformed from_der()
and from_pem() will raise UnexpectedDER or MalformedPointError.
from ecdsa import SigningKey, NIST384p
sk = SigningKey.generate(curve=NIST384p)
sk_pem = sk.to_pem()
sk2 = SigningKey.from_pem(sk_pem)
# sk and sk2 are the same key
Likewise, the VerifyingKey can be serialized in the same way:
vk.to_string()/VerifyingKey.from_string(), to_pem()/from_pem(), and
to_der()/from_der(). The same curve= argument is needed for
VerifyingKey.from_string().
from ecdsa import SigningKey, VerifyingKey, NIST384p
sk = SigningKey.generate(curve=NIST384p)
vk = sk.verifying_key
vk_string = vk.to_string()
vk2 = VerifyingKey.from_string(vk_string, curve=NIST384p)
# vk and vk2 are the same key
from ecdsa import SigningKey, VerifyingKey, NIST384p
sk = SigningKey.generate(curve=NIST384p)
vk = sk.verifying_key
vk_pem = vk.to_pem()
vk2 = VerifyingKey.from_pem(vk_pem)
# vk and vk2 are the same key
There are a couple of different ways to compute a signature. Fundamentally,
ECDSA takes a number that represents the data being signed, and returns a
pair of numbers that represent the signature. The hashfunc= argument to
sk.sign() and vk.verify() is used to turn an arbitrary string into
fixed-length digest, which is then turned into a number that ECDSA can sign,
and both sign and verify must use the same approach. The default value is
hashlib.sha1, but if you use NIST256p or a longer curve, you can use
hashlib.sha256 instead.
There are also multiple ways to represent a signature. The default
sk.sign() and vk.verify() methods present it as a short string, for
simplicity and minimal overhead. To use a different scheme, use the
sk.sign(sigencode=) and vk.verify(sigdecode=) arguments. There are helper
functions in the ecdsa.util module that can be useful here.
It is also possible to create a SigningKey from a "seed", which is
deterministic. This can be used in protocols where you want to derive
consistent signing keys from some other secret, for example when you want
three separate keys and only want to store a single master secret. You should
start with a uniformly-distributed unguessable seed with about curve.baselen
bytes of entropy, and then use one of the helper functions in ecdsa.util to
convert it into an integer in the correct range, and then finally pass it
into SigningKey.from_secret_exponent(), like this:
import os
from ecdsa import NIST384p, SigningKey
from ecdsa.util import randrange_from_seed__trytryagain
def make_key(seed):
secexp = randrange_from_seed__trytryagain(seed, NIST384p.order)
return SigningKey.from_secret_exponent(secexp, curve=NIST384p)
seed = os.urandom(NIST384p.baselen) # or other starting point
sk1a = make_key(seed)
sk1b = make_key(seed)
# note: sk1a and sk1b are the same key
assert sk1a.to_string() == sk1b.to_string()
sk2 = make_key(b"2-"+seed) # different key
assert sk1a.to_string() != sk2.to_string()
In case the application will verify a lot of signatures made with a single key, it's possible to precompute some of the internal values to make signature verification significantly faster. The break-even point occurs at about 100 signatures verified.
To perform precomputation, you can call the precompute() method
on VerifyingKey instance:
from ecdsa import SigningKey, NIST384p
sk = SigningKey.generate(curve=NIST384p)
vk = sk.verifying_key
vk.precompute()
signature = sk.sign(b"message")
assert vk.verify(signature, b"message")
Once precompute() was called, all signature verifications with this key will
be faster to execute.
OpenSSL Compatibility
To produce signatures that can be verified by OpenSSL tools, or to verify signatures that were produced by those tools, use:
# openssl ecparam -name prime256v1 -genkey -out sk.pem
# openssl ec -in sk.pem -pubout -out vk.pem
# echo "data for signing" > data
# openssl dgst -sha256 -sign sk.pem -out data.sig data
# openssl dgst -sha256 -verify vk.pem -signature data.sig data
# openssl dgst -sha256 -prverify sk.pem -signature data.sig data
import hashlib
from ecdsa import SigningKey, VerifyingKey
from ecdsa.util import sigencode_der, sigdecode_der
with open("vk.pem") as f:
vk = VerifyingKey.from_pem(f.read())
with open("data", "rb") as f:
data = f.read()
with open("data.sig", "rb") as f:
signature = f.read()
assert vk.verify(signature, data, hashlib.sha256, sigdecode=sigdecode_der)
with open("sk.pem") as f:
sk = SigningKey.from_pem(f.read(), hashlib.sha256)
new_signature = sk.sign_deterministic(data, sigencode=sigencode_der)
with open("data.sig2", "wb") as f:
f.write(new_signature)
# openssl dgst -sha256 -verify vk.pem -signature data.sig2 data
Note: if compatibility with OpenSSL 1.0.0 or earlier is necessary, the
sigencode_string and sigdecode_string from ecdsa.util can be used for
respectively writing and reading the signatures.
