[tor-dev] Proposal 216: Improved circuit-creation key exchange

[Nick Mathewson]

Hi, all.

This is just the ntor proposal draft, as circulated last year, but
with a proposal number assigned to it, and a closing section about how
to make Tor actually work with it.



Filename: 216-ntor-handshake.txt
Title: Improved circuit-creation key exchange
Author:  Nick Mathewson
Created: 11-May-2011
Status: Open

Summary:

  This is an attempt to translate the proposed circuit handshake from
  "Anonymity and one-way authentication in key-exchange protocols" by
  Goldberg, Stebila, and Ustaoglu, into a Tor proposal format.

  It assumes that proposal 200 is implemented, to provide an extended CREATE
  cell format that can indicate what type of handshake is in use.

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 a,A=KEYGEN() yield a new private-public keypair in G, where a is the
  secret key and A = EXP(g,a).  If additional checks are needed to insure
  a valid keypair, they should be performed.

  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 "ntor-curve25519-sha256-1"  (We might want to make
  this shorter if it turns out to save us a block of hashing somewhere.)

  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) == curve25519(.,b,a), and g == 9 .  Let KEYGEN() do the
  appropriate manipulations when generating the secret key (clearing the
  low bits, twiddling the high bits).

  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 with b, B = KEYGEN().  The router publishes B in its server descriptor.

  To send a create cell, the client generates a keypair x,X = KEYGEN(), and
  sends a CREATE cell with contents:

    NODEID:     ID             -- H_LENGTH bytes
    KEYID:      KEYID(B)       -- H_LENGTH bytes
    CLIENT_PK:  X              -- G_LENGTH bytes

  The server generates a keypair of y,Y = KEYGEN(), and computes

    secret_input = EXP(X,y) | EXP(X,b) | ID | B | X | Y | PROTOID
    KEY_SEED = H(secret_input, t_key)
    verify = H(secret_input, t_verify)
    auth_input = verify | ID | B | Y | X | PROTOID | "Server"

  The server sends a CREATED cell containing:

    SERVER_PK:  Y                     -- G_LENGTH bytes
    AUTH:       H(auth_input, t_mac)  -- H_LENGTH byets

  The client then checks Y is in G^* [see NOTE below], and computes

    secret_input = EXP(Y,x) | EXP(B,x) | ID | B | X | Y | PROTOID
    KEY_SEED = H(secret_input, t_key)
    verify = H(secret_input, t_verify)
    auth_input = verify | ID | B | Y | X | PROTOID | "Server"

    The client verifies that AUTH == H(auth_input, t_mac).

  [NOTE: It may be adequate to check that EXP(Y,x) is not the point at
  infinity.  See tor-dev thread.]

  Both parties now have a shared value for KEY_SEED.  They expand this into
  the keys needed for the Tor relay protocol.

Key expansion:

  Currently, the key expansion formula used by Tor here is

       K = SHA(K0 | [00]) | SHA(K0 | [01]) | SHA(K0 | [02]) | ...

       where K0==g^xy, and K is divvied up into Df, Db, Kf, and Kb portions.

  Instead, let's have it be

       K = K_0 | K_1 | K_2 | K_3 | ...

       Where K_0     = H(m_expand | INT8(i) , KEY_SEED )
         and K_(i+1) = H(K_i | m_expand | INT8(i) , KEY_SEED )
         and m_expend is an arbitrarily chosen value,
         and INT8(i) is a octet with the value "i".

  Ian says this is due to a construction from Krawczyk at
  http://eprint.iacr.org/2010/264 .

  Let m_expand be PROTOID | ":key_expand"

Performance notes:

  In Tor's current circuit creation handshake, the client does:
     One RSA public-key encryption
     A full DH handshake in Z_p
     A short AES encryption
     Five SHA1s for key expansion
  And the server does:
     One RSA private-key decryption
     A full DH handshake in Z_p
     A short AES decryption
     Five SHA1s for key expansion

  While in the revised handshake, the client does:
     A full DH handshake
     A public-half of a DH handshake
     3 H operations for the handshake
     3 H operations for the key expansion
  and the server does:
     A full DH handshake
     A private-half of a DH handshake
     3 H operations for the handshake
     3 H operations for the key expansion

Integrating with the rest of Tor:

  Add a new optional entry to router descriptors and microdescriptors:

     "onion-key-ntor" SP Base64Key NL

  where Base64Key is a base-64 encoded 32-byte value, with padding
  omitted.

  Add a new consensus method to tell servers to copy "onion-key-ntor"
  entries to from router descriptors to microdescriptors.

  Add a "UseNTorHandshake" configuration option and a corresponding
  consensus parameter to control whether clients use the ntor
  handshake.  If the configuration option is "auto", clients should
  obey the consensus parameter.  Have the configuration default be
  "auto" and the consensus value initially be "0".

  Reserve the handshake type [00 01] for this handshake in CREATE2 and
  EXTEND2 cells.