Date: Fri, 28 Feb 2020 13:31:29 +0000
To: Stepan Snigirev <snigirev.stepan@gmail.com>,
 Bitcoin Protocol Discussion <bitcoin-dev@lists.linuxfoundation.org>
From: ZmnSCPxj <ZmnSCPxj@protonmail.com>
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Subject: Re: [bitcoin-dev] Nonce blinding protocol for hardware wallets and
	airgapped signers
Precedence: list

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 u=
se to sign transactions can be compromised. It may happen via a supply chai=
n 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 ke=
ys somewhere else. It doubles the attack surface - now we need to maintain =
two independent signers from different vendors that use the same private ke=
y and the same deterministic algorithm for a nonce generation. In addition =
to that, as Pieter mentioned in the Schnorr-BIP, deterministic nonces are v=
ulnerable 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 fro=
m the signer and doesn't require any secret material outside the signer.
>
> I suggest the following implementation of the protocol for signing a mess=
age `m`:
>
> 1. Host picks a random number `n` and sends its hash together with the me=
ssage `m` to the signer.
> 2. Signer computes a nonce `k` it wants to use for signing. It can be eit=
her a deterministic scheme or using RNG. Signer commits to the chosen nonce=
 by sending the corresponding point `R=3DkG` to the host.

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

Let us consider the case where the hardware signer has its power supply com=
ing 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 hack=
er with physical access can just unplug it).

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

What would have to be done would be derive `k` from the message `m` plus th=
e `sha256(n)` and the privkey.
Perhaps you considered this already, but it may be useful to have it explic=
itly stated that this has to be mixed as well, i.e. if `k` is generated det=
erministically it has to be `k =3D f(sha256(n), m, privkey)` where `f()` is=
 some suitable hashing function.

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

Regards,
ZmnSCPxj