Skip to content

Commit

Permalink
Merge 6aa9b24 into 5fa2fd8
Browse files Browse the repository at this point in the history
  • Loading branch information
@tomato42
tomato42 committed Oct 19, 2019
2 parents 5fa2fd8 + 6aa9b24 commit 8022fb0
Show file tree
Hide file tree
Showing 2 changed files with 167 additions and 71 deletions.
218 changes: 151 additions & 67 deletions README.md
View file
Original file line number Diff line number Diff line change
Expand Up @@ -15,47 +15,65 @@ into other protocols.
## Features

This library provides key generation, signing, and verifying, for five
popular NIST "Suite B" GF(p) 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 also includes the 256-bit curve used
by Bitcoin, whose short name is secp256k1. No other curves are included, but
it would not be too hard to add more.
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 also includes the
256-bit curve used by Bitcoin, whose short name is `secp256k1`. No other curves
are included, but it would not be 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
implementaions like pypy and pypy3
implementations like pypy and pypy3

To run the OpenSSL compatibility tests, the 'openssl' tool must be on your
$PATH. This release has been tested successfully against both OpenSSL 0.9.8o
and 1.0.0a .
$PATH. This release has been tested successfully against OpenSSL 0.9.8o,
1.0.0a, 1.0.2f and 1.1.1d (among others).

## Speed

The following table shows how long this library takes to generate keypairs
(keygen=), to sign data (sign=), and to verify those signatures (verify=), on
my 2008 Mac laptop. All times are in seconds. It also shows the length of a
signature (in bytes): the verifying ("public") key is typically the same
length as the signature, and the signing ("private") key is half that length.
(`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:

* NIST192p: siglen= 48, keygen=0.160s, sign=0.058s, verify=0.116s
* NIST224p: siglen= 56, keygen=0.230s, sign=0.086s, verify=0.165s
* NIST256p: siglen= 64, keygen=0.305s, sign=0.112s, verify=0.220s
* NIST384p: siglen= 96, keygen=0.801s, sign=0.289s, verify=0.558s
* NIST521p: siglen=132, keygen=1.582s, sign=0.584s, verify=1.152s
```
siglen keygen keygen/s sign sign/s verify verify/s
NIST192p: 48 0.03183s 31.42 0.01127s 88.70 0.02253s 44.39
NIST224p: 56 0.04304s 23.24 0.01548s 64.59 0.03122s 32.03
NIST256p: 64 0.05720s 17.48 0.02055s 48.67 0.04075s 24.54
NIST384p: 96 0.13216s 7.57 0.04696s 21.29 0.09400s 10.64
NIST521p: 132 0.25805s 3.88 0.09329s 10.72 0.18841s 5.31
SECP256k1: 64 0.05677s 17.61 0.02073s 48.23 0.04067s 24.59
```

For comparison, a quality C++ implementation of ECDSA (Crypto++) typically
computes a NIST256p signature in 2.88ms and a verification in 8.53ms, about
30-40x faster.
For comparison, a highly optimised implementation (including curve-specific
assemply) like OpenSSL provides following performance numbers on the same
machine:
```
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
```

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)

Expand All @@ -76,73 +94,103 @@ more for the wrapper. To run them all, do this:

tox -e coverage

On my 2014 Mac Mini, the combined tests take about 20 seconds to run. On a
2.4GHz P4 Linux box, they take 81 seconds.
On an Intel Core i7 4790K@4.0GHz, the combined tests take about 8 minutes to
run.

One component of `test_pyecdsa.py` checks compatibility with OpenSSL, by
running the "openssl" CLI tool. If this tool is not on your $PATH, you may
want to comment out this test (the easiest way is to add a line that says
"del OpenSSL" to the end of test_pyecdsa.py).
running the "openssl" CLI tool, make sure it's in your `PATH` if you want
to test it.

