Nonce blinding protocol for hardware wallets and airgapped signers

This topic appeared in the list a few times so I would like to discuss it in more detail and maybe push forward to standardization.

We have to accept that any hardware wallet or an air-gapped computer we use to sign transactions can be compromised. It may happen via a supply chain attack or malicious firmware update.

If the signer is isolated (faraday cage, airgap and so on), it still can leak private keys to the outside world by choosing nonces for signatures in a funny way such that the attacker can calculate our private keys. Back in the days, I wrote a small post [1] and a proof-of-concept demo [2] of this attack.

Deterministic nonce generation can be verified only if we have private keys somewhere else. It doubles the attack surface - now we need to maintain two independent signers from different vendors that use the same private key and the same deterministic algorithm for a nonce generation. In addition to that, as Pieter mentioned in the Schnorr-BIP, deterministic nonces are vulnerable to glitch attacks [3].

A simple way to fix it is by forcing the signer to use additional entropy from the host. This protocol takes away the privilege of picking nonce from the signer and doesn't require any secret material outside the signer.

I suggest the following implementation of the protocol for signing a message `m`:

1. Host picks a random number `n` and sends its hash together with the message `m` to the signer. 2. Signer computes a nonce `k` it wants to use for signing. It can be either a deterministic scheme or using RNG. Signer commits to the chosen nonce by sending the corresponding point `R=kG` to the host. 3. Host sends the preimage `n` to the signer 4. Signer tweaks the nonce by this number `k'=k+n`, signs the message and sends back the signature (R',s) 5. Host verifies that the public point in the signature is tweaked by n: `R'==R+nG`

ASCII-art:

   Host                                Untrusted signer
1. Pick random n   --- sha256(n),m -->  calculate nonce k
2.                 <------ R=kG ------  commit to k
3. Send preimage   -------- n ------->  sign with nonce k'=k+n
4. Verify R'==R+nG <------- sig ------

I believe this protocol solves the problem. A drawback of this scheme is that the number of communication rounds doubles, so it might be pretty inconvenient for air-gapped remotely located signers.

I also suggest the following extensions that might be helpful for certain use-cases

# Extensions

## Multiple hosts

There are some use-cases where multiple hosts are involved in the setup and all hosts don't trust each other and the signer. So all of them want to give extra entropy to the signer and verify that it was included. At the moment I have exactly this scenario - our main MCU doesn't trust the proprietary closed-source secure element, and the computer doesn't trust the whole hardware wallet. We need a way to convince both of them that their entropy was used in the nonce.

It can be solved by concatenating hashes and preimages:

Host1 ------- h(n1) --> Host 2 -- h(n1) h(n2) --> Signer
      <--- R+n2 G -----        <------- R -------
      ------- n1 ----->        ------ n1 n2 ----> sign with k''=k+n1+n2
Ver: R''==R'+n1 G       Ver: R''==R+n2 G + n1 G

In this case, the first host doesn't even notice that the second host was also using this protocol and mixing in the entropy. And the signer only needs to add one extra number to the nonce.

## Stateless random signer

If the signer wants to generate a nonce non-deterministically but doesn't have an ability to store a generated nonce it may send back to the host some meta-information that would help it to re-generate the same nonce later. It can be for example additional random data used in a deterministic scheme, either encrypted and authenticated or just as a plain text (I am more a fan of encrypted though).

Generally, the host shouldn't care what this data is about - he just stores the data between rounds and sends it back to the signer with the next round.

# Implementation for PSBT

We can either use proprietary fields [4] or define key-value pairs and add them to the BIP-174. Depends if anyone else is interested in using this protocol or not.

I would suggest the following key-value per-input pairs assuming multiple hosts want to mix in external entropy:

1. Key: {PSBT_IN_EXT_NONCE_HASH}|{pubkey}, Value:
{sha256(n1)}|{sha256(n2)}|...
2. Key: {PSBT_IN_NONCE_COMMITMENT}|{pubkey}, Value: {33-byte R point}
3. Key: {PSBT_IN_NONCE_SIGNER_METADATA}|{pubkey}, Value: {anything}
4. Key: {PSBT_IN_EXT_NONCE_PREIMAGE}|{pubkey}, Value: {n1}|{n2}|...

