635 lines
28 KiB
Markdown
635 lines
28 KiB
Markdown
# Pure-Python ECDSA and ECDH
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[](https://github.com/tlsfuzzer/python-ecdsa/actions?query=workflow%3A%22GitHub+CI%22+branch%3Amaster)
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[](https://coveralls.io/github/tlsfuzzer/python-ecdsa?branch=master)
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[](https://travis-ci.com/github/tlsfuzzer/python-ecdsa/jobs/458951056#L544)
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[](https://lgtm.com/projects/g/tlsfuzzer/python-ecdsa/context:python)
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[](https://lgtm.com/projects/g/tlsfuzzer/python-ecdsa/alerts/)
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[](https://pypi.python.org/pypi/ecdsa/)
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This is an easy-to-use implementation of ECC (Elliptic Curve Cryptography)
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with support for ECDSA (Elliptic Curve Digital Signature Algorithm) and ECDH
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(Elliptic Curve Diffie-Hellman), implemented purely in Python, released under
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the MIT license. With this library, you can quickly create key pairs (signing
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key and verifying key), sign messages, and verify the signatures. You can
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also agree on a shared secret key based on exchanged public keys.
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The keys and signatures are very short, making them easy to handle and
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incorporate into other protocols.
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## Features
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This library provides key generation, signing, verifying, and shared secret
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derivation for five
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popular NIST "Suite B" GF(p) (_prime field_) curves, with key lengths of 192,
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224, 256, 384, and 521 bits. The "short names" for these curves, as known by
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the OpenSSL tool (`openssl ecparam -list_curves`), are: `prime192v1`,
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`secp224r1`, `prime256v1`, `secp384r1`, and `secp521r1`. It includes the
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256-bit curve `secp256k1` used by Bitcoin. There is also support for the
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regular (non-twisted) variants of Brainpool curves from 160 to 512 bits. The
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"short names" of those curves are: `brainpoolP160r1`, `brainpoolP192r1`,
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`brainpoolP224r1`, `brainpoolP256r1`, `brainpoolP320r1`, `brainpoolP384r1`,
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`brainpoolP512r1`. Few of the small curves from SEC standard are also
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included (mainly to speed-up testing of the library), those are:
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`secp112r1`, `secp112r2`, `secp128r1`, and `secp160r1`.
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No other curves are included, but it is not too hard to add support for more
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curves over prime fields.
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## Dependencies
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This library uses only Python and the 'six' package. It is compatible with
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Python 2.6, 2.7, and 3.3+. It also supports execution on alternative
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implementations like pypy and pypy3.
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If `gmpy2` or `gmpy` is installed, they will be used for faster arithmetic.
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Either of them can be installed after this library is installed,
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`python-ecdsa` will detect their presence on start-up and use them
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automatically.
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You should prefer `gmpy2` on Python3 for optimal performance.
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To run the OpenSSL compatibility tests, the 'openssl' tool must be in your
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`PATH`. This release has been tested successfully against OpenSSL 0.9.8o,
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1.0.0a, 1.0.2f and 1.1.1d (among others).
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## Installation
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This library is available on PyPI, it's recommended to install it using `pip`:
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```
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pip install ecdsa
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```
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In case higher performance is wanted and using native code is not a problem,
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it's possible to specify installation together with `gmpy2`:
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```
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pip install ecdsa[gmpy2]
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```
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or (slower, legacy option):
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```
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pip install ecdsa[gmpy]
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```
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## Speed
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The following table shows how long this library takes to generate key pairs
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(`keygen`), to sign data (`sign`), to verify those signatures (`verify`),
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to derive a shared secret (`ecdh`), and
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to verify the signatures with no key-specific precomputation (`no PC verify`).
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All those values are in seconds.
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For convenience, the inverses of those values are also provided:
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how many keys per second can be generated (`keygen/s`), how many signatures
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can be made per second (`sign/s`), how many signatures can be verified
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per second (`verify/s`), how many shared secrets can be derived per second
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(`ecdh/s`), and how many signatures with no key specific
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precomputation can be verified per second (`no PC verify/s`). The size of raw
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signature (generally the smallest
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the way a signature can be encoded) is also provided in the `siglen` column.
