Internet-Draft PQ SSH October 2020
Kampanakis, et al. Expires 24 April 2021 [Page]
Workgroup:
CURDLE
Internet-Draft:
draft-kampanakis-curdle-pq-ssh-00
Published:
Intended Status:
Experimental
Expires:
Authors:
P. Kampanakis
Cisco Systems
D. Stebila
University of Waterloo
M. Friedl
OpenSSH
T. Hansen
AWS
D. Sikeridis
University of New Mexico

Post-quantum public key algorithms for the Secure Shell (SSH) protocol

Abstract

This document defines hybrid key exchange methods based on classical ECDH key exchange and post-quantum key encapsulation schemes. These methods are defined for use in the SSH Transport Layer Protocol. It also defines post-quantum public key authentication methods based on post-quantum signature schemes. These methods are defined for use in the SSH Authentication Protocol.

EDNOTE: The goal of this draft is to start the standardization of PQ algorithms in SSH early to mitigate the potential record-and-harvest later with a quantum computer attacks. This draft is not expected to be finalized before the NIST PQ Project has standardized PQ algorithms. After NIST has standardized then this document will replace TBD1, TBD3 with the appropriate algorithms and parameters before proceeding to ratification.

EDNOTE: Discussion of this work is encouraged to happen on the IETF WG Mailing List or in the GitHub repository which contains the draft: https://github.com/csosto-pk/pq-ssh/issues .

Change Log [EDNOTE: Remove befor publicaton].

draft-kampanakis-curdle-pq-ssh-00
  • Initial draft

Status of This Memo

This Internet-Draft is submitted in full conformance with the provisions of BCP 78 and BCP 79.

Internet-Drafts are working documents of the Internet Engineering Task Force (IETF). Note that other groups may also distribute working documents as Internet-Drafts. The list of current Internet-Drafts is at https://datatracker.ietf.org/drafts/current/.

Internet-Drafts are draft documents valid for a maximum of six months and may be updated, replaced, or obsoleted by other documents at any time. It is inappropriate to use Internet-Drafts as reference material or to cite them other than as "work in progress."

This Internet-Draft will expire on 24 April 2021.

1. Introduction

Secure Shell (SSH) [RFC4251] performs key establishment using key exchange methods based exclusively on (Elliptic Curve) Diffie-Hellman style schemes. SSH [RFC4252], [RFC8332], [RFC5656], [RFC8709] also defines public key authentication methods based on RSA or ECDSA/EdDSA signature schemes. The cryptographic security of these key exchange and signature schemes relies on certain instances of the discrete logarithm and integer factorization problems being computationally infeasable to solve for adversaries.

However, when sufficiently large quantum computers become available these instances would no longer be computationally infeasable rendering the current key exchange and authentication methods in SSH insecure [I-D.hoffman-c2pq]. While large quantum computers are not available today an adversary can record the encrypted communication sent between the client and server in an SSH session and then later decrypt the communication when sufficiently large quantum computers become available. This kind of attack is known as a "record-and-harvest" attack. Record-and-harvest attacks do not apply retroactively to authentication but a quantum computer could threaten SSH authentication by impersonating as a legitimate client or server.

This document proposes to address the problem by extending the SSH Transport Layer Protocol [RFC4253] with hybrid key exchange methods and the SSH Authentication Protocol [RFC4252] with public key methods based on post-quantum signature schemes. A hybrid key exchange method maintains the same level of security provided by current key exchange methods, but also adds quantum resistance. The security provided by the individual key exchange scheme in a hybrid key exchange method is independent. This means that the hybrid key exchange method will always be at least as secure as the most secure key exchange scheme executed as part of the hybrid key exchange method.

In the context of the NIST Post-Quantum Cryptography Standardization Project [NIST_PQ], key exchange algorithms are formulated as key encapsulation mechanisms (KEMs), which consist of three algorithms:

  • 'KeyGen() -> (pk, sk)': A probabilistic key generation algorithm, which generates a public key 'pk' and a secret key 'sk'.
  • 'Encaps(pk) -> (ct, ss)': A probabilistic encapsulation algorithm, which takes as input a public key 'pk' and outputs a ciphertext 'ct' and shared secret 'ss'.
  • 'Decaps(sk, ct) -> ss': A decapsulation algorithm, which takes as input a secret key 'sk' and ciphertext 'ct' and outputs a shared secret 'ss', or in some cases a distinguished error value.

