[Bitcoin-development] Is this a safe thing to be doing with ECC addition? (Oracle protocol)

[Alan Reiner]

Note that one of the reasons why this is insecure is because EC point
addition is invertible.  EC-scalar multiplication is not, thus why EC
Diffie-Hellman is secure even when this asymmetry exists.

A good cryptosystem doesn't have strange restrictions, like "your public
key can only be public sometimes, but needs to protected like your
private key other times."  If you have to worry about things like that,
you're doing it wrong :)

-Alan


On 03/08/2014 05:37 AM, Joel Kaartinen wrote:
> If both parties insist on seeing a hash of the other party's public
> key before they'll show their own public key, they can be sure that
> the public key is not chosen based on the public key they themselves
> presented.
>
> Although, I have to wonder, why not just use multisig?
>
> - Joel
>
> On 08.03.2014 10:51, Edmund Edgar wrote:
>> On 8 March 2014 17:10, Alan Reiner <etotheipi at gmail.com
>> <mailto:etotheipi at gmail.com>> wrote:
>>  
>>
>>     I create a new keypair, <c_pub> with <c_priv> which I know (it
>>     can be any arbitrary key pair).  But I don't give you <c_pub>, I
>>     give you  <b_pub> = <c_pub> minus <a_pub> (which I can do because
>>     I've seen <a_pub> before doing this). 
>>
>>     Sure, I don't know the private key for <b_pub>, but it doesn't
>>     matter... because what
>>
>>     <b_pub> + <a_pub> = <c_pub> (mine)
>>
>>     You have no way to detect this condition, because you don't know
>>     what c_pub/c_priv I created, so you can only detect this after
>>     it's too late (after I abuse the private key)
>>
>>
>> Thanks Alan and Forrest, that makes sense. So to salvage the
>> situation in the original case, we have to make sure the parties
>> exchange their public keys first, before they're allowed to see the
>> public keys they'll be combining them with. 
>>
>> -- 
>> -- 
>> Edmund Edgar
>> Founder, Social Minds Inc (KK)
>> Twitter: @edmundedgar
>> Linked In: edmundedgar
>> Skype: edmundedgar
>> http://www.socialminds.jp
>>
>> Reality Keys
>> @realitykeys
>> ed at realitykeys.com <mailto:ed at realitykeys.com>
>> https://www.realitykeys.com
>>
>>
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