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Use `tox -e speed` to generate this table on your own computer.
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On an Intel Core i7 4790K @ 4.0GHz I'm getting the following performance:
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```
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siglen keygen keygen/s sign sign/s verify verify/s no PC verify no PC verify/s
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NIST192p: 48 0.00032s 3134.06 0.00033s 2985.53 0.00063s 1598.36 0.00129s 774.43
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NIST224p: 56 0.00040s 2469.24 0.00042s 2367.88 0.00081s 1233.41 0.00170s 586.66
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NIST256p: 64 0.00051s 1952.73 0.00054s 1867.80 0.00098s 1021.86 0.00212s 471.27
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NIST384p: 96 0.00107s 935.92 0.00111s 904.23 0.00203s 491.77 0.00446s 224.00
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NIST521p: 132 0.00210s 475.52 0.00215s 464.16 0.00398s 251.28 0.00874s 114.39
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SECP256k1: 64 0.00052s 1921.54 0.00054s 1847.49 0.00105s 948.68 0.00210s 477.01
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BRAINPOOLP160r1: 40 0.00025s 4003.88 0.00026s 3845.12 0.00053s 1893.93 0.00105s 949.92
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BRAINPOOLP192r1: 48 0.00033s 3043.97 0.00034s 2975.98 0.00063s 1581.50 0.00135s 742.29
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BRAINPOOLP224r1: 56 0.00041s 2436.44 0.00043s 2315.51 0.00078s 1278.49 0.00180s 556.16
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BRAINPOOLP256r1: 64 0.00053s 1892.49 0.00054s 1846.24 0.00114s 875.64 0.00229s 437.25
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BRAINPOOLP320r1: 80 0.00073s 1361.26 0.00076s 1309.25 0.00143s 699.29 0.00322s 310.49
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BRAINPOOLP384r1: 96 0.00107s 931.29 0.00111s 901.80 0.00230s 434.19 0.00476s 210.20
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BRAINPOOLP512r1: 128 0.00207s 483.41 0.00212s 471.42 0.00425s 235.43 0.00912s 109.61
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SECP112r1: 28 0.00015s 6672.53 0.00016s 6440.34 0.00031s 3265.41 0.00056s 1774.20
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SECP112r2: 28 0.00015s 6697.11 0.00015s 6479.98 0.00028s 3524.72 0.00058s 1716.16
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SECP128r1: 32 0.00018s 5497.65 0.00019s 5272.89 0.00036s 2747.39 0.00072s 1396.16
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SECP160r1: 42 0.00025s 3949.32 0.00026s 3894.45 0.00046s 2153.85 0.00102s 985.07
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Ed25519: 64 0.00076s 1324.48 0.00042s 2405.01 0.00109s 918.05 0.00344s 290.50
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Ed448: 114 0.00176s 569.53 0.00115s 870.94 0.00282s 355.04 0.01024s 97.69
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ecdh ecdh/s
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NIST192p: 0.00104s 964.89
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NIST224p: 0.00134s 748.63
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NIST256p: 0.00170s 587.08
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NIST384p: 0.00352s 283.90
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NIST521p: 0.00717s 139.51
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SECP256k1: 0.00154s 648.40
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BRAINPOOLP160r1: 0.00082s 1220.70
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BRAINPOOLP192r1: 0.00105s 956.75
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BRAINPOOLP224r1: 0.00136s 734.52
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BRAINPOOLP256r1: 0.00178s 563.32
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BRAINPOOLP320r1: 0.00252s 397.23
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BRAINPOOLP384r1: 0.00376s 266.27
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BRAINPOOLP512r1: 0.00733s 136.35
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SECP112r1: 0.00046s 2180.40
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SECP112r2: 0.00045s 2229.14
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SECP128r1: 0.00054s 1868.15
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SECP160r1: 0.00080s 1243.98
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```
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To test performance with `gmpy2` loaded, use `tox -e speedgmpy2`.
