``` 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) ```