```
Filename: 269-hybrid-handshake.txt
Title: Transitionally secure hybrid handshakes
Author: John Schanck, William Whyte, Zhenfei Zhang,
Nick Mathewson, Isis Lovecruft, Peter Schwabe
Created: 7 June 2016
Updated: 2 Sept 2016
Status: Needs-Revision
1. Introduction
This document describes a generic method for integrating a post-quantum key
encapsulation mechanism (KEM) into an ntor-like handshake. A full discussion
of the protocol and its proof of security may be found in [SWZ16].
1.1 Motivation: Transitional forward-secret key agreement
All currently deployed forward-secret key agreement protocols are
vulnerable to quantum cryptanalysis. The obvious countermeasure is to
switch to a key agreement mechanism that uses post-quantum primitives for
both authentication and confidentiality.
This option should be explored, but providing post-quantum router
authentication in Tor would require a new consensus method and new
microdescriptor elements. Since post-quantum public keys and signatures can
be quite large, this may be a very expensive modification.
In the near future it will suffice to use a "transitional" key agreement
protocol -- one that provides pre-quantum authentication and post-quantum
confidentiality. Such a protocol is secure in the transition between pre-
and post-quantum settings and provides forward secrecy against adversaries
who gain quantum computing capabilities after session negotiation.
1.2 Motivation: Fail-safe plug & play for post-quantum KEMs
We propose a modular design that allows any post-quantum KEM to be included
in the handshake. As there may be some uncertainty as to the security of
the currently available post-quantum KEMs, and their implementations, we
ensure that the scheme safely degrades to ntor in the event of a complete
break on the KEM.
2. Proposal
2.1 Overview
We re-use the public key infrastructure currently used by ntor. Each
server publishes a static Diffie-Hellman (DH) onion key. Each client is
assumed to have a certified copy of each server's public onion key and each
server's "identity digest". To establish a session key, we propose that the
client send two ephemeral public keys to the server. The first is an
ephemeral DH key, the second is an ephemeral public key for a post-quantum
KEM. The server responds with an ephemeral DH public key and an
encapsulation of a random secret under the client's ephemeral KEM key. The
two parties then derive a shared secret from: 1) the static-ephemeral DH
share, 2) the ephemeral-ephemeral DH share, 3) the encapsulated secret, 4)
the transcript of their communication.
2.2 Notation
Public, non-secret, values are denoted in UPPER CASE.
Private, secret, values are denoted in lower case.
We use multiplicative notation for Diffie-Hellman operations.
2.3 Parameters
DH A Diffie-Hellman primitive
KEM A post-quantum key encapsulation mechanism
H A cryptographic hash function
LAMBDA (bits) Pre-quantum bit security parameter
MU (bits) 2*LAMBDA
KEY_LEN (bits) Length of session key material to output
H_LEN (bytes) Length of output of H
ID_LEN (bytes) Length of server identity digest
DH_LEN (bytes) Length of DH public key
KEM_PK_LEN (bytes) Length of KEM public key
KEM_C_LEN (bytes) Length of KEM ciphertext
PROTOID (string) "hybrid-[DH]-[KEM]-[H]-[revision]"
T_KEY (string) PROTOID | ":key"
T_AUTH (string) PROTOID | ":auth"
Note: [DH], [KEM], and [H] are strings that uniquely identify
the primitive, e.g. "x25519"
2.4 Subroutines
HMAC(key, msg):
The pseudorandom function defined in [RFC2104] with H
as the underlying hash function.
EXTRACT(salt, secret):
A randomness extractor with output of length >= MU bits.
For most choices of H one should use the HMAC based
randomness extractor defined in [RFC5869]:
EXTRACT(salt, secret) := HMAC(salt, secret).
If MU = 256 and H is SHAKE-128 with MU bit output, or
if MU = 512 and H is SHAKE-256 with MU bit output, then
one may instead define:
EXTRACT(salt, secret) := H(salt | secret).
