``` Filename: 263-ntru-for-pq-handshake.txt Title: Request to change key exchange protocol for handshake v1.2 Author: John SCHANCK, William WHYTE and Zhenfei ZHANG Created: 29 Aug 2015 Updated: 4 Feb 2016 Status: Obsolete This proposal was made obsolete by proposal #269. 1. Introduction Recognized handshake types are: 0x0000 TAP -- the original Tor handshake; 0x0001 reserved 0x0002 ntor -- the ntor+curve25519+sha256 handshake; Request for a new (set of) handshake type: 0x010X ntor+qsh -- the hybrid of ntor+curve25519+sha3 handshake and a quantum-safe key encapsulation mechanism where 0X0101 ntor+qsh -- refers to this modular design; no specific Key Encapsulation Mechanism (KEM) is assigned. 0X0102 ntor+ntru -- the quantum safe KEM is based on NTRUEncrypt, with parameter ntrueess443ep2 0X0103 ntor+rlwe -- the quantum safe KEM is based on ring learning with error encryption scheme; parameter not specified DEPENDENCY: Proposal 249: Allow CREATE cells with >505 bytes of handshake data 1.1 Motivation: Quantum-safe forward-secure key agreement We are trying to add Quantum-safe forward-secrecy to the key agreement in tor handshake. (Classical) forward-secrecy means that if the long-term key is compromised, the communication prior to this compromise still stays secure. Similarly, Quantum-safe forward-secrecy implies if the long-term key is compromised due to attackers with quantum-computing capabilities, the prior communication still remains secure. Current approaches for handling key agreement, for instance the ntor handshake protocol, do not have this feature. ntor uses ECC, which will be broken when quantum computers become available. This allows the simple yet very effective harvest-then-decrypt attack, where an adversary with significant storage capabilities harvests Tor handshakes now and decrypts them in the future. The proposed handshake protocol achieves quantum-safe forward-secrecy and stops those attacks by introducing a secondary short-term pre-master secret that is transported via a quantum-safe method. In the case where the long-term key is compromised via quantum algorithm, the attacker still needs to recover the second pre-master secret to be able to decrypt the communication. 1.2 Motivation: Allowing plug & play for quantum-safe encryption algorithms We would like to be conservative on the selection of quantum-safe encryption algorithm. For this purpose, we propose a modular design that allows any quantum-safe encryption algorithm to be included in this handshake framework. We will illustrate the proposal with NTRUEncrypt encryption algorithm. 2. Proposal 2.1 Overview In Tor, authentication is one-way in the authenticated key-exchange protocol. This proposed new handshake protocol is consistent with that approach. We aim to provide quantum-safe forward-secrecy and modular design to the Tor handshake, with the minimum impact on the current version. We aim to use as many existing mechanisms as possible. For purposes of comparison, proposed modifications are indicated with * at the beginning of the corresponding line, the original approaches in ntor are marked with # when applicable. In order to enable variant quantum-safe algorithms for Tor handshake, we propose a modular approach that allows any quantum-safe encryption algorithm to be adopted in this framework. Our approach is a hybridization of ntor protocol and a KEM. We instantiate this framework with NTRUEncrypt, a lattice-based encryption scheme that is believed to be quantum resistant. This framework is expandable to other quantum-safe encryptions such as Ring Learning with Error (R-LWE) based schemes. 2.1.1 Achieved Property: 1) The proposed key exchange method is quantum-safe forward-secure: two secrets are exchanged, one protected by ECC, one protected by NTRUEncrypt, and then put through the native Tor Key Derivation Function (KDF) to derive the encryption and authentication keys. Both secrets are protected with one-time keys for their respective public key algorithms. 2) The proposed key exchange method provides one-way authentication: The server is authenticated, while the client remains anonymous. 3) The protocol is at least as secure as ntor. In the case where the quantum-safe encryption algorithm fails, the protocol is indentical to ntor protocol. 2.1.2 General idea: When a client wishes to establish a one-way authenticated key K with a server, a session key is established through the following steps: 1) Establish a common secret E (classical cryptography, i.e., ECC) using a one-way authenticated key exchange protocol. #ntor currently uses this approach#; 2) Establish a common "parallel" secret P using a key encapsulation mechanism similar to TLS_RSA. In this feature request we use NTRUEncrypt as an example. 3) Establish a new session key k = KDF(E|P, info, i), where KDF is a Key Derivation Function. 