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https://github.com/tintinweb/ecdsa-private-key-recovery
A simple library to recover the private key of ECDSA and DSA signatures sharing the same nonce k and therefore having identical signature parameter r
https://github.com/tintinweb/ecdsa-private-key-recovery
bitcoin blockchain dsa ecdsa litecoin recovery
Last synced: 6 days ago
JSON representation
A simple library to recover the private key of ECDSA and DSA signatures sharing the same nonce k and therefore having identical signature parameter r
- Host: GitHub
- URL: https://github.com/tintinweb/ecdsa-private-key-recovery
- Owner: tintinweb
- License: gpl-2.0
- Created: 2017-07-20T22:17:56.000Z (over 7 years ago)
- Default Branch: master
- Last Pushed: 2022-02-16T16:31:07.000Z (almost 3 years ago)
- Last Synced: 2025-01-06T03:08:54.360Z (13 days ago)
- Topics: bitcoin, blockchain, dsa, ecdsa, litecoin, recovery
- Language: Python
- Homepage:
- Size: 38.1 KB
- Stars: 410
- Watchers: 27
- Forks: 128
- Open Issues: 3
-
Metadata Files:
- Readme: README.md
- License: LICENSE
Awesome Lists containing this project
- awesome-hacking-lists - tintinweb/ecdsa-private-key-recovery - A simple library to recover the private key of ECDSA and DSA signatures sharing the same nonce k and therefore having identical signature parameter r (Python)
README
# ecdsa-key-recovery
Perform ECDSA and DSA Nonce Reuse private key recovery attacks
###### This is kind of an improved version of the DSA only variant from https://github.com/tintinweb/DSAregenK
Let's recover the private-key for two signatures sharing the same `nonce k`. Note how choosing the same `nonce k` results in both signatures having an identical signature value `r`. To find good candidates for an ECDSA nonce reuse check for signatures sharing the same `r`, `pubkey` on `curve` for different messages (or hashes). E.g. blockchain projects based off `bitcoind` are usually good sources of ECDSA signature material.
* **sampleA** (**r**, *sA, hashA*, pubkey, curve)
* **sampleB** (**r**, *sB, hashB*, pubkey, curve)
```python
sampleA = EcDsaSignature(r, sA, hashA, pubkey, curve)
sampleB = EcDsaSignature(r, sB, hashB, pubkey, curve) # same privkey as sampleA, identical r due to nonce reuse k.
# recover the private key
sampleA.recover_nonce_reuse(sampleB) # populates sampleA with the recovered private key ready for use
print sampleA.privkey
```
#### setup
Python 2.x:
```
#> virtualenv -p python2.7 .env27
#> . .env27/bin/activate
(.env27) #> python -m pip install -r requirements.txt
(.env27) #> python setup.py install
(.env27) #> python tests/test_ecdsa_key_recovery.py
```
Python 3.x:
```
#> virtualenv -p python3 .env3
#> . .env3/bin/activate
(.env3) #> python -m pip install -r requirements.txt
(.env3) #> python setup.py install
(.env3) #> python tests/test_ecdsa_key_recovery.py
```
#### Recovering Private Keys from the Bitcoin Blockchain
[tools/README.md](tools/README.md)
| BTC Address | Base58 Privkey | r|
| ------------- | ------------- | -------------|
| 1A8TY7dxURcsRtPBs7fP6bDVzAgpgP4962 |5JsYaHVGCUzuXaQ5VkaA21VFPJFuArRWfSB77sqzWkWuTMMjXsT | 113563387324078878147267949860139475116142082788494055785668341901521289846519 |
