Network Working Group | L. Bruckert |

Internet-Draft | J. Merkle |

Intended status: Informational | secunet Security Networks |

Expires: March 6, 2020 | M. Lochter |

BSI | |

September 3, 2019 |

ECC Brainpool Curves for Transport Layer Security (TLS) Version 1.3

draft-bruckert-brainpool-for-tls13-06

ECC Brainpool curves were an option for authentication and key exchange in the Transport Layer Security (TLS) protocol version 1.2, but were deprecated by the IETF for use with TLS version 1.3 because they had little usage. However, these curves have not been shown to have significant cryptographical weaknesses, and there is some interest in using several of these curves in TLS 1.3.

This document provides the necessary protocol mechanisms for using ECC Brainpool curves in TLS 1.3. This approach is not endorsed by the IETF.

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/.

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This Internet-Draft will expire on March 6, 2020.

Copyright (c) 2019 IETF Trust and the persons identified as the document authors. All rights reserved.

This document is subject to BCP 78 and the IETF Trust's Legal Provisions Relating to IETF Documents (https://trustee.ietf.org/license-info) in effect on the date of publication of this document. Please review these documents carefully, as they describe your rights and restrictions with respect to this document. Code Components extracted from this document must include Simplified BSD License text as described in Section 4.e of the Trust Legal Provisions and are provided without warranty as described in the Simplified BSD License.

- 1. Introduction
- 2. Requirements Terminology
- 3. Brainpool NamedGroup Types
- 4. Brainpool SignatureScheme Types
- 5. IANA Considerations
- 6. Security Considerations
- 7. References
- 7.1. Normative References
- 7.2. Informative References
- Appendix A. Test Vectors
- A.1. 256 Bit Curve
- A.2. 384 Bit Curve
- A.3. 512 Bit Curve
- Authors' Addresses

[RFC5639] specifies a new set of elliptic curve groups over finite prime fields for use in cryptographic applications. These groups, denoted as ECC Brainpool curves, were generated in a verifiably pseudo-random way and comply with the security requirements of relevant standards from ISO [ISO1] [ISO2], ANSI [ANSI1], NIST [FIPS], and SecG [SEC2].

[RFC8422] defines the usage of elliptic curves for authentication and key agreement in TLS 1.2 and earlier versions, and [RFC7027] defines the usage of the ECC Brainpool curves for authentication and key exchange in TLS. The latter is applicable to TLS 1.2 and earlier versions, but not to TLS 1.3 that deprecates the ECC Brainpool Curve IDs defined in [RFC7027] due to the lack of widespread deployment However, there is some interest in using these curves in TLS 1.3.

The negotiation of ECC Brainpool Curves for key exchange in TLS 1.3 according to [RFC8446] requires the definition and assignment of additional NamedGroup IDs. This document provides the necessary definition and assignment of additional SignatureScheme IDs for using three ECC Brainpool Curves from [RFC5639].

This approach is not endorsed by the IETF. Implementers and deployers need to be aware of the strengths and weaknesses of all security mechanisms that they use.

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].

According to [RFC8446], the "supported_groups" extension is used for the negotiation of Diffie-Hellman groups and elliptic curve groups for key exchange during a handshake starting a new TLS session. This document adds new named groups for three elliptic curves defined in [RFC5639] to the "supported_groups" extension as follows.

enum { brainpoolP256r1tls13(0x001f), brainpoolP384r1tls13(0x0020), brainpoolP512r1tls13(0x0021) } NamedGroup;

The encoding of ECDHE parameters for sec256r1, secp384r1, and secp521r1 as defined in section 4.2.8.2 of [RFC8446] also applies to this document.

Test vectors for a Diffie-Hellman key exchange using these elliptic curves are provided in Appendix A.

According to [RFC8446], the name space SignatureScheme is used for the negotiation of elliptic curve groups for authentication via the "signature_algorithms" extension. Besides, it is required to specify the hash function that is used to hash the message before signing. This document adds new SignatureScheme types for three elliptic curves defined in [RFC5639] as follows.

enum { ecdsa_brainpoolP256r1tls13_sha256(0x081A), ecdsa_brainpoolP384r1tls13_sha384(0x081B), ecdsa_brainpoolP512r1tls13_sha512(0x081C) } SignatureScheme;

IANA is requested to update the references for the ECC Brainpool curves listed in the Transport Layer Security (TLS) Parameters registry "TLS Supported Groups" [IANA-TLS] to this document.

Value | Description | DTLS-OK | Recommended | Reference |
---|---|---|---|---|

0x001f | brainpoolP256r1tls13 | Y | N | This doc |

0x0020 | brainpoolP384r1tls13 | Y | N | This doc |

0x0021 | brainpoolP512r1tls13 | Y | N | This doc |

IANA is requested to update the references for the ECC Brainpool curves in the Transport Layer Security (TLS) Parameters registry "TLS SignatureScheme" [IANA-TLS] to this document.

Value | Description | DTLS-OK | Recommended | Reference |
---|---|---|---|---|

0x081A | ecdsa_brainpoolP256r1tls13_sha256 | Y | N | This doc |

0x081B | ecdsa_brainpoolP384r1tls13_sha384 | Y | N | This doc |

0x081C | ecdsa_brainpoolP512r1tls13_sha512 | Y | N | This doc |

The security considerations of [RFC8446] apply accordingly.

The confidentiality, authenticity and integrity of the TLS communication is limited by the weakest cryptographic primitive applied. In order to achieve a maximum security level when using one of the elliptic curves from Table 1 for key exchange and / or one of the signature algorithms from Table 2 for authentication in TLS, the key derivation function, the algorithms and key lengths of symmetric encryption and message authentication as well as the algorithm, bit length and hash function used for signature generation should be chosen at commensurate strengths, for example according to the recommendations of [NIST800-57] and [RFC5639]. Furthermore, the private Diffie-Hellman keys should be generated from a random keystream with a length equal to the length of the order of the group E(GF(p)) defined in [RFC5639]. The value of the private Diffie-Hellman keys should be less than the order of the group E(GF(p)).