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On the same machine I'm getting the following performance with `gmpy2`:
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```
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siglen keygen keygen/s sign sign/s verify verify/s no PC verify no PC verify/s
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NIST192p: 48 0.00017s 5933.40 0.00017s 5751.70 0.00032s 3125.28 0.00067s 1502.41
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NIST224p: 56 0.00021s 4782.87 0.00022s 4610.05 0.00040s 2487.04 0.00089s 1126.90
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NIST256p: 64 0.00023s 4263.98 0.00024s 4125.16 0.00045s 2200.88 0.00098s 1016.82
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NIST384p: 96 0.00041s 2449.54 0.00042s 2399.96 0.00083s 1210.57 0.00172s 581.43
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NIST521p: 132 0.00071s 1416.07 0.00072s 1389.81 0.00144s 692.93 0.00312s 320.40
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SECP256k1: 64 0.00024s 4245.05 0.00024s 4122.09 0.00045s 2206.40 0.00094s 1068.32
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BRAINPOOLP160r1: 40 0.00014s 6939.17 0.00015s 6681.55 0.00029s 3452.43 0.00057s 1769.81
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BRAINPOOLP192r1: 48 0.00017s 5920.05 0.00017s 5774.36 0.00034s 2979.00 0.00069s 1453.19
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BRAINPOOLP224r1: 56 0.00021s 4732.12 0.00022s 4622.65 0.00041s 2422.47 0.00087s 1149.87
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BRAINPOOLP256r1: 64 0.00024s 4233.02 0.00024s 4115.20 0.00047s 2143.27 0.00098s 1015.60
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BRAINPOOLP320r1: 80 0.00032s 3162.38 0.00032s 3077.62 0.00063s 1598.83 0.00136s 737.34
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BRAINPOOLP384r1: 96 0.00041s 2436.88 0.00042s 2395.62 0.00083s 1202.68 0.00178s 562.85
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BRAINPOOLP512r1: 128 0.00063s 1587.60 0.00064s 1558.83 0.00125s 799.96 0.00281s 355.83
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SECP112r1: 28 0.00009s 11118.66 0.00009s 10775.48 0.00018s 5456.00 0.00033s 3020.83
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SECP112r2: 28 0.00009s 11322.97 0.00009s 10857.71 0.00017s 5748.77 0.00032s 3094.28
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SECP128r1: 32 0.00010s 10078.39 0.00010s 9665.27 0.00019s 5200.58 0.00036s 2760.88
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SECP160r1: 42 0.00015s 6875.51 0.00015s 6647.35 0.00029s 3422.41 0.00057s 1768.35
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Ed25519: 64 0.00030s 3322.56 0.00018s 5568.63 0.00046s 2165.35 0.00153s 654.02
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Ed448: 114 0.00060s 1680.53 0.00039s 2567.40 0.00096s 1036.67 0.00350s 285.62
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ecdh ecdh/s
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NIST192p: 0.00050s 1985.70
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NIST224p: 0.00066s 1524.16
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NIST256p: 0.00071s 1413.07
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NIST384p: 0.00127s 788.89
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NIST521p: 0.00230s 434.85
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SECP256k1: 0.00071s 1409.95
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BRAINPOOLP160r1: 0.00042s 2374.65
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BRAINPOOLP192r1: 0.00051s 1960.01
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BRAINPOOLP224r1: 0.00066s 1518.37
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BRAINPOOLP256r1: 0.00071s 1399.90
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BRAINPOOLP320r1: 0.00100s 997.21
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BRAINPOOLP384r1: 0.00129s 777.51
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BRAINPOOLP512r1: 0.00210s 475.99
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SECP112r1: 0.00022s 4457.70
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SECP112r2: 0.00024s 4252.33
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SECP128r1: 0.00028s 3589.31
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SECP160r1: 0.00043s 2305.02
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```
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(there's also `gmpy` version, execute it using `tox -e speedgmpy`)
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For comparison, a highly optimised implementation (including curve-specific
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assembly for some curves), like the one in OpenSSL 1.1.1d, provides the
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following performance numbers on the same machine.