Then the signature from the signer is placed into existing PSBT_IN_PARTIAL_SIG. Combiner and Finaliser should verify that nonce in the signature includes external entropy and may remove their own entropy from the set. They should also verify that the values of the fields did not change between rounds.

So, list, what do you think? Am I missing something? Would it be interesting to have this protocol standardized and deployed?

# References

[1] https://medium.com/cryptoadvance/hardware-wallets-can-be-hacked-but-this-is-fine-a6156bbd199 [2] https://github.com/stepansnigirev/chosen_nonce_demo/blob/master/HD_key.ipynb [3] https://github.com/bitcoin/bips/blob/master/bip-0340.mediawiki#alternative-signing [4] https://github.com/bitcoin/bips/blob/master/bip-0174.mediawiki#proprietary-use-type

I've been working on developing exactly this for a hardware wallet in working on as well. So far I only had a rough sketch of how the comments would flow. I'd be thrilled to see this standardized.

Thanks much,

--Brandon, sent by an android

-----Original Message----- From: Stepan Snigirev via bitcoin-dev <bitcoin-dev@lists•linuxfoundation•org> To: bitcoin-dev@lists•linuxfoundation•org Sent: Wed, 26 Feb 2020 19:13 Subject: [bitcoin-dev] Nonce blinding protocol for hardware wallets and airgapped signers

This topic appeared in the list a few times so I would like to discuss it in more detail and maybe push forward to standardization.

We have to accept that any hardware wallet or an air-gapped computer we use to sign transactions can be compromised. It may happen via a supply chain attack or malicious firmware update.

If the signer is isolated (faraday cage, airgap and so on), it still can leak private keys to the outside world by choosing nonces for signatures in a funny way such that the attacker can calculate our private keys. Back in the days, I wrote a small post [1] and a proof-of-concept demo [2] of this attack.

Deterministic nonce generation can be verified only if we have private keys somewhere else. It doubles the attack surface - now we need to maintain two independent signers from different vendors that use the same private key and the same deterministic algorithm for a nonce generation. In addition to that, as Pieter mentioned in the Schnorr-BIP, deterministic nonces are vulnerable to glitch attacks [3].

A simple way to fix it is by forcing the signer to use additional entropy from the host. This protocol takes away the privilege of picking nonce from the signer and doesn't require any secret material outside the signer.

I suggest the following implementation of the protocol for signing a message `m`:

1. Host picks a random number `n` and sends its hash together with the message `m` to the signer. 2. Signer computes a nonce `k` it wants to use for signing. It can be either a deterministic scheme or using RNG. Signer commits to the chosen nonce by sending the corresponding point `R=kG` to the host. 3. Host sends the preimage `n` to the signer 4. Signer tweaks the nonce by this number `k'=k+n`, signs the message and sends back the signature (R',s) 5. Host verifies that the public point in the signature is tweaked by n: `R'==R+nG`

ASCII-art:

   Host                                Untrusted signer
1. Pick random n   --- sha256(n),m -->  calculate nonce k
2.                 <------ R=kG ------  commit to k
3. Send preimage   -------- n ------->  sign with nonce k'=k+n
4. Verify R'==R+nG <------- sig ------

I believe this protocol solves the problem. A drawback of this scheme is that the number of communication rounds doubles, so it might be pretty inconvenient for air-gapped remotely located signers.

I also suggest the following extensions that might be helpful for certain use-cases

# Extensions

## Multiple hosts

There are some use-cases where multiple hosts are involved in the setup and all hosts don't trust each other and the signer. So all of them want to give extra entropy to the signer and verify that it was included. At the moment I have exactly this scenario - our main MCU doesn't trust the proprietary closed-source secure element, and the computer doesn't trust the whole hardware wallet. We need a way to convince both of them that their entropy was used in the nonce.

