[Cryptography] Is it mathematically provably impossible to construct a mechanism to test for back doors in programs?

[Bear]

On Mon, 2014-06-02 at 07:50 -0400, Phillip Hallam-Baker wrote:

> We can achieve a robust notary infrastructure that is proof against
> defection for considerably less money. Let there be 32 independent
> notary log maintainers who maintain a Harber-Stornetta style hash
> chain log (i.e. what is used in Certificate Transparency). Each notary
> has very limited defection opportunities and any defection would be
> quickly noticed.

This provides identifiable points of attack for adversaries of the 
system.  what the NSA &co have been teaching us is that if agencies
with legal authority are permitted to command breaches of trust and 
keep those breaches of trust secret, there can be no trusted 
authority.  

So, one day, your 32 independent notary log maintainers all get 
secret orders and have no legal recourse but to submit to jail if 
they do not participate in betraying or subverting the protocol.  
Further, they are forbidden or prevented from even sounding an 
alarm.  "Warrant canaries" are an endangered species; if they are 
identifiable to their audiences they are identifiable to their 
predators. 

I don't like the bitcoin proof-of-work system; it guarantees that 
the expense of creating bitcoins will hover right around equal to 
their market value (ie, the point at which the marginal profit of
bitcoin farming reaches zero), and constitutes an outright theft 
of subsidized electrical utilities, etc.  But the problem it solves
is how to proceed with zero-trust, and a solution that requires 
identifiable trusted authorities is no solution. 

			Bear