Re: Removing 1 modular exponentiation

2007-03-09 Thread Watson Ladd
James Muir wrote: The following recent preprint deals with the subject of this thread: A. Kate, G. Zaverucha and I. Goldberg Pairing-Based Onion Routing pdf CACR 2007-08 http://www.cacr.math.uwaterloo.ca/techreports/2007/cacr2007-08.pdf -James Nice. Patents are going to be an issue

Re: Removing 1 modular exponentiation

2007-03-09 Thread Watson Ladd
Fergie wrote: -- James Muir [EMAIL PROTECTED] wrote: The following recent preprint deals with the subject of this thread: A. Kate, G. Zaverucha and I. Goldberg Pairing-Based Onion Routing pdf CACR 2007-08 http://www.cacr.math.uwaterloo.ca/techreports/2007/cacr2007-08.pdf I'm

Re: Removing 1 modular exponentiation

2007-03-08 Thread James Muir
The following recent preprint deals with the subject of this thread: A. Kate, G. Zaverucha and I. Goldberg Pairing-Based Onion Routing pdf CACR 2007-08 http://www.cacr.math.uwaterloo.ca/techreports/2007/cacr2007-08.pdf -James

Re: Removing 1 modular exponentiation

2007-03-08 Thread Fergie
-BEGIN PGP SIGNED MESSAGE- Hash: SHA1 - -- James Muir [EMAIL PROTECTED] wrote: The following recent preprint deals with the subject of this thread: A. Kate, G. Zaverucha and I. Goldberg Pairing-Based Onion Routing pdf CACR 2007-08

Re: Removing 1 modular exponentiation

2007-02-19 Thread Mike Perry
Thus spake Watson Ladd ([EMAIL PROTECTED]): Hello! Tor currently uses RSA encrypted DH exchanges. This requires that the server and client both make 3 exponentiations: Two for DH, One for RSA. But we can reduce this significantly. I've already presented this before, but now I think I can

Re: Removing 1 modular exponentiation

2007-02-19 Thread James Muir
Mike Perry wrote: Thus spake Watson Ladd ([EMAIL PROTECTED]): Hello! Tor currently uses RSA encrypted DH exchanges. This requires that the server and client both make 3 exponentiations: Two for DH, One for RSA. But we can reduce this significantly. I've already presented this before, but now I

Re: Removing 1 modular exponentiation

2007-02-19 Thread Watson Ladd
that's not really a problem. all computations are done in the group ZZ_p. 1/k really means the inverse of k modulo the order of g in ZZ_p. So b/k does not have to be an integer. putting the security of the scheme aside, one question that comes to mind is how Alice (the OP) is going to get

Re: Removing 1 modular exponentiation

2007-02-19 Thread James Muir
putting the security of the scheme aside, one question that comes to mind is how Alice (the OP) is going to get an authentic copy of Ricky's DH public key, y. One way to do this is to include it in the router descriptors. But then we have to ask if it's worth adding a new public key for each OR

Re: Removing 1 modular exponentiation

2007-02-19 Thread Mike Perry
Thus spake James Muir ([EMAIL PROTECTED]): Mike Perry wrote: Thus spake Watson Ladd ([EMAIL PROTECTED]): Well, one immediate problem is that b/k has to be an integer.. So b=rk for some random r and b is thus not completely random.. To clarify the effects of this, you should rewrite your

Re: Removing 1 modular exponentiation

2007-02-19 Thread James Muir
Problem is: (g^X)^k = g for some given k. Find X equivalent to 1/k. Rewrite as (g^k)^X = g Seems like you need to take the Discrete Log of both sides to get your X=1/k value. This is hard. Since we are working modulo p and we know that g is a generator of ZZ_p its order is p-1. So, to find

Re: Removing 1 modular exponentiation

2007-02-19 Thread Watson Ladd
James Muir wrote: putting the security of the scheme aside, one question that comes to mind is how Alice (the OP) is going to get an authentic copy of Ricky's DH public key, y. One way to do this is to include it in the router descriptors. But then we have to ask if it's worth adding a new

Re: Removing 1 modular exponentiation

2007-02-19 Thread James Muir
We already distribute different keys for the current protocol. But the one I proposed is insecure so we might as well forget about it. Schnorr signatures are secure and are intended for this purpose, but we can only use them after 2008. the way things are done now, each OR has two public keys

Re: Removing 1 modular exponentiation

2007-02-19 Thread Watson Ladd
James Muir wrote: You may already know that the current scheme has a security reduction (Goldberg, PET 2006), so I imagine there would have to be a comparable argument before the powers that be would consider a new scheme. Out of curiosity, what is it about your scheme that makes you say

Re: Removing 1 modular exponentiation

2007-02-19 Thread Mike Perry
Thus spake Watson Ladd ([EMAIL PROTECTED]): James Muir wrote: You may already know that the current scheme has a security reduction (Goldberg, PET 2006), so I imagine there would have to be a comparable argument before the powers that be would consider a new scheme. Out of