It can be solved by concatenating hashes and preimages:

Host1 ------- h(n1) --> Host 2 -- h(n1) h(n2) --> Signer
      <--- R+n2 G -----        <------- R -------
      ------- n1 ----->        ------ n1 n2 ----> sign with k''=k+n1+n2
Ver: R''==R'+n1 G       Ver: R''==R+n2 G + n1 G

In this case, the first host doesn't even notice that the second host was also using this protocol and mixing in the entropy. And the signer only needs to add one extra number to the nonce.

## Stateless random signer

If the signer wants to generate a nonce non-deterministically but doesn't have an ability to store a generated nonce it may send back to the host some meta-information that would help it to re-generate the same nonce later. It can be for example additional random data used in a deterministic scheme, either encrypted and authenticated or just as a plain text (I am more a fan of encrypted though).

Generally, the host shouldn't care what this data is about - he just stores the data between rounds and sends it back to the signer with the next round.

# Implementation for PSBT

We can either use proprietary fields [4] or define key-value pairs and add them to the BIP-174. Depends if anyone else is interested in using this protocol or not.

I would suggest the following key-value per-input pairs assuming multiple hosts want to mix in external entropy:

1. Key: {PSBT_IN_EXT_NONCE_HASH}|{pubkey}, Value:
{sha256(n1)}|{sha256(n2)}|...
2. Key: {PSBT_IN_NONCE_COMMITMENT}|{pubkey}, Value: {33-byte R point}
3. Key: {PSBT_IN_NONCE_SIGNER_METADATA}|{pubkey}, Value: {anything}
4. Key: {PSBT_IN_EXT_NONCE_PREIMAGE}|{pubkey}, Value: {n1}|{n2}|...

Then the signature from the signer is placed into existing PSBT_IN_PARTIAL_SIG. Combiner and Finaliser should verify that nonce in the signature includes external entropy and may remove their own entropy from the set. They should also verify that the values of the fields did not change between rounds.

So, list, what do you think? Am I missing something? Would it be interesting to have this protocol standardized and deployed?

# References

[1] https://medium.com/cryptoadvance/hardware-wallets-can-be-hacked-but-this-is-fine-a6156bbd199 [2] https://github.com/stepansnigirev/chosen_nonce_demo/blob/master/HD_key.ipynb [3] https://github.com/bitcoin/bips/blob/master/bip-0340.mediawiki#alternative-signing [4] https://github.com/bitcoin/bips/blob/master/bip-0174.mediawiki#proprietary-use-type

Good morning Stepan,

> This topic appeared in the list a few times so I would like to discuss it in more detail and maybe push forward to standardization.
>
> We have to accept that any hardware wallet or an air-gapped computer we use to sign transactions can be compromised. It may happen via a supply chain attack or malicious firmware update.
>
> If the signer is isolated (faraday cage, airgap and so on), it still can leak private keys to the outside world by choosing nonces for signatures in a funny way such that the attacker can calculate our private keys. Back in the days, I wrote a small post [1] and a proof-of-concept demo [2] of this attack.
>
> Deterministic nonce generation can be verified only if we have private keys somewhere else. It doubles the attack surface - now we need to maintain two independent signers from different vendors that use the same private key and the same deterministic algorithm for a nonce generation. In addition to that, as Pieter mentioned in the Schnorr-BIP, deterministic nonces are vulnerable to glitch attacks [3].
>
> A simple way to fix it is by forcing the signer to use additional entropy from the host. This protocol takes away the privilege of picking nonce from the signer and doesn't require any secret material outside the signer.
>
> I suggest the following implementation of the protocol for signing a message `m`:
>
> 1. Host picks a random number `n` and sends its hash together with the message `m` to the signer.
> 2. Signer computes a nonce `k` it wants to use for signing. It can be either a deterministic scheme or using RNG. Signer commits to the chosen nonce by sending the corresponding point `R=kG` to the host.

I think it would be unsafe to use a deterministic scheme, that takes as input the message m and the privkey only.

Let us consider the case where the hardware signer has its power supply coming from USB and the communication channel is over USB as well. Thus, the host can selectively turn on/off the hardware signer (e.g. a hacker with physical access can just unplug it).