EXPAND(seed, context, len):
The HMAC based key expansion function defined in [RFC5869].
Outputs the first len bits of
K = K_1 | K_2 | K_3 | ...
where
K_0 = empty string (zero bits)
K_i = HMAC(seed, K_(i-1) | context | INT8(i)).
Alternatively, an eXtendable Output Function (XOF) may be used.
In which case,
EXPAND(seed, context, len) = XOF(seed | context, len)
DH_GEN() -> (x, X):
Diffie-Hellman keypair generation. Secret key x, public key X.
DH_MUL(P,x) -> xP:
Scalar multiplication in the DH group of the base point P by
the scalar x.
KEM_GEN() -> (sk, PK):
Key generation for KEM.
KEM_ENC(PK) -> (m, C):
Encapsulation, C, of a uniform random message m under public key PK.
KEM_DEC(C, sk):
Decapsulation of the ciphertext C with respect to the secret key sk.
KEYID(A) -> A or H(A):
For DH groups with long element presentations it may be desirable to
identify a key by its hash. For typical elliptic curve groups this should
be the identity map.
2.5 Handshake
To perform the handshake, the client needs to know the identity digest and
an onion key for the router. The onion key must be for the specified DH
scheme (e.g. x25519). Call the router's identity digest "ID" and its public
onion key "A". The following Client Init / Server Response / Client Finish
sequence defines the hybrid-DH-KEM protocol. See Fig. 1 for a schematic
depiction of the same operations.
- Client Init ------------------------------------------------------------
The client generates ephemeral key pairs:
x, X = DH_GEN()
esk, EPK = KEM_GEN()
The client sends a CREATE cell with contents:
ID [ID_LEN bytes]
KEYID(A) [H_LEN bytes]
X [DH_LEN bytes]
EPK [KEM_PK_LEN bytes]
- Server Response --------------------------------------------------------
The server generates an ephemeral DH keypair:
y, Y := DH_GEN()
The server computes the three secret shares:
s0 := H(DH_MUL(X,a))
s1 := DH_MUL(X,y)
s2, C := KEM_ENC(EPK)
The server extracts the seed:
SALT := ID | A | X | EPK
secret := s0 | s1 | s2
seed := EXTRACT(SALT, secret)
The server derives the authentication tag:
verify := EXPAND(seed, T_AUTH, MU)
TRANSCRIPT := ID | A | X | EPK | Y | C | PROTOID
AUTH := HMAC(verify, TRANSCRIPT)
The server sends a CREATED cell with contents:
Y [DH_LEN bytes]
C [KEM_C_LEN bytes]
AUTH [CEIL(MU/8) bytes]
- Client Finish ----------------------------------------------------------
The client computes the three secret shares:
s0 := H(DH_MUL(A,x))
s1 := DH_MUL(Y,x)
s2 := KEM_DEC(C, esk)
The client then derives the seed:
SALT := ID | A | X | EPK
secret := s0 | s1 | s2
seed := EXTRACT(SALT, secret);
The client derives the authentication tag:
verify := EXPAND(seed, T_AUTH, MU)
TRANSCRIPT := ID | A | X | EPK | Y | C | PROTOID
AUTH := HMAC(verify, TRANSCRIPT)
The client verifies that AUTH matches the tag received from the server.
If the authentication check fails the client aborts the session.
- Key derivation ---------------------------------------------------------
Both parties derive the shared key from the seed:
key := EXPAND(seed, T_KEY, KEY_LEN).