| 1A8TY7dxURcsRtPBs7fP6bDVzAgpgP4962 | 5JsYaHVGCUzuXaQ5VkaA21VFPJFuArRWfSB77sqzWkWuTMMjXsT | 18380471981355278106073484610981598768079378179376623360720556873242139981984|
|1C8x2hqqgE2b3TZPQcFgas73xYWNh6TK9W|5JKkG6KXLCCPXN9m29ype6My7eR4AnCLaHKYrLvn6d3nd8BLjjw| 19682383735358733565748628081379024202682929012377912380310432818686294127462|
|1A8TY7dxURcsRtPBs7fP6bDVzAgpgP4962|5JsYaHVGCUzuXaQ5VkaA21VFPJFuArRWfSB77sqzWkWuTMMjXsT|6828441658514710620715231245132541628903431519484374098968817647395811175535|
### Example
create recoverable signature objects:
```python
from ecdsa_key_recovery import DsaSignature, EcDsaSignature, ecdsa, bignum_to_hex, bytes_fromhex
# specify curve
curve = ecdsa.SECP256k1
# create standard ecdsa pubkey object from hex-encoded string
pub = ecdsa.VerifyingKey.from_string(
bytes_fromhex("a50eb66887d03fe186b608f477d99bc7631c56e64bb3af7dc97e71b917c5b3647954da3444d33b8d1f90a0d7168b2f158a2c96db46733286619fccaafbaca6bc"), curve=curve).pubkey
# create sampleA and sampleB recoverable signature objects.
# long r, long s, bytestr hash, pubkey obj.
sampleA = EcDsaSignature((3791300999159503489677918361931161866594575396347524089635269728181147153565, #r
49278124892733989732191499899232294894006923837369646645433456321810805698952), #s
bytes_fromhex(bignum_to_hex(
765305792208265383632692154455217324493836948492122104105982244897804317926)),
pub)
sampleB = EcDsaSignature((3791300999159503489677918361931161866594575396347524089635269728181147153565, #r
34219161137924321997544914393542829576622483871868414202725846673961120333282), #s'
bytes_fromhex(bignum_to_hex(
23350593486085962838556474743103510803442242293209938584974526279226240784097)),
pub)
# key not yet recovered
assert (sampleA.x is None)
```
recover the private key for **sampleA**
```python
# attempt to recover key - this updated object sampleA
sampleA.recover_nonce_reuse(sampleB) # recover privatekey shared with sampleB
assert (sampleA.x is not None) # assert privkey recovery succeeded. This gives us a ready to use ECDSA privkey object
assert sampleA.privkey
```
#### output
```
INFO:__main__:------------EcDSA------------
DEBUG:__main__: - recovering private-key from nonce reuse ...
DEBUG:__main__: - Private key recovered!
-----BEGIN EC PRIVATE KEY-----
MHQCAQEEIOdzzzX85WfQYiIDwo9nR4ozYbrn5utDZrUOHSfrHtguoAcGBSuBBAAK
oUQDQgAEpQ62aIfQP+GGtgj0d9mbx2McVuZLs699yX5xuRfFs2R5VNo0RNM7jR+Q
oNcWiy8ViiyW20ZzMoZhn8yq+6ymvA==
-----END EC PRIVATE KEY-----
DEBUG:__main__: - recovering private-key from nonce reuse ...
DEBUG:__main__: - Private key recovered!
-----BEGIN EC PRIVATE KEY-----
MHQCAQEEIOdzzzX85WfQYiIDwo9nR4ozYbrn5utDZrUOHSfrHtguoAcGBSuBBAAK
oUQDQgAEpQ62aIfQP+GGtgj0d9mbx2McVuZLs699yX5xuRfFs2R5VNo0RNM7jR+Q
oNcWiy8ViiyW20ZzMoZhn8yq+6ymvA==
-----END EC PRIVATE KEY-----
INFO:__main__:------------DSA------------
DEBUG:__main__:generated sample signatures: (('\x96.\xed\x06?Tx\x87\x96\xc0Jxe\xc1\xb7\xa0}\xbaSl', (962114315288785318297754502373467834746102876259L, 152066227943132308247866282041325280216845090990L), <_DSAobj @0x2c49a80 y,g,p(1024),q>), ('\xf2\x9a\x9a\x81\xa8\x1b\x071Z1\xe28\xd3\x993\xff\xc7[b\xab', (962114315288785318297754502373467834746102876259L, 357089477795349418794190243474458899186606359757L), <_DSAobj @0x2c788f0 y,g,p(1024),q>))
DEBUG:__main__:Signature Objects: [, ]
DEBUG:__main__: - recovering privatekey from nonce reuse...