2.1.3 Building Blocks 1) ntor: ECDH-type key agreement protocol with one-way authentication; ##existing approach: See 5.1.4 tor-spec.txt## 2) A quantum-safe encryption algorithm: we use QSE to refer to the quantum-safe encryption algorithm, and use NTRUEncrypt as our example; **new approach** 3) SHA3-256 hash function (see FIPS 202), and SHAKE256 KDF; ##previous approach: HMAC-based Extract-and-Expand KDF-RFC5869## 2.2 The protocol 2.2.1 Initialization H(x,t) as SHA3-256 with message x and key t. H_LENGTH = 32 ID_LENGTH = 20 G_LENGTH = 32 * QSPK_LENGTH = XXX length of QSE public key * QSC_LENGTH = XXX length of QSE cipher * PROTOID = "ntor-curve25519-sha3-1-[qseid]" #pre PROTOID = "ntor-curve25519-sha256-1" t_mac = PROTOID | ":mac" t_key = PROTOID | ":key_extract" t_verify = PROTOID | ":verify" These three variables define three different cryptographic hash functions: hash1 = H(*, t_mac); hash2 = H(*, t_key); hash3 = H(*, t_verify); MULT(A,b) = the multiplication of the curve25519 point 'A' by the scalar 'b'. G = The preferred base point for curve25519 KEYGEN() = The curve25519 key generation algorithm, returning a private/public keypair. m_expand = PROTOID | ":key_expand" curve25519 b, B = KEYGEN(); * QSH * QSSK,QSPK = QSKEYGEN(); * cipher = QSENCRYPT (*, PK); * message = QSDECRYPT (*, SK); 2.2.2 Handshake To perform the handshake, the client needs to know an identity key digest for the server, and an ntor onion key (a curve25519 public key) for that server. Call the ntor onion key "B". The client generates a temporary key pair: x, X = KEYGEN(); and a QSE temporary key pair: * QSSK, QSPK = QSKEYGEN(); ================================================================================ and generates a client-side handshake with contents: NODEID Server identity digest [ID_LENGTH bytes] KEYID KEYID(B) [H_LENGTH bytes] CLIENT_PK X [G_LENGTH bytes] * QSPK QSPK [QSPK_LENGTH bytes] ================================================================================ The server generates an ephemeral curve25519 keypair: y, Y = KEYGEN(); and an ephemeral "parallel" secret for encryption with QSE: * PAR_SEC P [H_LENGTH bytes] and computes: * C = ENCRYPT( P | B | Y, QSPK); Then it uses its ntor private key 'b' to compute an ECC secret E = EXP(X,y) | EXP(X,b) | B | X | Y and computes: * secret_input = E | P | QSPK | ID | PROTOID #pre secret_input = E | ID | PROTOID KEY_SEED = H(secret_input, t_key) verify = H(secret_input, t_verify) * auth_input = verify | B | Y | X | C | QSPK | ID | PROTOID | "Server" #pre auth_input = verify | B | Y | X | ID | PROTOID | "Server" ================================================================================ The server's handshake reply is: AUTH H(auth_input, t_mac) [H_LENGTH bytes] * QSCIPHER C [QSPK_LENGTH bytes] Note: in previous ntor protocol the server also needs to send #pre SERVER_PK Y [G_LENGTH bytes] This value is now encrypted in C, so the server does not need to send Y. ================================================================================ The client decrypts C, then checks Y is in G^*, and computes E = EXP(Y,x) | EXP(B,x) | B | X | Y * P' = DECRYPT(C, QSSK) extract P,B from P' (P' = P|B), verifies B, and computes * secret_input = E | P | QSPK | ID | PROTOID #pre secret_input = E | ID | PROTOID KEY_SEED = H(secret_input, t_key) verify = H(secret_input, t_verify) * auth_input = verify | B | Y | X | C | ID | PROTOID | "Server" #pre auth_input = verify | B | Y | X | ID | PROTOID | "Server" The client verifies that AUTH == H(auth_input, t_mac). Both parties now have a shared value for KEY_SEED. This value will be used during Key Derivation Function. 2.3 Instantiation with NTRUEncrypt The example uses the NTRU parameter set NTRU_EESS443EP2. This has keys and ciphertexts of length 610 bytes. This parameter set delivers 128 bits classical security and quantum security. This parameter set uses product form NTRU polynomials. For 256 bits classical and quantum security, use NTRU_EESS743EP2. We adjust the following parameters: handshake type: 0X0102 ntor+ntru the quantum safe KEM is based on NTRUEncrypt, with parameter ntrueess443ep2 PROTOID = "ntor-curve25519-sha3-1-ntrueess443ep2" QSPK_LENGTH = 610 length of NTRU_EESS443EP2 public key QSC_LENGTH = 610 length of NTRU_EESS443EP2 cipher NTRUEncrypt can be adopted in our framework without further modification. 3. Security Concerns The proof of security can be found at https://eprint.iacr.org/2015/287 We highlight some desired features. 3.1 One-way Authentication The one-way authentication feature is inherent from the ntor protocol. 3.2 Multiple Encryption The technique to combine two encryption schemes used in 2.2.4 is named Multiple Encryption. Discussion of appropriate security models can be found in [DK05]. Proof that the proposed handshake is secure under this model can be found at https://eprint.iacr.org/2015/287. 3.3 Cryptographic hash function The default hash function HMAC_SHA256 from Tor suffices to provide desired security for the present day. However, to be more future proof, we propose to use SHA3 when Tor starts to migrate to SHA3. 3.4 Key Encapsulation Mechanism The KEM in our protocol can be proved to be KEM-CCA-2 secure. 3.5 Quantum-safe Forward Secrecy Quantum-safe forward secrecy is achieved. 3.6 Quantum-safe authentication The proposed protocol is secure only until a quantum computer is developed that is capable of breaking the onion keys in real time. Such a computer can compromise the authentication of ntor online; the security of this approach depends on the authentication being secure at the time the handshake is executed. This approach is intended to provide security against the harvest-then-decrypt attack while an acceptable quantum-safe approach with security against an active attacker is developed. 4. Candidate quantum-safe encryption algorithms Two candidate quantum-safe encryption algorithms are under consideration. NTRUEncrypt, with parameter set ntrueess443ep2 provides 128 bits classcial and quantum security. The parameter sets is available for use now. LWE-based key exchange, based on Peikert's idea [Pei14]. Parameter sets suitable for this framework (the newerhop vairant) is still under development. 5. Bibliography [DK05] Y. Dodis, J. Katz, "Chosen-Ciphertext Security of Mulitple Encryption", Theory of Cryptography Conference, 2005. http://link.springer.com/chapter/10.1007%2F978-3-540-30576-7_11 (conference version) or http://cs.nyu.edu/~dodis/ps/2enc.pdf (preprint) [Pei14] C. Peikert, "Lattice Cryptography for the Internet", PQCrypto 2014. ```