.--------------------------------------------------------------------------.
| Fig. 1: The hybrid-DH-KEM handshake. |
.--------------------------------------------------------------------------.
| |
| Initiator Responder with identity key ID |
| --------- --------- and onion key A |
| |
| x, X := DH_GEN() |
| esk, EPK := KEM_GEN() |
| CREATE_DATA := ID | A | X | EPK |
| |
| --- CREATE_DATA ---> |
| |
| y, Y := DH_GEN() |
| s0 := H(DH_MUL(X,a)) |
| s1 := DH_MUL(X,y) |
| s2, C := KEM_ENC(EPK) |
| SALT := ID | A | X | EPK |
| secret := s0 | s1 | s2 |
| seed := EXTRACT(SALT, secret) |
| verify := EXPAND(seed, T_AUTH, MU) |
| TRANSCRIPT := ID | A | X | Y | EPK | C | PROTOID |
| AUTH := HMAC(verify, TRANSCRIPT) |
| key := EXPAND(seed, T_KEY, KEY_LEN) |
| CREATED_DATA := Y | C | AUTH |
| |
| <-- CREATED_DATA --- |
| |
| s0 := H(DH_MUL(A,x)) |
| s1 := DH_MUL(Y,x) |
| s2 := KEM_DEC(C, esk) |
| SALT := ID | A | X | EPK |
| secret := s0 | s1 | s2 |
| seed := EXTRACT(SALT, secret) |
| verify := EXPAND(seed, T_AUTH, MU) |
| TRANSCRIPT := ID | A | X | Y | EPK | C |
| |
| assert AUTH == HMAC(verify, TRANSCRIPT) |
| key := EXPAND(seed, T_KEY, KEY_LEN) |
'--------------------------------------------------------------------------'
3. Changes from ntor
The hybrid-null handshake differs from ntor in a few ways.
First there are some superficial differences.
The protocol IDs differ:
ntor PROTOID "ntor-curve25519-sha256-1",
hybrid-null PROTOID "hybrid-x25519-null-sha256-1",
and the context strings differ:
ntor T_MAC PROTOID | ":mac",
ntor T_KEY PROTOID | ":key_extract",
ntor T_VERIFY PROTOID | ":verify",
ntor M_EXPAND PROTOID | ":key_expand",
hybrid-null T_KEY PROTOID | ":key",
hybrid-null T_AUTH PROTOID | ":auth".
Then there are significant differences in how the authentication tag
(AUTH) and key (key) are derived. The following description uses the
HMAC based definitions of EXTRACT and EXPAND.
In ntor the server computes
secret_input := EXP(X,y) | EXP(X,a) | ID | A | X | Y | PROTOID
seed := HMAC(T_KEY, secret_input)
verify := HMAC(T_VERIFY, seed)
auth_input := verify | ID | A | Y | X | PROTOID | "Server"
AUTH := HMAC(T_MAC, auth_input)
key := EXPAND(seed, M_EXPAND, KEY_LEN)
In hybrid-null the server computes
SALT := ID | A | X
secret_input := H(EXP(X,a)) | EXP(X,y)
seed := EXTRACT(SALT, secret_input)
verify := EXPAND(seed, T_AUTH, MU)
TRANSCRIPT := ID | A | X | Y | PROTOID
AUTH := HMAC(verify, TRANSCRIPT)
key := EXPAND(seed, T_KEY, KEY_LEN)
First, note that hybrid-null hashes EXP(X,a). This is due to
the fact that weaker assumptions were used to prove the security
of hybrid-null than were used to prove the security of ntor. While
this may seem artificial we recommend keeping it.
Second, ntor uses fixed HMAC keys for all sessions. This is unlikely
to be a real-world security issue, but it requires stronger assumptions
about HMAC than if the order of the arguments were reversed.
Finally, ntor uses a mixture of public and secret data in auth_input,
whereas the equivalent term in hybrid-null is the public transcript.
4. Versions
[XXX rewrite section w/ new versioning proposal]
Recognized handshake types are:
0x0000 TAP -- the original Tor handshake;
0x0001 reserved
0x0002 ntor -- the ntor-x25519-sha256 handshake;
Request for new handshake types:
0x010X hybrid-XX -- a hybrid of a x25519 handshake
and a post-quantum key encapsulation mechanism
where
0x0101 hybrid-null -- No post-quantum key encapsulation mechanism.
