-pip

-"python-ecdsa" Copyright (c) 2010 Brian Warner

-

-Portions written in 2005 by Peter Pearson and placed in the public domain.

-

-Permission is hereby granted, free of charge, to any person

-obtaining a copy of this software and associated documentation

-files (the "Software"), to deal in the Software without

-restriction, including without limitation the rights to use,

-copy, modify, merge, publish, distribute, sublicense, and/or sell

-copies of the Software, and to permit persons to whom the

-Software is furnished to do so, subject to the following

-conditions:

-

-The above copyright notice and this permission notice shall be

-included in all copies or substantial portions of the Software.

-

-THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND,

-EXPRESS OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES

-OF MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE AND

-NONINFRINGEMENT. IN NO EVENT SHALL THE AUTHORS OR COPYRIGHT

-HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER LIABILITY,

-WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING

-FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR

-OTHER DEALINGS IN THE SOFTWARE.

-Metadata-Version: 2.1

-Name: ecdsa

-Version: 0.18.0

-Summary: ECDSA cryptographic signature library (pure python)

-Home-page: http://github.com/tlsfuzzer/python-ecdsa

-Author: Brian Warner

-Author-email: [email protected]

-License: MIT

-Platform: UNKNOWN

-Classifier: Programming Language :: Python

-Classifier: Programming Language :: Python :: 2

-Classifier: Programming Language :: Python :: 2.6

-Classifier: Programming Language :: Python :: 2.7

-Classifier: Programming Language :: Python :: 3

-Classifier: Programming Language :: Python :: 3.3

-Classifier: Programming Language :: Python :: 3.4

-Classifier: Programming Language :: Python :: 3.5

-Classifier: Programming Language :: Python :: 3.6

-Classifier: Programming Language :: Python :: 3.7

-Classifier: Programming Language :: Python :: 3.8

-Classifier: Programming Language :: Python :: 3.9

-Classifier: Programming Language :: Python :: 3.10

-Classifier: Programming Language :: Python :: 3.11

-Requires-Python: >=2.6, !=3.0.*, !=3.1.*, !=3.2.*

-Description-Content-Type: text/markdown

-License-File: LICENSE

-Requires-Dist: six (>=1.9.0)

-Provides-Extra: gmpy

-Requires-Dist: gmpy ; extra == 'gmpy'

-Provides-Extra: gmpy2

-Requires-Dist: gmpy2 ; extra == 'gmpy2'

-

-# Pure-Python ECDSA and ECDH

-

-[](https://github.com/tlsfuzzer/python-ecdsa/actions?query=workflow%3A%22GitHub+CI%22+branch%3Amaster)

-[](https://ecdsa.readthedocs.io/en/latest/?badge=latest)

-[](https://coveralls.io/github/tlsfuzzer/python-ecdsa?branch=master)

-

-[](https://lgtm.com/projects/g/tlsfuzzer/python-ecdsa/context:python)

-[](https://lgtm.com/projects/g/tlsfuzzer/python-ecdsa/alerts/)

-[](https://pypi.python.org/pypi/ecdsa/)

-

-

-

-This is an easy-to-use implementation of ECC (Elliptic Curve Cryptography)

-with support for ECDSA (Elliptic Curve Digital Signature Algorithm),

-EdDSA (Edwards-curve Digital Signature Algorithm) and ECDH

-(Elliptic Curve Diffie-Hellman), implemented purely in Python, released under

-the MIT license. With this library, you can quickly create key pairs (signing

-key and verifying key), sign messages, and verify the signatures. You can

-also agree on a shared secret key based on exchanged public keys.

-The keys and signatures are very short, making them easy to handle and

-incorporate into other protocols.

-

-**NOTE: This library should not be used in production settings, see [Security](#Security) for more details.**

-

-## Features

-

-This library provides key generation, signing, verifying, and shared secret

-derivation 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`. Few of the small curves from SEC standard are also

-included (mainly to speed-up testing of the library), those are:

-`secp112r1`, `secp112r2`, `secp128r1`, and `secp160r1`.

-Key generation, siging and verifying is also supported for Ed25519 and

-Ed448 curves.

-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 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.

-You should prefer `gmpy2` on Python3 for optimal performance.