The main security property for KEMs is indistinguishability under adaptive chosen ciphertext attack (IND-CCA2), which means that shared secret values should be indistinguishable from random strings even given the ability to have arbitrary ciphertexts decapsulated. IND-CCA2 corresponds to security against an active attacker, and the public key / secret key pair can be treated as a long-term key or reused. A weaker security notion is indistinguishability under chosen plaintext attack (IND-CPA), which means that the shared secret values should be indistinguishable from random strings given a copy of the public key. IND-CPA roughly corresponds to security against a passive attacker, and sometimes corresponds to one-time key exchange.

The corresponding post-quantum signature algorithms defined in the NIST Post-Quantum Cryptography Standardization Project [NIST_PQ] are

  • 'KeyGen() -> (pk, sk)': A probabilistic key generation algorithm, which generates a public key 'pk' and a secret key 'sk'.
  • 'Sign(m, sk) -> sig': A deterministic signing algorithm, which takes as input a message 'm' and a private key 'sk' and outputs a signature 'sig'.
  • 'Verify(m, pk, sigma) -> pass/fail': A verification algorithm, which takes as input a message 'm', a public key 'pk' and a signature 'sig' and outputs a verification pass or failure of the signature on the message.

The post-quantum KEMs used for hybrid key exchange in the document are TBD1. The post-quantum signature algorithm used for key based authentication is TBD3. [EDNOTE: Placeholder. Algorithms will be identified after NIST Round 3 concludes.] The post-quantum algorithms are defined in NIST Post-quantum Project [NIST_PQ]. [EDNOTE: Update link. Algorithms can change based on NIST's Round 3 standardization].

1.1. Requirements Language

The key words "MUST", "MUST NOT", "REQUIRED", "SHALL", "SHALL NOT", "SHOULD", "SHOULD NOT", "RECOMMENDED", "MAY", and "OPTIONAL" in this document are to be interpreted as described in RFC 2119 [RFC2119].

2. Hybrid Key Exchange

2.1. Hybrid Key Exchange Method Abstraction

This section defines the abstract structure of a hybrid key exchange method. The structure must be instantiated with two key exchange schemes. The byte, string and mpint are to be interpreted in this document as described in [RFC4251].

The client sends

       byte SSH_MSG_HBR_INIT
       string C_INIT

where C_INIT would be the concatenation of C_PQ and C_CL.

The server sends

       byte SSH_MSG_HBR_REPLY
       string S_REPLY

where S_REPLY would be the concatenation of S_PQ and S_CL.

[EDNOTE: Initially we were using S_CL, S_PQ, C_CL, C_PQ which were encoding the server and client client and server classical and post-quantum public key/ciphertext as its own string. We since switched to an encoding method which concatenates them together as a single string in the C_INIT, S_REPLY message. This method concatenates the raw values rather than the length of each value plus the value. The total length of the concatenation is still known, but the relative lengths of the individual values that were concatenated is no longer part of the representation. If that is the WG consensus we need to put a note of this in the Appendix for historical reference and expand on the concatenated string here in this section.]

C_PQ represents the 'pk' output of the corresponding KEMs' 'KeyGen' at the client. S_PQ represents the ciphertext 'ct' output of the corresponding KEMs' 'Encaps' algorithm generated by the server to the client's public key. The client decapsulates the ciphertext by using its private key which leads to K_PQ, a post-quantum shared secret for SSH.

C_CL and S_CL represent the ephemeral public key of the client and server respectively used for the classical (EC)DH key exchange which leads to K_CL, a classical shared secret for SSH.

2.2. Key Derivation

The shared secrets K_CL and K_PQ are the output from the two key exchange schemes X and Y, respectively, that instantiates an abstract hybrid key exchange method Section 2.1. The SSH shared secret K is derived as the hash algorithm specified in the named hybrid key exchange method name over the concatenation of K_PQ and K_CL:

        K = HASH(K_PQ, K_CL)

The resulting bytes are fed as to the key exchange method's hash function to generate encryption keys.

