[tor-dev] Proposal 223: Ace: Improved circuit-creation key exchange
Nick Mathewson
nickm at torproject.org
Wed Nov 20 16:02:11 UTC 2013
Hi, all!
Here's Esfandiar Mohammadi's proposal for the Ace handshake. It should
have been added as a numbered proposal back in July; I think I lost
track of everything while the dev meeting was happening.
Please let me know if you have more proposals that should be assigned
numbers but haven't gotten one yet.
Filename: 223-ace-handshake.txt
Title: Ace: Improved circuit-creation key exchange
Author: Esfandiar Mohammadi
Created: 22-July-2013
Status: Open
History:
22-July-2013 -- Submitted
20-Nov-2013 -- Reformatted slightly, wrapped lines, added
references, adjusted the KDF [nickm]
Summary:
This is an attempt to translate the proposed circuit handshake from
"Ace: An Efficient Key-Exchange Protocol for Onion Routing" by
Backes, Kate, and Mohammadi into a Tor proposal format.
The specification assumes an implementation of scalar multiplication
and addition of two curve elements, as in Robert Ransom's celator
library.
Notation:
Let a|b be the concatenation of a with b.
Let H(x,t) be a tweakable hash function of output width H_LENGTH
bytes.
Let t_mac, t_key, and t_verify be a set of arbitrarily-chosen
tweaks for the hash function.
Let EXP(a,b) be a^b in some appropriate group G where the
appropriate DH parameters hold. Let's say elements of this group,
when represented as byte strings, are all G_LENGTH bytes long.
Let's say we are using a generator g for this group.
Let MUTLIEXPONEN (a,b,c,d) be (a^b)*(c^d) in some appropriate
group G where the appropriate DH parameters hold. Let's say
elements of this group, when represented as byte strings, are all
G_LENGTH bytes long. Let's say we are using a generator g for
this group.
Let PROTOID be a string designating this variant of the protocol.
Let KEYID be a collision-resistant (but not necessarily preimage-resistant)
hash function on members of G, of output length H_LENGTH bytes.
Instantiation:
Let's call this PROTOID "ace-curve25519-ed-uncompressed-sha256-1"
Set H(x,t) == HMAC_SHA256 with message x and key t. So H_LENGTH == 32.
Set t_mac == PROTOID | ":mac"
t_key == PROTOID | ":key"
t_verify == PROTOID | ":verify"
Set EXP(a,b) == scalar_mult_curve25519(a,b),
MUTLIEXPONEN(a,b) == dblscalarmult_curve25519(a,b,c,d), and g == 9 .
Set KEYID(B) == B. (We don't need to use a hash function here, since our
keys are already very short. It is trivially collision-resistant, since
KEYID(A)==KEYID(B) iff A==B.)
Protocol:
Take a router with identity key digest ID.
As setup, the router generates a secret key b, and a public onion key
B = EXP(g,b). The router publishes B in its server descriptor.
To send a create cell, the client generates two keypairs of x_1,
X_1=EXP(g,x_1) and x_2, X_2=EXP(g,x_2) and sends a CREATE cell
with contents:
NODEID: ID -- H_LENGTH bytes
KEYID: KEYID(B) -- H_LENGTH bytes
CLIENT_PK: X_1, X_2 -- 2 x G_LENGTH bytes
The server checks X_1, X_2, generates a keypair of y, Y=EXP(g,y)
and computes
point = MUTLIEXPONEN(X_1,y,X_2,b)
secret_input = point | ID | B | X_1 | X_2 | Y | PROTOID
KEY_SEED = H(secret_input | "Key Seed", t_key)
KEY_VERIFY = H(secret_input | "HMac Seed", t_verify)
auth_input = ID | Y | X_1 | X_2 | PROTOID | "Server"
The server sends a CREATED cell containing:
SERVER_PK: Y -- G_LENGTH bytes
AUTH: H(auth_input, KEY_VERIFY) -- H_LENGTH bytes
The client then checks Y, and computes
point = MUTLIEXPONEN(Y,x_1,B,x_2)
secret_input = | ID | B | X_1 | X_2 | Y | PROTOID
KEY_SEED = H(secret_input | "Key Seed", t_key)
KEY_VERIFY = H(secret_input | "HMac Seed", t_verify)
auth_input = ID | B | Y | X_1 | X_2 | PROTOID | "Server"
The client verifies that AUTH == H(auth_input, KEY_VERIFY).
Both parties now have a shared value for KEY_SEED. They expand
this into the keys needed for the Tor relay protocol.
Key expansion:
When using this handshake, clients and servers should expand keys
using HKDF as with the ntor handshake today.
See also:
http://www.infsec.cs.uni-saarland.de/~mohammadi/ace/ace.html
for implementations, academic paper, and benchmarking code.
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