With R determined from m and the privkey, then the host knows the R that the signer will use, and can arrange an n that cancels that R and adds a specific R it wants to target. It could, for example, arrange to have two different `m` signed with the same `R'`.

What would have to be done would be derive `k` from the message `m` plus the `sha256(n)` and the privkey. Perhaps you considered this already, but it may be useful to have it explicitly stated that this has to be mixed as well, i.e. if `k` is generated deterministically it has to be `k = f(sha256(n), m, privkey)` where `f()` is some suitable hashing function.

Otherwise a completely-random `k` would be much better, but the signer might not have enough resources to gather sufficient entropy.

Regards, ZmnSCPxj

Dear ZmnSCPxj,

> I think it would be unsafe to use a deterministic scheme, that takes as

input the message m and the privkey only.

Yes, using only the message and the private key is unsafe. Signer should use all the data coming from the host, so f(sha256(n), m, privkey) is a good candidate. If more than one blinding factor is sent - all of them should be used as well.

> Otherwise a completely-random `k` would be much better, but the signer

might not have enough resources to gather sufficient entropy.

I am not a big fan of pure RNG-generated nonces, so I would suggest to use this entropy only as additional data for a deterministic scheme. For example, Yubikey had a problem with RNG initialization that caused leakage of the private key [1]. If the signer has any source of entropy, even if it is not a very good one, the entropy from this source can be mixed into the nonce generation function: f(sha256(n),m,privkey,entropy).

Another issue is that deterministic nonce generation is vulnerable to glitch attacks - if I ask the wallet to sign the same message twice but after nonce generation I glitch and flip a bit in the message, I will get two signatures with the same nonce but with different messages - from these signatures I can calculate the private key. So I would recommend to include a monotonic counter into the nonce generation function as well: f(sha256(n), m, privkey, entropy, counter) As usual, counter should be increased _before_ signing.

Ref: [1] https://www.yubico.com/support/security-advisories/ysa-2019-02/#technical-details

Best, Stepan

Thanks for starting this initiative; it has been a long standing goal of mine to implement and release this protocol. Your blog post on the topic actually inspired me to pick up this work again a few months ago.

Jonas Nick has implemented the protocol in the secp256k1 library for Schnorr sigs here: https://github.com/bitcoin-core/secp256k1/pull/590

I have backported the same scheme to ECDSA in the secp256k1 library here, so it can be used also for current transactions:

https://github.com/bitcoin-core/secp256k1/pull/669

I also made proof of concepts for the BitBox02 hw wallet firmware and BitBoxApp wallet to verify that the protocol also works well in practice.

The actual scheme used in those implementations is a generalized sign-to-contract scheme, where the final nonce is computed as `k' = k + H(k*G, n)` instead of `k'=k+n`, but otherwise it works mostly the same for the anti nonce covert channel protocol. I suggest to use this scheme in PSBT as well.

> We can either use proprietary fields [4] or define key-value pairs and add
> them to the BIP-174. Depends if anyone else is interested in using this
> protocol or not.

I'd definitely be interested in seeing widespread support for this, and standardizing it would help with that.

With PSBT used with an air-gapped signer, there is increased danger in implementing the protocol wrongly by relying on the contents of the PSBT alone in the final verification step of a signature. The PSBT must be verified carefully against state stored by the host for the PSBT. Otherwise the signer can for example change or pre-fill the relevant NONCE fields and leak the private keys anyway. Is there a current best practice for how a PSBT can be identified by the host to store/retrieve the state?

Are there other examples in PSBT where the host can't trust the contents of the PSBT the signer returns (except of course for the parts the user can verify themselves, like recipients, amounts, etc.)? In any case, guidelines or conventions on how to avoid the pitfalls would be good.

Best, Marko

+1 love that progress is being made on this. Excited to implement it once it’s ready.

Would love if things like the incrementing number were included in the standard as well.