0x0102 hybrid-ees443ep2 -- Using NTRUEncrypt parameter set ntrueess443ep2
0x0103 hybrid-newhope -- Using the New Hope R-LWE scheme
DEPENDENCY:
Proposal 249: Allow CREATE cells with >505 bytes of handshake data
5. Bibliography
[SWZ16] Schanck, J., Whyte, W., and Z. Zhang, "Circuit extension handshakes
for Tor achieving forward secrecy in a quantum world", PETS 2016,
DOI 10.1515/popets-2016-0037, June 2016.
[RFC2104] Krawczyk, H., Bellare, M., and R. Canetti,
"HMAC: Keyed-Hashing for Message Authentication",
RFC 2104, DOI 10.17487/RFC2104, February 1997
[RFC5869] Krawczyk, H. and P. Eronen,
"HMAC-based Extract-and-Expand Key Derivation Function (HKDF)",
RFC 5869, DOI 10.17487/RFC5869, May 2010
A1. Instantiation with NTRUEncrypt
This example uses the NTRU parameter set EESS443EP2 [XXX cite] which is
estimated at the 128 bit security level for both pre- and post-quantum
settings.
EES443EP2 specifies three algorithms:
EES443EP2_GEN() -> (sk, PK),
EES443EP2_ENCRYPT(m, PK) -> C,
EES443EP2_DECRYPT(C, sk) -> m.
The m parameter for EES443EP2_ENCRYPT can be at most 49 bytes.
We define EES443EP2_MAX_M_LEN := 49.
0x0102 hybrid-x25519-ees443ep2-shake128-1
--------------------
DH := x25519
KEM := EES443EP2
H := SHAKE-128 with 256 bit output
LAMBDA := 128
MU := 256
H_LEN := 32
ID_LEN := 20
DH_LEN := 32
KEM_PK_LEN := 615
KEM_C_LEN := 610
KEY_LEN := XXX
PROTOID := "hybrid-x25519-ees443ep2-shake128-1"
T_KEY := "hybrid-x25519-ees443ep2-shake128-1:key"
T_AUTH := "hybrid-x25519-ees443ep2-shake128-1:auth"
Subroutines
-----------
HMAC(key, message) := SHAKE-128(key | message, MU)
EXTRACT(salt, secret) := SHAKE-128(salt | secret, MU)
EXPAND(seed, context, len) := SHAKE-128(seed | context, len)
KEM_GEN() := EES443EP2_GEN()
KEM_ENC(PK) := (s, C)
where s = RANDOMBYTES(EES443EP2_MAX_M_LEN)
and C = EES443EP2_ENCRYPT(s, PK)
KEM_DEC(C, sk) := EES443EP2_DECRYPT(C, sk)
A2. Instantiation with NewHope
[XXX write intro]
0x0103 hybrid-x25519-newhope-shake128-1
--------------------
DH := x25519
KEM := NEWHOPE
H := SHAKE-128 with 256 bit output
LAMBDA := 128
MU := 256
H_LEN := 32
ID_LEN := 20
DH_LEN := 32
KEM_PK_LEN := 1824
KEM_C_LEN := 2048
KEY_LEN := XXX
PROTOID := "hybrid-x25519-newhope-shake128-1"
T_KEY := "hybrid-x25519-newhope-shake128-1:key"
T_AUTH := "hybrid-x25519-newhope-shake128-1:auth"
Subroutines
-----------
HMAC(key, message) := SHAKE-128(key | message, MU)
EXTRACT(salt, secret) := SHAKE-128(salt | secret, MU)
EXPAND(seed, context, len) -> SHAKE-128(seed | context, len)
KEM_GEN() -> (sk, PK)
where SEED := RANDOMBYTES(MU)
(sk,B) := NEWHOPE_KEYGEN(A_SEED)
PK := B | A_SEED
KEM_ENC(PK) -> NEWHOPE_ENCAPS(PK)
KEM_DEC(C, sk) -> NEWHOPE_DECAPS(C, sk)
```