-

-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, 1.1.1d and 3.0.1 (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 key pairs

-(`keygen`), to sign data (`sign`), to verify those signatures (`verify`),

-to derive a shared secret (`ecdh`), and

-to verify the signatures with no key-specific precomputation (`no PC 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`), how many signatures can be verified

-per second (`verify/s`), how many shared secrets can be derived per second

-(`ecdh/s`), and how many signatures with no key specific

-precomputation can be verified per second (`no PC verify/s`). The size of raw

-signature (generally the smallest

-the 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 no PC verify no PC verify/s

- NIST192p: 48 0.00032s 3134.06 0.00033s 2985.53 0.00063s 1598.36 0.00129s 774.43

- NIST224p: 56 0.00040s 2469.24 0.00042s 2367.88 0.00081s 1233.41 0.00170s 586.66

- NIST256p: 64 0.00051s 1952.73 0.00054s 1867.80 0.00098s 1021.86 0.00212s 471.27

- NIST384p: 96 0.00107s 935.92 0.00111s 904.23 0.00203s 491.77 0.00446s 224.00

- NIST521p: 132 0.00210s 475.52 0.00215s 464.16 0.00398s 251.28 0.00874s 114.39

- SECP256k1: 64 0.00052s 1921.54 0.00054s 1847.49 0.00105s 948.68 0.00210s 477.01

- BRAINPOOLP160r1: 40 0.00025s 4003.88 0.00026s 3845.12 0.00053s 1893.93 0.00105s 949.92

- BRAINPOOLP192r1: 48 0.00033s 3043.97 0.00034s 2975.98 0.00063s 1581.50 0.00135s 742.29

- BRAINPOOLP224r1: 56 0.00041s 2436.44 0.00043s 2315.51 0.00078s 1278.49 0.00180s 556.16

- BRAINPOOLP256r1: 64 0.00053s 1892.49 0.00054s 1846.24 0.00114s 875.64 0.00229s 437.25

- BRAINPOOLP320r1: 80 0.00073s 1361.26 0.00076s 1309.25 0.00143s 699.29 0.00322s 310.49

- BRAINPOOLP384r1: 96 0.00107s 931.29 0.00111s 901.80 0.00230s 434.19 0.00476s 210.20

- BRAINPOOLP512r1: 128 0.00207s 483.41 0.00212s 471.42 0.00425s 235.43 0.00912s 109.61

- SECP112r1: 28 0.00015s 6672.53 0.00016s 6440.34 0.00031s 3265.41 0.00056s 1774.20

- SECP112r2: 28 0.00015s 6697.11 0.00015s 6479.98 0.00028s 3524.72 0.00058s 1716.16

- SECP128r1: 32 0.00018s 5497.65 0.00019s 5272.89 0.00036s 2747.39 0.00072s 1396.16

- SECP160r1: 42 0.00025s 3949.32 0.00026s 3894.45 0.00046s 2153.85 0.00102s 985.07

- Ed25519: 64 0.00076s 1324.48 0.00042s 2405.01 0.00109s 918.05 0.00344s 290.50

- Ed448: 114 0.00176s 569.53 0.00115s 870.94 0.00282s 355.04 0.01024s 97.69

-

- ecdh ecdh/s

- NIST192p: 0.00104s 964.89

- NIST224p: 0.00134s 748.63

- NIST256p: 0.00170s 587.08

- NIST384p: 0.00352s 283.90

- NIST521p: 0.00717s 139.51

- SECP256k1: 0.00154s 648.40

- BRAINPOOLP160r1: 0.00082s 1220.70

- BRAINPOOLP192r1: 0.00105s 956.75

- BRAINPOOLP224r1: 0.00136s 734.52

- BRAINPOOLP256r1: 0.00178s 563.32

- BRAINPOOLP320r1: 0.00252s 397.23

- BRAINPOOLP384r1: 0.00376s 266.27

- BRAINPOOLP512r1: 0.00733s 136.35

- SECP112r1: 0.00046s 2180.40

- SECP112r2: 0.00045s 2229.14

- SECP128r1: 0.00054s 1868.15

- SECP160r1: 0.00080s 1243.98

-```

-

-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 no PC verify no PC verify/s

- NIST192p: 48 0.00017s 5933.40 0.00017s 5751.70 0.00032s 3125.28 0.00067s 1502.41

- NIST224p: 56 0.00021s 4782.87 0.00022s 4610.05 0.00040s 2487.04 0.00089s 1126.90

- NIST256p: 64 0.00023s 4263.98 0.00024s 4125.16 0.00045s 2200.88 0.00098s 1016.82

- NIST384p: 96 0.00041s 2449.54 0.00042s 2399.96 0.00083s 1210.57 0.00172s 581.43

- NIST521p: 132 0.00071s 1416.07 0.00072s 1389.81 0.00144s 692.93 0.00312s 320.40

- SECP256k1: 64 0.00024s 4245.05 0.00024s 4122.09 0.00045s 2206.40 0.00094s 1068.32

- BRAINPOOLP160r1: 40 0.00014s 6939.17 0.00015s 6681.55 0.00029s 3452.43 0.00057s 1769.81

- BRAINPOOLP192r1: 48 0.00017s 5920.05 0.00017s 5774.36 0.00034s 2979.00 0.00069s 1453.19

- BRAINPOOLP224r1: 56 0.00021s 4732.12 0.00022s 4622.65 0.00041s 2422.47 0.00087s 1149.87