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Run `openssl speed ecdsa` and `openssl speed ecdh` to reproduce it:
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```
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sign verify sign/s verify/s
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192 bits ecdsa (nistp192) 0.0002s 0.0002s 4785.6 5380.7
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224 bits ecdsa (nistp224) 0.0000s 0.0001s 22475.6 9822.0
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256 bits ecdsa (nistp256) 0.0000s 0.0001s 45069.6 14166.6
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384 bits ecdsa (nistp384) 0.0008s 0.0006s 1265.6 1648.1
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521 bits ecdsa (nistp521) 0.0003s 0.0005s 3753.1 1819.5
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256 bits ecdsa (brainpoolP256r1) 0.0003s 0.0003s 2983.5 3333.2
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384 bits ecdsa (brainpoolP384r1) 0.0008s 0.0007s 1258.8 1528.1
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512 bits ecdsa (brainpoolP512r1) 0.0015s 0.0012s 675.1 860.1
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sign verify sign/s verify/s
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253 bits EdDSA (Ed25519) 0.0000s 0.0001s 28217.9 10897.7
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456 bits EdDSA (Ed448) 0.0003s 0.0005s 3926.5 2147.7
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op op/s
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192 bits ecdh (nistp192) 0.0002s 4853.4
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224 bits ecdh (nistp224) 0.0001s 15252.1
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256 bits ecdh (nistp256) 0.0001s 18436.3
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384 bits ecdh (nistp384) 0.0008s 1292.7
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521 bits ecdh (nistp521) 0.0003s 2884.7
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256 bits ecdh (brainpoolP256r1) 0.0003s 3066.5
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384 bits ecdh (brainpoolP384r1) 0.0008s 1298.0
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512 bits ecdh (brainpoolP512r1) 0.0014s 694.8
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```
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Keys and signature can be serialized in different ways (see Usage, below).
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For a NIST192p key, the three basic representations require strings of the
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following lengths (in bytes):
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to_string: signkey= 24, verifykey= 48, signature=48
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compressed: signkey=n/a, verifykey= 25, signature=n/a
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DER: signkey=106, verifykey= 80, signature=55
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PEM: signkey=278, verifykey=162, (no support for PEM signatures)
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## History
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In 2006, Peter Pearson announced his pure-python implementation of ECDSA in a
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[message to sci.crypt][1], available from his [download site][2]. In 2010,
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Brian Warner wrote a wrapper around this code, to make it a bit easier and
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safer to use. In 2020, Hubert Kario included an implementation of elliptic
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curve cryptography that uses Jacobian coordinates internally, improving
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performance about 20-fold. You are looking at the README for this wrapper.
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[1]: http://www.derkeiler.com/Newsgroups/sci.crypt/2006-01/msg00651.html
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[2]: http://webpages.charter.net/curryfans/peter/downloads.html
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## Testing
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To run the full test suite, do this:
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tox -e coverage
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On an Intel Core i7 4790K @ 4.0GHz, the tests take about 18 seconds to execute.
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The test suite uses
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[`hypothesis`](https://github.com/HypothesisWorks/hypothesis) so there is some
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inherent variability in the test suite execution time.
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One part of `test_pyecdsa.py` and `test_ecdh.py` checks compatibility with
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OpenSSL, by running the "openssl" CLI tool, make sure it's in your `PATH` if
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you want to test compatibility with it (if OpenSSL is missing, too old, or
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doesn't support all the curves supported in upstream releases you will see
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skipped tests in the above `coverage` run).
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## Security
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This library was not designed with security in mind. If you are processing
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data that needs to be protected we suggest you use a quality wrapper around
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OpenSSL. [pyca/cryptography](https://cryptography.io) is one example of such
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a wrapper. The primary use-case of this library is as a portable library for
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interoperability testing and as a teaching tool.