FIPS-compliance of shared secret concatenation. [NIST-SP-800-56C] or [NIST-SP-800-135] give NIST recommendations for key derivation methods in key exchange protocols. Some hybrid combinations may combine the shared secret from a NIST-approved algorithm (e.g., ECDH using the nistp256/secp256r1 curve) with a shared secret from a non-approved algorithm (e.g., post-quantum). [NIST-SP-800-56C] lists simple concatenation as an approved method for generation of a hybrid shared secret in which one of the constituent shared secret is from an approved method.

2.3. HASH

The derivation of encryption keys MUST be done according to Section 7.2 in [RFC4253] with a modification on the exchange hash H. The hybrid key exchange hash H is the result of computing the HASH, where HASH is the hash algorithm specified in the named hybrid key exchange method name, over the concatenation of the following

      string V_C, client identification string (CR and LF excluded)
      string V_S, server identification string (CR and LF excluded)
      string I_C, payload of the client's SSH_MSG_KEXINIT
      string I_S, payload of the server's SSH_MSG_KEXINIT
      string C_INIT, client message octet string
      string S_REPLY, server message octet string
      string K, SSH shared secret

The HASH functions used for the definitions in this specification are SHA-256 [nist-sha2] [RFC4634][EDNOTE: Update here if necessary].

2.4. Hybrid Key Exchange Method Names

The hybrid key exchange method names defined in this document are

      ecdh-nistp256-TBD1-sha256
      x25519-TBD1-sha256
      sntrup4591761x25519-sha512@tinyssh.org (currently implemented)

[EDNOTE: Placeholder. Algorithms will be identified after NIST Round 3 concludes.]

2.4.1. ecdh-nistp256-TBD1-sha256

ecdh-nistp256-TBD1-sha256 defines that the classical C_CL or S_CL from the client or server NIST P-256 curve public key as defined in [nist-sp800-186]. Private and public keys are generated as described therein. Public keys are defined as strings of 32 bytes for NIST P-256. The K_CL shared secret is generated from the exchanged C_CL and S_CL public keys as defined in [RFC5656] (key agreement method ecdh-sha2-nistp256) with SHA-256 [nist-sha2] [RFC4634] .

The post-quantum C_PQ or S_PQ string from the client and server are TBD1. The K_PQ shared secret is decapsulated from the ciphertext S_PQ using the client private key [EDNOTE: Placeholder. Update based on the algorithm identified after NIST Round 3 concludes.]

2.4.2. x25519-TBD1-sha256

x25519-TBD1-sha256 defines that the classical C_CL or S_CL from the client or server is Curve25519 public key as defined in [RFC7748]. Private and public keys are generated as described therein. Public keys are defined as strings of 32 bytes for Curve25519. The K_CL shared secret is generated from the exchanged C_CL and S_CL public keys as defined in [RFC8731] (key agreement method curve25519-sha256) with SHA-256 [nist-sha2] [RFC4634] .

The post-quantum C_PQ or S_PQ string from the client and server are TBD1. The K_PQ shared secret is decapsulated from the ciphertext S_PQ using the client private key as defined in [EDNOTE: Placeholder. Update based on the algorithm identified after NIST Round 3 concludes.]

3. Key Authentication

[EDNOTE: Discuss if hybrid auth keys which combine classical and PQ signatures are necessary. Since authentication cannot be broken retroactively, even if the PQ signature algorithms got broken, we could switch to a classical algorithm to at least keep the classical security. On the other hand, that would take time to deploy while these entities would be vulnerabile to impersonation attacks. Hybrid signatures add some overhead, but could provide the peace of mind of remaining secure with the classical algorithm without scrambling to deploy a change even if the PQ algorithms got broken. ]

3.1. Public Key Format 

      string    "ssh-TBD3"
      string    key

Here, 'key' is the x-octet public key described in the TBD3 specification.

[EDNOTE: Placeholder. Algorithms will be identified after NIST Round 3 concludes.]

