NoneRe: Recipient Anonymity

[Anonymous]

Matt Ghio wrote:

> A group of servers collects messages of equal length for anonymous
> recipients.  All servers exchange messages so that each has copies of all
> messages.
> 
> A recipient wishes to retrieve a message from the servers without any
> server knowing which message he is receiving.  The recipient selects a
> group of n servers.  From each server, S_1...S_n-1, he requests a random
> selection of messages, with a 50% probability that any particular message
> will be selected.  The server returns the xor of all messages requested.
> He sends the final server a request which is the xor of all the previous
> requests and the one single message that he wants.
> 
> The xor of all the responses is the desired message.  It is impossible to
> determine which message was received unless all servers collude.


So what you're saying is:

                             - Messages - 
           A B C D E F G H I J K L M N O P Q R S T U V W X Y Z

Server 1:  1 0 1 1 0 1 0 0 1 0 1 0 0 0 1 0 1 1 0 1 0 1 0 0 1 1
Server 2:  0 1 1 0 1 1 1 0 1 0 0 0 1 0 0 1 0 1 0 1 0 0 0 1 0 0
Server 3:  1 1 0 1 1 0 1 0 0 0 1 0 1 0 1 1 0 0 0 0 0 1 0 1 1 1


So server 1 sends back the xor of messages A,C,D,F...Z; server 2 sends
back the xor of B,C,E,F,G...etc.  The xor of all of that cancels out
everything except Message Q.  But as long as at least one of the servers
doesn't keep logs then nobody will know that except the person who
downloaded it. 

Clever.  It sure beats reply-blocks.  :)