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**This library does not protect against side-channel attacks.**
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Do not allow attackers to measure how long it takes you to generate a key pair
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or sign a message. Do not allow attackers to run code on the same physical
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machine when key pair generation or signing is taking place (this includes
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virtual machines). Do not allow attackers to measure how much power your
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computer uses while generating the key pair or signing a message. Do not allow
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attackers to measure RF interference coming from your computer while generating
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a key pair or signing a message. Note: just loading the private key will cause
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key pair generation. Other operations or attack vectors may also be
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vulnerable to attacks. **For a sophisticated attacker observing just one
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operation with a private key will be sufficient to completely
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reconstruct the private key**.
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Please also note that any Pure-python cryptographic library will be vulnerable
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to the same side-channel attacks. This is because Python does not provide
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side-channel secure primitives (with the exception of
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[`hmac.compare_digest()`][3]), making side-channel secure programming
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impossible.
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This library depends upon a strong source of random numbers. Do not use it on
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a system where `os.urandom()` does not provide cryptographically secure
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random numbers.
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[3]: https://docs.python.org/3/library/hmac.html#hmac.compare_digest
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## Usage
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You start by creating a `SigningKey`. You can use this to sign data, by passing
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in data as a byte string and getting back the signature (also a byte string).
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You can also ask a `SigningKey` to give you the corresponding `VerifyingKey`.
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The `VerifyingKey` can be used to verify a signature, by passing it both the
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data string and the signature byte string: it either returns True or raises
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`BadSignatureError`.
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```python
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from ecdsa import SigningKey
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sk = SigningKey.generate() # uses NIST192p
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vk = sk.verifying_key
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signature = sk.sign(b"message")
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assert vk.verify(signature, b"message")
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```
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Each `SigningKey`/`VerifyingKey` is associated with a specific curve, like
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NIST192p (the default one). Longer curves are more secure, but take longer to
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use, and result in longer keys and signatures.
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```python
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from ecdsa import SigningKey, NIST384p
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sk = SigningKey.generate(curve=NIST384p)
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vk = sk.verifying_key
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signature = sk.sign(b"message")
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assert vk.verify(signature, b"message")
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```
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The `SigningKey` can be serialized into several different formats: the shortest
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is to call `s=sk.to_string()`, and then re-create it with
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`SigningKey.from_string(s, curve)` . This short form does not record the
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curve, so you must be sure to pass to `from_string()` the same curve you used
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for the original key. The short form of a NIST192p-based signing key is just 24
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bytes long. If a point encoding is invalid or it does not lie on the specified
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curve, `from_string()` will raise `MalformedPointError`.
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```python
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from ecdsa import SigningKey, NIST384p
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sk = SigningKey.generate(curve=NIST384p)
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sk_string = sk.to_string()
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sk2 = SigningKey.from_string(sk_string, curve=NIST384p)
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print(sk_string.hex())
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print(sk2.to_string().hex())
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```
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Note: while the methods are called `to_string()` the type they return is
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actually `bytes`, the "string" part is leftover from Python 2.
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`sk.to_pem()` and `sk.to_der()` will serialize the signing key into the same
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formats that OpenSSL uses. The PEM file looks like the familiar ASCII-armored
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`"-----BEGIN EC PRIVATE KEY-----"` base64-encoded format, and the DER format
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is a shorter binary form of the same data.
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`SigningKey.from_pem()/.from_der()` will undo this serialization. These
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formats include the curve name, so you do not need to pass in a curve
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identifier to the deserializer. In case the file is malformed `from_der()`
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and `from_pem()` will raise `UnexpectedDER` or` MalformedPointError`.
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```python
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from ecdsa import SigningKey, NIST384p
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sk = SigningKey.generate(curve=NIST384p)
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sk_pem = sk.to_pem()
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sk2 = SigningKey.from_pem(sk_pem)
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# sk and sk2 are the same key
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```
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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()
|
|
```
|