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diff --git a/frozen_deps/ecdsa-0.16.1.dist-info/METADATA b/frozen_deps/ecdsa-0.16.1.dist-info/METADATA new file mode 100644 index 0000000..983a64a --- /dev/null +++ b/frozen_deps/ecdsa-0.16.1.dist-info/METADATA @@ -0,0 +1,626 @@ +Metadata-Version: 2.1 +Name: ecdsa +Version: 0.16.1 +Summary: ECDSA cryptographic signature library (pure python) +Home-page: http://github.com/warner/python-ecdsa +Author: Brian Warner +Author-email: warner@lothar.com +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 +Requires-Python: >=2.6, !=3.0.*, !=3.1.*, !=3.2.* +Description-Content-Type: text/markdown +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 + +[](http://travis-ci.org/warner/python-ecdsa) +[](https://coveralls.io/r/warner/python-ecdsa) +[](https://travis-ci.org/warner/python-ecdsa/jobs/626479178#L776) +[](https://pypi.python.org/pypi/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][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. 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. + +[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 16 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` 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](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 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()`][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 +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 keypair 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 keypair: + +```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() +``` + + |