3.2. Signature Format 

       string  "ssh-TBD3"
       string  signature

Here, 'signature' is the x-octet signature produced in accordance with the TBD3 specification.

[EDNOTE: Placeholder. Algorithms will be identified after NIST Round 3 concludes.]

3.3. Signing and Verification

Signatures are generated according to the procedure in TBD3 specification

Signatures are verified according to the procedure in TBD3 specification

[EDNOTE: Placeholder. Algorithms will be identified after NIST Round 3 concludes.]

4. Message Size

An implementation adhering to [RFC4253] must be able to support packets with an uncompressed payload length of 32768 bytes or less and a total packet size of 35000 bytes or less (including 'packet_length', 'padding_length', 'payload', 'random padding', and 'mac'). These numbers represent what must be 'minimally supported' by implementations. This can present a problem when using post-quantum key exchange schemes because some post-quantum schemes can produce much larger messages than what is normally produced by existing key exchange methods defined for SSH. This document does not define any named domain parameters (see Section 7) that cause any hybrid key exchange method related packets to exceed the minimally supported packet length. This document does not define behaviour in cases where a hybrid key exchange message cause a packet to exceed the minimally supported packet length.

6. IANA Considerations

This memo includes requests of IANA for SSH_MSG_HBR_INIT, SSH_MSG_HBR_REPLY, ecdh-nistp256-TBD1-sha256, x25519-TBD1-sha256, and ssh-TBD3.

7. Security Considerations

[EDNOTE: The security considerations given in [RFC5656] therefore also applies to the ECDH key exchange scheme defined in this document. Similarly for the X25519 document. PQ Algorithms are newer and standardized by NIST. And more. Should include something about the combination method for the KEM shared secrets. ]

[EDNOTE: Discussion on whether an IND-CCA KEM is required or whether IND-CPA suffices.] Any KEM used in the manner described in this document MUST explicitly be designed to be secure in the event that the public key is re-used, such as achieving IND-CCA2 security or having a transform like the Fujisaki-Okamoto transform [FO][HHK] applied. While it is recommended that implementations avoid reuse of KEM public keys, implementations that do reuse KEM public keys MUST ensure that the number of reuses of a KEM public key abides by any bounds in the specification of the KEM or subsequent security analyses. Implementations MUST NOT reuse randomness in the generation of KEM ciphertexts.

Public keys, ciphertexts, and secrets should be constant length. This document assumes that the length of each public key, ciphertext, and shared secret is fixed once the algorithm is fixed. This is the case for all Round 3 finalists and alternate candidates.

Note that variable-length secrets are, generally speaking, dangerous. In particular, when using key material of variable length and processing it using hash functions, a timing side channel may arise. In broad terms, when the secret is longer, the hash function may need to process more blocks internally. In some unfortunate circumstances, this has led to timing attacks, e.g. the Lucky Thirteen [LUCKY13] and Raccoon [RACCOON] attacks.

Therefore, this specification MUST only be used with algorithms which have fixed-length shared secrets (after the variant has been fixed by the algorithm identifier in the Method Names negotiation in Section 2.4).

8. References

8.1. Normative References

[RFC2119]
Bradner, S., "Key words for use in RFCs to Indicate Requirement Levels", BCP 14, RFC 2119, DOI 10.17487/RFC2119, , <https://www.rfc-editor.org/info/rfc2119>.
[RFC4251]
Ylonen, T. and C. Lonvick, Ed., "The Secure Shell (SSH) Protocol Architecture", RFC 4251, DOI 10.17487/RFC4251, , <https://www.rfc-editor.org/info/rfc4251>.
[RFC4252]
Ylonen, T. and C. Lonvick, Ed., "The Secure Shell (SSH) Authentication Protocol", RFC 4252, DOI 10.17487/RFC4252, , <https://www.rfc-editor.org/info/rfc4252>.
[RFC4253]
Ylonen, T. and C. Lonvick, Ed., "The Secure Shell (SSH) Transport Layer Protocol", RFC 4253, DOI 10.17487/RFC4253, , <https://www.rfc-editor.org/info/rfc4253>.

