exploiting ecdsa failures in the bitcoin blockchain - filip… · a signed statement, published to...
TRANSCRIPT
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Filippo Valsorda
Exploiting ECDSA Failures in the
Bitcoin Blockchain
HITB2014KUL
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CloudFlare security team @FiloSottile
I mess with cryptography. And open source.
!
filippo.io
Filippo Valsorda
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But you probably know me for this
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https://filippo.io/heartbleed
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Bitcoin
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Public key + Private key
A wallet
The address: hash ( public key )1DY5YvRxSwomrK7nELDZzAidQQ6ktjRR9A
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A signed statement, published to the world
and recorded in the blockchain
A transaction
“This money I can spend, can now be spent by Y”
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A: This money I can spend, can now be spent by X…: This money I can spend, can now be spent by ……: This money I can spend, can now be spent by …
…: This money I can spend, can now be spent by …X: This money I can spend, can now be spent by Y
…: This money I can spend, can now be spent by ……: This money I can spend, can now be spent by …
Y has this money to spend
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A: This money I can spend, can now be spent by X
Signed with A’s private key
Hash of X’s public key
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OP_DUP OP_HASH160 <pubKeyHash> OP_EQUALVERIFY OP_CHECKSIG
<sig> <pubKey>
Actually
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ECDSA
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A EC based signature scheme
As seen in TLS, DNSSEc, the PS3…
Elliptic Curve Digital Signature Algorithm
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Global: point G on a curve Private key: a random number d
Public key: d X G
A summary
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e = hash(message) k = a random number
(x, y) = k X G r = x
Signature
Sig: [r,(e+r*d)/k]
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Unless…
Seems fine, right?
What happens if that k is not random?
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k1 = k2 (x, y) = k X G r = x
r1 = r2
If you reuse k
Sig1: [r,(e1+r*d)/k] Sig2: [r,(e2+r*d)/k]
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If you reuse k
Sig1: [ r ,(e1+r*d)/k] Sig2: [ r ,(e2+r*d)/k]
k1 = k2 (x, y) = k X G r = x
r1 = r2
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If you reuse k
Sig1: [r, (e1+r*d)/k ] Sig2: [r, (e2+r*d)/k ]
k1 = k2 (x, y) = k X G r = x
r1 = r2
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k = (e1 - e2)/ (e1+r*d)/k - (e2+r*d)/k]
If you reuse k
d = [(e1+r*d)/k]*k-e1 r
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Boom.
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Text Text Text Text Text Text Text Text Text
Imperialviolet
Accent Accent Accent
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Text Text Text Text Text Text Text Text Text
Sony’s ECDSA code
Mittwoch, 29. Dezember 2010
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the
blockchain
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To spend money: the public key of the address;
a signature w/ that key
Reminder
when money is moved a signature is published
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for block in chain: for tx in block: for input in tx: ...
An easy search
A input is money being spent in the tx
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Extract r from the signature; take note of where we found
it in a lookup table; check if we found it before.
An easy search
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Done!If anyone reuses k,
we will find two equal r.
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Well… No. I mean, yes, but there are
100M inputs in the blockchain.
Done!
Out of memory! :(
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First pass: filter the possible r. Add to a Bloom filter, if present add to a set.
!
Second pass: if r present in the set, export sig and pubkey.
A smarter search
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A smarter search
r = 42 r = 42
Bloom filter+ Blockchain
Set
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A smarter searchBloom filter
? Blockchain
42
✓
r = 42 r = 42
+
Set
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A smarter search
? ✓
Final list Sig, Pubkey, Tx…
r = 42 r = 42
42
Set
1936Blockchain
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Group the list by (r, pubkey) and recover d
from pairs of signatures!
Finally
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A ready to use toolBlockchainr
github.com/filosottile/blockchainr
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Results
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https://filippo.io/hitb
If you want to follow from home
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Does this happen?
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Yes.
Does this happen?
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Vertical: address Color: r
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weird Multisignature transactions
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1KtjBE8yDxoqNTSyLG2re4qtKK19KpvVLT 1BkE8ttBRUKVNTj3Lx1EPsw7vVbhuLZhBt
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Vertical: address Color: r
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“gomez” 1GozmcsMBC7bnMVUQLTKEw5vBxbSeG4erW / 1HKywxiL4JziqXrzLKhmB6a74ma6kxbSDj
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Repeated r in the same transaction
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https://bitcointalk.org/index.php?topic=271486
“Bad signatures leading to 55.82152538 BTC theft (so far)”
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https://bitcointalk.org/index.php?topic=277595
Blockchain.info security [FUNDS STOLEN]
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Text Text Text Text Text Text Text Text Text
TEXT TEXT TEXT TEXT
Accent Accent Accent
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Nick sullivan “exploiting randomness” demo
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The fix
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k must be secret and unique
What’s needed
Not necessarily random
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Generate k deterministically, as a function of private key
and message.
RFC 6979
k = HMAC_DRBG ( d, H (m) )
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Bitcoin core
unsafe: openssl patch by AGL waiting on master
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electrum
safe since v1.9 correct use of python-ecdsa
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Multibit / bitcoinj
safe correct use of bouncycastle
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Blockchain.info
Unsafe relies on the browser RNG (if any!)
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bitrated / bitcoinjs-lib
Safe Hashes privkey, message and random
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Armory
unsafe (? - 90%) crypto++ seems to use a random value
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Trezor
Safe Implements RFC 6979
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Q&A
@filosottile filippo.io/hitb-slides