The keys also can be written in format that openssl can handle:
from ecdsa import SigningKey, VerifyingKey
with open("sk.pem") as f:
sk = SigningKey.from_pem(f.read())
with open("sk.pem", "wb") as f:
f.write(sk.to_pem())
with open("vk.pem") as f:
vk = VerifyingKey.from_pem(f.read())
with open("vk.pem", "wb") as f:
f.write(vk.to_pem())
Entropy
Creating a signing key with SigningKey.generate() requires some form of
entropy (as opposed to
from_secret_exponent/from_string/from_der/from_pem,
which are deterministic and do not require an entropy source). The default
source is os.urandom(), but you can pass any other function that behaves
like os.urandom as the entropy= argument to do something different. This
may be useful in unit tests, where you want to achieve repeatable results. The
ecdsa.util.PRNG utility is handy here: it takes a seed and produces a strong
pseudo-random stream from it:
from ecdsa.util import PRNG
from ecdsa import SigningKey
rng1 = PRNG(b"seed")
sk1 = SigningKey.generate(entropy=rng1)
rng2 = PRNG(b"seed")
sk2 = SigningKey.generate(entropy=rng2)
# sk1 and sk2 are the same key
Likewise, ECDSA signature generation requires a random number, and each
signature must use a different one (using the same number twice will
immediately reveal the private signing key). The sk.sign() method takes an
entropy= argument which behaves the same as SigningKey.generate(entropy=).
Deterministic Signatures
If you call SigningKey.sign_deterministic(data) instead of .sign(data),
the code will generate a deterministic signature instead of a random one.
This uses the algorithm from RFC6979 to safely generate a unique k value,
derived from the private key and the message being signed. Each time you sign
the same message with the same key, you will get the same signature (using
the same k).
This may become the default in a future version, as it is not vulnerable to failures of the entropy source.
Examples
Create a NIST192p keypair and immediately save both to disk:
from ecdsa import SigningKey
sk = SigningKey.generate()
vk = sk.verifying_key
with open("private.pem", "wb") as f:
f.write(sk.to_pem())
with open("public.pem", "wb") as f:
f.write(vk.to_pem())
Load a signing key from disk, use it to sign a message (using SHA-1), and write the signature to disk:
from ecdsa import SigningKey
with open("private.pem") as f:
sk = SigningKey.from_pem(f.read())
with open("message", "rb") as f:
message = f.read()
sig = sk.sign(message)
with open("signature", "wb") as f:
f.write(sig)
Load the verifying key, message, and signature from disk, and verify the signature (assume SHA-1 hash):
from ecdsa import VerifyingKey, BadSignatureError
vk = VerifyingKey.from_pem(open("public.pem").read())
with open("message", "rb") as f:
message = f.read()
with open("signature", "rb") as f:
sig = f.read()
try:
vk.verify(sig, message)
print "good signature"
except BadSignatureError:
print "BAD SIGNATURE"
Create a NIST521p keypair:
from ecdsa import SigningKey, NIST521p
sk = SigningKey.generate(curve=NIST521p)
vk = sk.verifying_key
Create three independent signing keys from a master seed:
from ecdsa import NIST192p, SigningKey
from ecdsa.util import randrange_from_seed__trytryagain
def make_key_from_seed(seed, curve=NIST192p):
secexp = randrange_from_seed__trytryagain(seed, curve.order)
return SigningKey.from_secret_exponent(secexp, curve)
sk1 = make_key_from_seed("1:%s" % seed)
sk2 = make_key_from_seed("2:%s" % seed)
sk3 = make_key_from_seed("3:%s" % seed)
Load a verifying key from disk and print it using hex encoding in uncompressed and compressed format (defined in X9.62 and SEC1 standards):
from ecdsa import VerifyingKey
with open("public.pem") as f:
vk = VerifyingKey.from_pem(f.read())
print("uncompressed: {0}".format(vk.to_string("uncompressed").hex()))
print("compressed: {0}".format(vk.to_string("compressed").hex()))
Load a verifying key from a hex string from compressed format, output uncompressed:
from ecdsa import VerifyingKey, NIST256p
comp_str = '022799c0d0ee09772fdd337d4f28dc155581951d07082fb19a38aa396b67e77759'
vk = VerifyingKey.from_string(bytearray.fromhex(comp_str), curve=NIST256p)
print(vk.to_string("uncompressed").hex())
ECDH key exchange with remote party
from ecdsa import ECDH, NIST256p
ecdh = ECDH(curve=NIST256p)
ecdh.generate_private_key()
local_public_key = ecdh.get_public_key()
#send `local_public_key` to remote party and receive `remote_public_key` from remote party
with open("remote_public_key.pem") as e:
remote_public_key = e.read()
ecdh.load_received_public_key_pem(remote_public_key)
secret = ecdh.generate_sharedsecret_bytes()