Cheers! 🍻

On Fri, Feb 28, 2020 at 9:51 AM Marko via bitcoin-dev < bitcoin-dev@lists•linuxfoundation•org> wrote:

> Thanks for starting this initiative; it has been a long standing goal of
> mine to implement and release this protocol. Your blog post on the topic
> actually inspired me to pick up this work again a few months ago.
>
> Jonas Nick has implemented the protocol in the secp256k1 library for
> Schnorr sigs here: https://github.com/bitcoin-core/secp256k1/pull/590
>
> I have backported the same scheme to ECDSA in the secp256k1 library
> here, so it can be used also for current transactions:
>
> https://github.com/bitcoin-core/secp256k1/pull/669
>
> I also made proof of concepts for the BitBox02 hw wallet firmware and
> BitBoxApp wallet to verify that the protocol also works well in practice.
>
> The actual scheme used in those implementations is a generalized
> sign-to-contract scheme, where the final nonce is computed as `k' = k +
> H(k*G, n)` instead of `k'=k+n`, but otherwise it works mostly the same
> for the anti nonce covert channel protocol. I suggest to use this scheme
> in PSBT as well.
>
> > We can either use proprietary fields [4] or define key-value pairs and
> add
> > them to the BIP-174. Depends if anyone else is interested in using this
> > protocol or not.
>
> I'd definitely be interested in seeing widespread support for this, and
> standardizing it would help with that.
>
> With PSBT used with an air-gapped signer, there is increased danger in
> implementing the protocol wrongly by relying on the contents of the PSBT
> alone in the final verification step of a signature. The PSBT must be
> verified carefully against state stored by the host for the PSBT.
> Otherwise the signer can for example change or pre-fill the relevant
> NONCE fields and leak the private keys anyway. Is there a current best
> practice for how a PSBT can be identified by the host to store/retrieve
> the state?
>
> Are there other examples in PSBT where the host can't trust the contents
> of the PSBT the signer returns (except of course for the parts the user
> can verify themselves, like recipients, amounts, etc.)? In any case,
> guidelines or conventions on how to avoid the pitfalls would be good.
>
> Best, Marko
>
> _______________________________________________
> bitcoin-dev mailing list
> bitcoin-dev@lists•linuxfoundation•org
> https://lists.linuxfoundation.org/mailman/listinfo/bitcoin-dev
>

Stepan have you spent any time considering a scheme that could involve HD keys, preregistering n (ie. 1000) preimages, or something similar to reduce the number of rounds at time of signing?

Would a zero knowledge solution allow for a reduction in rounds?

On Wed, Feb 26, 2020 at 7:13 PM Stepan Snigirev via bitcoin-dev < bitcoin-dev@lists•linuxfoundation•org> wrote:

