[FoRK] Crypto protocol for only good news?

Stephen D. Williams <sdw at lig.net> on Wed Apr 9 12:11:49 PDT 2008

Yea, I know, I warped back 2 years.  ;-)  I'm clearing out my queue.

sdw

Stephen D. Williams wrote:
> The best solution, it seems to me, is to hide whether the "test" (or 
> "watched the game" or "consent to tell") was given.  If parents don't 
> know that a sex test was done, they can only be surprised positively 
> if it is a boy.  If you don't know if your friend has watched the 
> game, then it is not telling that he doesn't tell you they won.  At 
> the expiration of the suspense period, birth or having seen the game, 
> it is fine to share what you knew as the embargo is over.
>
> In cases of mutual  "positive surprise", it might suffice to have both 
> parties secretly vote on whether to tell the result of a sub-test.  If 
> you don't know whether your mate said "don't tell me the sex" vs. 
> "don't tell me the sex unless it is male", then it is not telling when 
> you aren't told the sex.
>
> The Heisenberg Positive Certainty Principle, or something.  An 
> unwatched test may not exist so a missing answer doesn't tell you 
> anything.
>
> sdw
>
> mattj at newsblip.com wrote:
>> Reza had some helpful comments offline which raised the useful idea 
>> of adding another actor or step.  Thanks!
>>
>>> Reza wrote:
>>>
>>> In other words, what you've outlined is a system that has three 
>>> black-boxes:
>>> parents, child, and the sonographer... If you introduce a forth, say 
>>> a little
>>> bird flying around counting quantum spins... and say that:
>>>
>>> GenderOfBabyToBeToldToTheParents = RealGender [OPERATOR] Randomizer
>>>
>>> Where Randomizer is the news that the bird tells the sonographer at 
>>> the time
>>> and under the terms of its own choosing.
>>
>> So here's my current thinking...
>>
>> First, to sidestep the geopolitical issues of gender selection, I'll 
>> use a new example: you've taped the big game, and you don't want your 
>> friend to tell you who won before you've had a chance to watch it... 
>> unless your team won, in which case you're glad to hear about it.  
>> I'm going to temporarily call this the Fair-Weather Bit problem, 
>> because you only want to hear the bit value in one case; I'm hoping 
>> someone can clue me in to any existing terminology.  (The approach 
>> below has a Monty Hall Problem flavor, in a sense.)
>>
>> You cannot have a 100% chance of learning they won without setting up 
>> a 100% chance of learning that they lost. So, this becomes a question 
>> of how risk averse you are in this situation.  If you mostly want to 
>> know about a win, we can structure things to give you a good chance 
>> of hearing that news. If you mostly want to avoid hearing about a 
>> loss, we can arrange that, too.
>>
>> But to start, let's just get a basic answer.  Here's my protocol:
>>
>> 1. Friend watches the game live.
>>    If your team wins, he writes "Win" on a piece of paper.
>>    If your team loses, he writes "Null" (no answer) on a piece of paper.
>>
>> 2. Friend seals the paper inside an envelope, and hands it to a 
>> trusted third party (say, the bartender at your local pub). Your 
>> friend does *not* tell the bartender what the (single bit) message is 
>> about, and the bartender does not know about the big game. (I know, 
>> "you call that a bartender?", but let's assume it.)
>>
>> 3. You show up, and per the protocol, trusted bartender flips a coin 
>> out of your view.  Then the bartender opens the envelope (also out of 
>> view).
>>    If it's heads, the bartender reads you the message your friend wrote.
>>    If it's tails, the bartender says "Null", pretending he's reading 
>> the message.
>>
>> Assuming your team has a 50-50 chance of winning, we expect to hear 
>> "Win" 25% of the time, and "Null" 75% of the time.  But we needn't be 
>> too sad if we hear "Null", because 2/3 of the time the "Null" will be 
>> a result of the bartender's coin toss.  Hearing "Null" means there's 
>> still a 1/3 chance they really won.
>>
>> We do ask the bartender to be deceptive here (pretending all "Nulls" 
>> are equal). However, he can't have a motive to tell you good or bad 
>> info, because unlike your friend he has no idea what this particular 
>> message means.
>>
>> Now, if you're not so risk averse, and you want a greater chance of 
>> hearing about a win, you replace the coin toss with some random 
>> number generator. Have the bartender read you the friend's message 
>> 90% of the time, and tell you "Null" for the other 10%.  This way, 
>> you have a 45% chance of hearing "Win", and if you hear "Null", 
>> there's still an 18% chance that your team won.
>>
>> Conversely, if you're highly risk averse, you can reverse the 90-10 
>> rule, which will give you a 5% chance of learning of a win, and a 45% 
>> chance that a "Null" is really a win.  Of course, you can pick any 
>> point you prefer on that spectrum.
>>
>> -Matt Jensen
>>  http://mattjensen.com
>>  Seattle
>>
>>> Quoting Matt Jensen <mattj at newsblip.com>:
>>>
>>>> I'm looking for a technique for revealing info, but only if the info
>>>> has one particular value.
>>>>
>>>> For example: Suppose a couple is pregnant with their second child. The
>>>> first kid is a girl, and though the couple will love the second kid
>>>> regardless of gender, they'd be extra excited if it turned out to be a
>>>> boy.  (Plus, they could start outfitting the nursery.)
>>>>
>>>> So, we now want to know if there's some procedure whereby they can
>>>> have the sonographer tell them if it's a boy, but not tell them
>>>> anything if it's a girl.  Obviously, not telling them anything tells
>>>> them it's a girl.  Anyway around this?
>>>>
>>>> Ideally, you'd like a 100% chance of learning that it's a boy.
>>>> However, in order trust an answer like "I can't tell you the result
>>>> because our protocol forbids it", it seems you have to accept a lower
>>>> chance of getting the good news.
>>>>
>>>> I suppose you could have the sonographer secretly flip a coin, and if
>>>> it's heads, she tells the parents the gender.  But if it's a girl you
>>>> actually have the sonographer lie to you, and tell you she got tails,
>>>> so she can't tell you the gender.  But even that tells you something:
>>>> there are two "tails" outcomes for  a girl and only one "tails"
>>>> outcome for a boy.
>>>>
>>>> I feel like there's a better answer to this question, but I'm missing
>>>> it.  Ideas?
>>>>
>>>> -Matt Jensen
>>>>   http://mattjensen.com
>>>>   Seattle
>>>>
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