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 timing 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 :)  And why we always recommend sticking to well-known, well-studied operations.

-Alan


On 03/08/2014 03:51 AM, Edmund Edgar wrote:
On 8 March 2014 17:10, Alan Reiner <etotheipi@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@realitykeys.com
https://www.realitykeys.com


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