> This topic appeared in the list a few times so I would like to discuss it
> in more detail and maybe push forward to standardization.
>
> We have to accept that any hardware wallet or an air-gapped computer we
> use to sign transactions can be compromised. It may happen via a supply
> chain attack or malicious firmware update.
>
> If the signer is isolated (faraday cage, airgap and so on), it still can
> leak private keys to the outside world by choosing nonces for signatures in
> a funny way such that the attacker can calculate our private keys. Back in
> the days, I wrote a small post [1] and a proof-of-concept demo [2] of this
> attack.
>
> Deterministic nonce generation can be verified only if we have private
> keys somewhere else. It doubles the attack surface - now we need to
> maintain two independent signers from different vendors that use the same
> private key and the same deterministic algorithm for a nonce generation. In
> addition to that, as Pieter mentioned in the Schnorr-BIP, deterministic
> nonces are vulnerable to glitch attacks [3].
>
> A simple way to fix it is by forcing the signer to use additional entropy
> from the host. This protocol takes away the privilege of picking nonce from
> the signer and doesn't require any secret material outside the signer.
>
> I suggest the following implementation of the protocol for signing a
> message `m`:
>
> 1. Host picks a random number `n` and sends its hash together with the
> message `m` to the signer.
> 2. Signer computes a nonce `k` it wants to use for signing. It can be
> either a deterministic scheme or using RNG. Signer commits to the chosen
> nonce by sending the corresponding point `R=kG` to the host.
> 3. Host sends the preimage `n` to the signer
> 4. Signer tweaks the nonce by this number `k'=k+n`, signs the message and
> sends back the signature (R',s)
> 5. Host verifies that the public point in the signature is tweaked by n:
> `R'==R+nG`
>
> ASCII-art:
>
>    Host                                Untrusted signer
> 1. Pick random n   --- sha256(n),m -->  calculate nonce k
> 2.                 <------ R=kG ------  commit to k
> 3. Send preimage   -------- n ------->  sign with nonce k'=k+n
> 4. Verify R'==R+nG <------- sig ------
>
> I believe this protocol solves the problem. A drawback of this scheme is
> that the number of communication rounds doubles, so it might be pretty
> inconvenient for air-gapped remotely located signers.
>
> I also suggest the following extensions that might be helpful for certain
> use-cases
>
> # Extensions
>
> ## Multiple hosts
>
> There are some use-cases where multiple hosts are involved in the setup
> and all hosts don't trust each other and the signer. So all of them want to
> give extra entropy to the signer and verify that it was included. At the
> moment I have exactly this scenario - our main MCU doesn't trust the
> proprietary closed-source secure element, and the computer doesn't trust
> the whole hardware wallet. We need a way to convince both of them that
> their entropy was used in the nonce.
>
> It can be solved by concatenating hashes and preimages:
>
> Host1 ------- h(n1) --> Host 2 -- h(n1) h(n2) --> Signer
>       <--- R+n2 G -----        <------- R -------
>       ------- n1 ----->        ------ n1 n2 ----> sign with k''=k+n1+n2
> Ver: R''==R'+n1 G       Ver: R''==R+n2 G + n1 G
>
> In this case, the first host doesn't even notice that the second host was
> also using this protocol and mixing in the entropy. And the signer only
> needs to add one extra number to the nonce.
>
> ## Stateless random signer
>
> If the signer wants to generate a nonce non-deterministically but doesn't
> have an ability to store a generated nonce it may send back to the host
> some meta-information that would help it to re-generate the same nonce
> later. It can be for example additional random data used in a deterministic
> scheme, either encrypted and authenticated or just as a plain text (I am
> more a fan of encrypted though).
>
> Generally, the host shouldn't care what this data is about - he just
> stores the data between rounds and sends it back to the signer with the
> next round.
>
> # Implementation for PSBT
>
> We can either use proprietary fields [4] or define key-value pairs and add
> them to the BIP-174. Depends if anyone else is interested in using this
> protocol or not.
>
> I would suggest the following key-value per-input pairs assuming multiple
> hosts want to mix in external entropy:
>
> 1. Key: {PSBT_IN_EXT_NONCE_HASH}|{pubkey}, Value:
> {sha256(n1)}|{sha256(n2)}|...
> 2. Key: {PSBT_IN_NONCE_COMMITMENT}|{pubkey}, Value: {33-byte R point}
> 3. Key: {PSBT_IN_NONCE_SIGNER_METADATA}|{pubkey}, Value: {anything}
> 4. Key: {PSBT_IN_EXT_NONCE_PREIMAGE}|{pubkey}, Value: {n1}|{n2}|...
>
> Then the signature from the signer is placed into existing
> PSBT_IN_PARTIAL_SIG. Combiner and Finaliser should verify that nonce in the
> signature includes external entropy and may remove their own entropy from
> the set. They should also verify that the values of the fields did not
> change between rounds.
>
> So, list, what do you think? Am I missing something? Would it be
> interesting to have this protocol standardized and deployed?
>
> # References
>
> [1]
> https://medium.com/cryptoadvance/hardware-wallets-can-be-hacked-but-this-is-fine-a6156bbd199
> [2]
> https://github.com/stepansnigirev/chosen_nonce_demo/blob/master/HD_key.ipynb
> [3]
> https://github.com/bitcoin/bips/blob/master/bip-0340.mediawiki#alternative-signing
> [4]
> https://github.com/bitcoin/bips/blob/master/bip-0174.mediawiki#proprietary-use-type
> _______________________________________________
> bitcoin-dev mailing list
> bitcoin-dev@lists•linuxfoundation•org
> https://lists.linuxfoundation.org/mailman/listinfo/bitcoin-dev
>