223-ace-handshake.txt

Filename: 223-ace-handshake.txt
Title: Ace: Improved circuit-creation key exchange
Author: Esfandiar Mohammadi, Aniket Kate, Michael Backes
Created: 22-July-2013
Status: Reserve

History:

   22-July-2013 -- Submitted
   20-Nov-2013  -- Reformatted slightly, wrapped lines, added
                   references, adjusted the KDF [nickm]
   20-Nov-2013  -- Clarified that there's only one group here [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 the same group G as above.

  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 | B | 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 = 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 | 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.