- BRAINPOOLP256r1: 64 0.00024s 4233.02 0.00024s 4115.20 0.00047s 2143.27 0.00098s 1015.60

- BRAINPOOLP320r1: 80 0.00032s 3162.38 0.00032s 3077.62 0.00063s 1598.83 0.00136s 737.34

- BRAINPOOLP384r1: 96 0.00041s 2436.88 0.00042s 2395.62 0.00083s 1202.68 0.00178s 562.85

- BRAINPOOLP512r1: 128 0.00063s 1587.60 0.00064s 1558.83 0.00125s 799.96 0.00281s 355.83

- SECP112r1: 28 0.00009s 11118.66 0.00009s 10775.48 0.00018s 5456.00 0.00033s 3020.83

- SECP112r2: 28 0.00009s 11322.97 0.00009s 10857.71 0.00017s 5748.77 0.00032s 3094.28

- SECP128r1: 32 0.00010s 10078.39 0.00010s 9665.27 0.00019s 5200.58 0.00036s 2760.88

- SECP160r1: 42 0.00015s 6875.51 0.00015s 6647.35 0.00029s 3422.41 0.00057s 1768.35

- Ed25519: 64 0.00030s 3322.56 0.00018s 5568.63 0.00046s 2165.35 0.00153s 654.02

- Ed448: 114 0.00060s 1680.53 0.00039s 2567.40 0.00096s 1036.67 0.00350s 285.62

-

- ecdh ecdh/s

- NIST192p: 0.00050s 1985.70

- NIST224p: 0.00066s 1524.16

- NIST256p: 0.00071s 1413.07

- NIST384p: 0.00127s 788.89

- NIST521p: 0.00230s 434.85

- SECP256k1: 0.00071s 1409.95

- BRAINPOOLP160r1: 0.00042s 2374.65

- BRAINPOOLP192r1: 0.00051s 1960.01

- BRAINPOOLP224r1: 0.00066s 1518.37

- BRAINPOOLP256r1: 0.00071s 1399.90

- BRAINPOOLP320r1: 0.00100s 997.21

- BRAINPOOLP384r1: 0.00129s 777.51

- BRAINPOOLP512r1: 0.00210s 475.99

- SECP112r1: 0.00022s 4457.70

- SECP112r2: 0.00024s 4252.33

- SECP128r1: 0.00028s 3589.31

- SECP160r1: 0.00043s 2305.02

-```

-

-(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 the

-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

-

- sign verify sign/s verify/s

- 253 bits EdDSA (Ed25519) 0.0000s 0.0001s 28217.9 10897.7

- 456 bits EdDSA (Ed448) 0.0003s 0.0005s 3926.5 2147.7

-

- 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][1], available from his [download site][2]. In 2010,

-Brian Warner wrote a wrapper around this code, to make it a bit easier and

-safer to use. In 2020, Hubert Kario 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.

-

-[1]: http://www.derkeiler.com/Newsgroups/sci.crypt/2006-01/msg00651.html

-[2]: http://webpages.charter.net/curryfans/peter/downloads.html

-

-## Testing

-

-To run the full test suite, do this:

-

- tox -e coverage

-

-On an Intel Core i7 4790K @ 4.0GHz, the tests take about 18 seconds to execute.

-The test suite uses

-[`hypothesis`](https://github.com/HypothesisWorks/hypothesis) so there is some

-inherent variability in the test suite execution time.

-

-One part of `test_pyecdsa.py` and `test_ecdh.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 (if OpenSSL is missing, too old, or

-doesn't support all the curves supported in upstream releases you will see

-skipped tests in the above `coverage` run).

-

-## 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](https://cryptography.io) 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 key pair

-or sign a message. Do not allow attackers to run code on the same physical

-machine when key pair 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 key pair or signing a message. Do not allow

-attackers to measure RF interference coming from your computer while generating

-a key pair or signing a message. Note: just loading the private key will cause

-key pair 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()`][3]), 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.

-

-[3]: https://docs.python.org/3/library/hmac.html#hmac.compare_digest

-

-## 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`.

-

-```python

-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.

-

-```python

-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`.

-

-```python

-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`.

-

-```python

-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()`.

-

-```python

-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 a

-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:

-

-```python

-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:

-```python

-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:

-

-```python

-# 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:

-

-```python

-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:

-

-```python

-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 key pair and immediately save both to disk:

-

-```python

-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:

-

-```python

-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):

-

-```python

-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 key pair:

-

-```python

-from ecdsa import SigningKey, NIST521p

-sk = SigningKey.generate(curve=NIST521p)

-vk = sk.verifying_key

-```

-

-Create three independent signing keys from a master seed:

-

-```python

-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):

-

-```python

-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:

-

-```python

-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:

-

-```python

-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()

-```

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