DEBUG:__main__: - Private key recovered!
-----BEGIN PRIVATE KEY-----
MIIBSgIBADCCASsGByqGSM44BAEwggEeAoGBAIAAAAAAAAAA8tZboZpqrRAwKtK0
mXxwct7Es1BBih3HheeLBMOHCqPlwJmfUA8kBZQZzu3V+at5IWlRi0fTikvNWuqN
GLqMkf0kqXOhzP8/hD7B/CUF1YedzGKqC2BfhX/RON+CD/mFi35As8G73O29GCUl
qMd0KYhHHtBvVPiLAhUA/5r9a94k/9/mHVub1U0WrAJv2B8CgYARyESPcKSpBEoT
nXlMrX1M71RySJL5nrqUKpFTFRSoIwX5sj7ZRfKSqbf2umwSu8LfCEOZ2qKu0+jp
+bUC0oihSjaVCrADZykPr67k9mt56xx1wP4vUJJNfM3Wkty5xsI3JtUFbQ5EzFAt
JhLRWxOqcGEm35ZPQ4ao1qZsIsSVCQQWAhRqVNUTHGUaRRA5lXlmN4sw9glosQ==
-----END PRIVATE KEY-----
DEBUG:__main__:generated sample signatures: (('\x96.\xed\x06?Tx\x87\x96\xc0Jxe\xc1\xb7\xa0}\xbaSl', (921214889680762780870505834724573810649257487648L, 1206590109737383111438209532388130932310558452933L), <_DSAobj @0x2c78cd8 y,g,p(1024),q>), ('\xf2\x9a\x9a\x81\xa8\x1b\x071Z1\xe28\xd3\x993\xff\xc7[b\xab', (921214889680762780870505834724573810649257487648L, 254170456806936279470958328275930254179957847437L), <_DSAobj @0x2c788f0 y,g,p(1024),q>))
DEBUG:__main__:Signature Objects: [, ]
DEBUG:__main__: - recovering privatekey from nonce reuse...
DEBUG:__main__: - Private key recovered!
-----BEGIN PRIVATE KEY-----
MIIBSwIBADCCASsGByqGSM44BAEwggEeAoGBAIAAAAAAAAAARApDBH1CEeZPeIM9
mMb6l3FyY8+AOy+cdiDzCaqlkIRVIRRxvnCH5oJ6gkinosGscZMTgF7IwQJzDHFm
oxvVdpACrj5Je+kpF6djefAbe+ByZ4FowkGq1EdMZF8aZzsik3CFkEA/vDsjvAsg
XmKRvOnFHkkFuKCRAhUA/+rcmBQ71NBsDzkbusi6NQpTNF8CgYAFVt8xSXTiCGn8
+bqWyoX+gjItArrT28o6fGnq+apjwasvWDHq1FETk/gwqTbTwWTiMo2eOTImRKDF
MbK1us+DjhloAUuhL6nCRQhsLs4Jq+8A/y7aol/HjCz1fHRKKDD9wqKDf2kWdI97
Kb2Hq4AUoJWTCT0ijX+oQJafbywjdwQXAhUAniK/kyRv/SFd1uJjuDMh0EntMws=
-----END PRIVATE KEY-----
```
The library is written in a way that it tries to upgrade `pubkey only ecdsa objects` to `private key enabled ecdsa objects` upon successful recovery. This makes it easy to work with recovered key objects. The library performs both **ECDSA** and **DSA** key recovery.