## Security

This library does not protect against timing attacks. Do not allow attackers
to measure how long it takes you to generate a keypair or sign a message.
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 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() is weak.
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 a data string and getting back the signature (also a 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 string: it either returns True or raises BadSignatureError.
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.get_verifying_key()
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
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.get_verifying_key()
signature = sk.sign("message")
assert vk.verify(signature, "message")
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
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 tell from_string() the same curve you used for
curve, so you must be sure to tell `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.
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)
# sk and sk2 are the same key
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.
and `from_pem()` will raise `UnexpectedDER` or` MalformedPointError`.

```python
from ecdsa import SigningKey, NIST384p
Expand All @@ -152,52 +200,53 @@ sk2 = SigningKey.from_pem(sk_pem)
# sk and sk2 are the same key
```

Likewise, the VerifyingKey can be serialized in the same way:
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
`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.get_verifying_key()
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.get_verifying_key()
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
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.
`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
funcions in the "ecdsa.util" module that can be useful here.
functions in the `ecdsa.util` module that can be useful here.

It is also possible to create a SigningKey from a "seed", which is
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
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

Expand All @@ -209,7 +258,9 @@ 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
sk2 = make_key("2-"+seed) # different key
assert sk1a.to_string() == sk1b.to_string()
sk2 = make_key(b"2-"+seed) # different key
assert sk1a.to_string() != sk2.to_string()
```

## OpenSSL Compatibility
Expand All @@ -218,24 +269,57 @@ 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 secp224r1 -genkey -out sk.pem
# openssl ecparam -name prime256v1 -genkey -out sk.pem
# openssl ec -in sk.pem -pubout -out vk.pem
# openssl dgst -ecdsa-with-SHA1 -sign sk.pem -out data.sig data
# openssl dgst -ecdsa-with-SHA1 -verify vk.pem -signature data.sig data
# openssl dgst -ecdsa-with-SHA1 -prverify sk.pem -signature data.sig data
# 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)

sk.sign(msg, hashfunc=hashlib.sha1, sigencode=ecdsa.util.sigencode_der)
vk.verify(sig, msg, hashfunc=hashlib.sha1, sigdecode=ecdsa.util.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
```

The keys that openssl handles can be read and written as follows:
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
sk = SigningKey.from_pem(open("sk.pem").read())
open("sk.pem","w").write(sk.to_pem())
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())

vk = VerifyingKey.from_pem(open("vk.pem").read())
open("vk.pem","w").write(vk.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
Expand Down
20 changes: 16 additions & 4 deletions speed.py
View file
Original file line number Diff line number Diff line change
@@ -1,5 +1,6 @@
import six
import timeit
from ecdsa.curves import curves

def do(setup_statements, statement):
# extracted from timeit.py
Expand All @@ -13,8 +14,17 @@ def do(setup_statements, statement):
break
return x / number

for curve in ["NIST192p", "NIST224p", "NIST256p", "SECP256k1",
"NIST384p", "NIST521p"]:
prnt_form = ("{name:>10}{sep:1} {siglen:>6} {keygen:>9{form}}{unit:1} "
"{keygen_inv:>9{form_inv}} {sign:>9{form}}{unit:1} "
"{sign_inv:>9{form_inv}} {verify:>9{form}}{unit:1} "
"{verify_inv:>9{form_inv}}")

print(prnt_form.format(siglen="siglen", keygen="keygen", keygen_inv="keygen/s",
sign="sign", sign_inv="sign/s", verify="verify",
verify_inv="verify/s", name="", sep="", unit="",
form="", form_inv=""))

for curve in [i.name for i in curves]:
S1 = "import six; from ecdsa import SigningKey, %s" % curve
S2 = "sk = SigningKey.generate(%s)" % curve
S3 = "msg = six.b('msg')"
Expand All @@ -31,5 +41,7 @@ def do(setup_statements, statement):
import ecdsa
c = getattr(ecdsa, curve)
sig = ecdsa.SigningKey.generate(c).sign(six.b("msg"))
print("%9s: siglen=%3d, keygen=%.3fs, sign=%.3fs, verify=%.3fs" \
% (curve, len(sig), keygen, sign, verf))
print(prnt_form.format(
name=curve, sep=":", siglen=len(sig), unit="s", keygen=keygen,
keygen_inv=1.0/keygen, sign=sign, sign_inv=1.0/sign, verify=verf,
verify_inv=1.0/verf, form=".5f", form_inv=".2f"))

0 comments on commit 8022fb0

Please sign in to comment.