8.2. Informative References

[FO]
Fujisaki, E. and T. Okamoto, "Secure Integration of Asymmetric and Symmetric Encryption Schemes", DOI 10.1007/s00145-011-9114-1, Journal of Cryptology Vol. 26, pp. 80-101, , <https://doi.org/10.1007/s00145-011-9114-1>.
[HHK]
Hofheinz, D., Hövelmanns, K., and E. Kiltz, "A Modular Analysis of the Fujisaki-Okamoto Transformation", DOI 10.1007/978-3-319-70500-2_12, Theory of Cryptography pp. 341-371, , <https://doi.org/10.1007/978-3-319-70500-2_12>.
[I-D.hoffman-c2pq]
Hoffman, P., "The Transition from Classical to Post-Quantum Cryptography", Work in Progress, Internet-Draft, draft-hoffman-c2pq-07, , <https://tools.ietf.org/html/draft-hoffman-c2pq-07>.
[LUCKY13]
Al Fardan, N.J. and K.G. Paterson, "Lucky Thirteen: Breaking the TLS and DTLS record protocols", , <https://ieeexplore.ieee.org/iel7/6547086/6547088/06547131.pdf>.
[nist-sha2]
NIST, "FIPS PUB 180-4", , <https://nvlpubs.nist.gov/nistpubs/FIPS/NIST.FIPS.180-4.pdf>.
[NIST-SP-800-135]
National Institute of Standards and Technology (NIST), "Recommendation for Existing Application-Specific Key Derivation Functions", , <https://doi.org/10.6028/NIST.SP.800-135r1>.
[NIST-SP-800-56C]
National Institute of Standards and Technology (NIST), "Recommendation for Key-Derivation Methods in Key-Establishment Schemes", , <https://doi.org/10.6028/NIST.SP.800-56Cr2>.
[nist-sp800-186]
NIST, "SP 800-186", , <https://nvlpubs.nist.gov/nistpubs/SpecialPublications/NIST.SP.800-186-draft.pdf>.
[NIST_PQ]
NIST, "Post-Quantum Cryptography", , <https://csrc.nist.gov/projects/post-quantum-cryptography>.
[RACCOON]
Merget, R., Brinkmann, M., Aviram, N., Somorovsky, J., Mittmann, J., and J. Schwenk, "Raccoon Attack: Finding and Exploiting Most-Significant-Bit-Oracles in TLS-DH(E)", , <https://raccoon-attack.com/>.
[RFC4634]
Eastlake 3rd, D. and T. Hansen, "US Secure Hash Algorithms (SHA and HMAC-SHA)", RFC 4634, DOI 10.17487/RFC4634, , <https://www.rfc-editor.org/info/rfc4634>.
[RFC5656]
Stebila, D. and J. Green, "Elliptic Curve Algorithm Integration in the Secure Shell Transport Layer", RFC 5656, DOI 10.17487/RFC5656, , <https://www.rfc-editor.org/info/rfc5656>.
[RFC7748]
Langley, A., Hamburg, M., and S. Turner, "Elliptic Curves for Security", RFC 7748, DOI 10.17487/RFC7748, , <https://www.rfc-editor.org/info/rfc7748>.
[RFC8332]
Bider, D., "Use of RSA Keys with SHA-256 and SHA-512 in the Secure Shell (SSH) Protocol", RFC 8332, DOI 10.17487/RFC8332, , <https://www.rfc-editor.org/info/rfc8332>.
[RFC8709]
Harris, B. and L. Velvindron, "Ed25519 and Ed448 Public Key Algorithms for the Secure Shell (SSH) Protocol", RFC 8709, DOI 10.17487/RFC8709, , <https://www.rfc-editor.org/info/rfc8709>.
[RFC8731]
Adamantiadis, A., Josefsson, S., and M. Baushke, "Secure Shell (SSH) Key Exchange Method Using Curve25519 and Curve448", RFC 8731, DOI 10.17487/RFC8731, , <https://www.rfc-editor.org/info/rfc8731>.

Authors' Addresses

Panos Kampanakis
Cisco Systems
Douglas Stebila
University of Waterloo
Markus Friedl
OpenSSH
Torben Hansen
AWS
Dimitrios Sikeridis
University of New Mexico