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Date: Sat, 02 Nov 2013 10:44:58 +0100
From: Thomas Voegtlin <thomasv1@gmx.de>
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Subject: Re: [Bitcoin-development] Proposal to replace BIP0039
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> To be specific, we (in cooperation with / inspired by Timo Hanke) 
> developed method how to prove that the seed generated by Trezor has 
> been created using combination of computer-provided entropy and 
> device-provided entropy, without leaking full private information to 
> other computer, just because we want Trezor to be blackbox-testable 
> and fully deterministic (seed generation is currently the only 
> operation which uses any source of RNG).
>

Thanks for the explanation. Here is how I understand how it works, 
please correct me if I'm wrong:

The user's computer picks a random number a, the Trezor picks a random 
number b.
Trezor adds a and b in the secp256k1 group, and this creates a master 
private key k.
Trezor sends the corresponding master public key K to the computer.
Thus, the computer can check that K was derived from a, without knowing b.
This also allows the computer to check that any bitcoin address derived 
from K is derived from a, without leaking b. (and reciprocally)

However, it seems to me that this property will work only with bip32 
public derivations; if a private derivation is used, don't you need to 
know k?