When using ECDHE key agreement with the curves brainpoolP256r1tls13, brainpoolP384r1tls13 or brainpoolP512r1tls13, the peers MUST validate each other's public value Q by ensuring that the point is a valid point on the elliptic curve. If this check is not conducted, an attacker can force the key exchange into a small subgroup, and the resulting shared secret can be guessed with significantly less effort.

Implementations of elliptic curve cryptography for TLS may be susceptible to side-channel attacks. Particular care should be taken for implementations that internally transform curve points to points on the corresponding "twisted curve", using the map (x',y') = (x*Z^2, y*Z^3) with the coefficient Z specified for that curve in [RFC5639], in order to take advantage of an an efficient arithmetic based on the twisted curve's special parameters (A = -3): although the twisted curve itself offers the same level of security as the corresponding random curve (through mathematical equivalence), arithmetic based on small curve parameters may be harder to protect against side-channel attacks. General guidance on resistence of elliptic curve cryptography implementations against side-channel-attacks is given in [BSI1] and [HMV].

[IANA-TLS] |
Internet Assigned Numbers Authority, "Transport Layer Security (TLS) Parameters" |

[RFC2119] |
Bradner, S., "Key words for use in RFCs to Indicate Requirement Levels", BCP 14, RFC 2119, March 1997. |

[RFC5639] |
Lochter, M. and J. Merkle, "Elliptic Curve Cryptography (ECC) Brainpool Standard Curves and Curve Generation", RFC 5639, March 2010. |

[RFC7027] |
Merkle, J. and M. Lochter, "Elliptic Curve Cryptography (ECC) Brainpool Curves for Transport Layer Security (TLS)", RFC 7027, DOI 10.17487/RFC7027, October 2013. |

[RFC8422] |
Nir, Y., Josefsson, S. and M. Pegourie-Gonnard, "Elliptic Curve Cryptography (ECC) Cipher Suites for Transport Layer Security (TLS) Versions 1.2 and Earlier", RFC 8422, DOI 10.17487/RFC8422, August 2018. |

[RFC8446] |
Rescorla, E., "The Transport Layer Security (TLS) Protocol Version 1.3", RFC 8446, DOI 10.17487/RFC8446, August 2018. |

This non-normative Appendix provides some test vectors for example Diffie-Hellman key exchanges using each of the curves defined in Table 1 . In all of the following sections the following notation is used: [SEC1].

- d_A: the secret key of party A
- x_qA: the x-coordinate of the public key of party A
- y_qA: the y-coordinate of the public key of party A
- d_B: the secret key of party B
- x_qB: the x-coordinate of the public key of party B
- y_qB: the y-coordinate of the public key of party B
- x_Z: the x-coordinate of the shared secret that results from completion of the Diffie-Hellman computation, i.e. the hex representation of the pre-master secret
- y_Z: the y-coordinate of the shared secret that results from completion of the Diffie-Hellman computation

The field elements x_qA, y_qA, x_qB, y_qB, x_Z, y_Z are represented as hexadecimal values using the FieldElement-to-OctetString conversion method specified in

Curve brainpoolP256r1

- dA = 81DB1EE100150FF2EA338D708271BE38300CB54241D79950F77B063039804F1D
- x_qA = 44106E913F92BC02A1705D9953A8414DB95E1AAA49E81D9E85F929A8E3100BE5
- y_qA = 8AB4846F11CACCB73CE49CBDD120F5A900A69FD32C272223F789EF10EB089BDC
- dB = 55E40BC41E37E3E2AD25C3C6654511FFA8474A91A0032087593852D3E7D76BD3
- x_qB = 8D2D688C6CF93E1160AD04CC4429117DC2C41825E1E9FCA0ADDD34E6F1B39F7B
- y_qB = 990C57520812BE512641E47034832106BC7D3E8DD0E4C7F1136D7006547CEC6A
- x_Z = 89AFC39D41D3B327814B80940B042590F96556EC91E6AE7939BCE31F3A18BF2B
- y_Z = 49C27868F4ECA2179BFD7D59B1E3BF34C1DBDE61AE12931648F43E59632504DE

Curve brainpoolP384r1

- dA = 1E20F5E048A5886F1F157C74E91BDE2B98C8B52D58E5003D57053FC4B0BD65D6F15EB5D1EE1610DF870795143627D042
- x_qA = 68B665DD91C195800650CDD363C625F4E742E8134667B767B1B476793588F885AB698C852D4A6E77A252D6380FCAF068
- y_qA = 55BC91A39C9EC01DEE36017B7D673A931236D2F1F5C83942D049E3FA20607493E0D038FF2FD30C2AB67D15C85F7FAA59
- dB = 032640BC6003C59260F7250C3DB58CE647F98E1260ACCE4ACDA3DD869F74E01F8BA5E0324309DB6A9831497ABAC96670
- x_qB = 4D44326F269A597A5B58BBA565DA5556ED7FD9A8A9EB76C25F46DB69D19DC8CE6AD18E404B15738B2086DF37E71D1EB4
- y_qB = 62D692136DE56CBE93BF5FA3188EF58BC8A3A0EC6C1E151A21038A42E9185329B5B275903D192F8D4E1F32FE9CC78C48
- x_Z = 0BD9D3A7EA0B3D519D09D8E48D0785FB744A6B355E6304BC51C229FBBCE239BBADF6403715C35D4FB2A5444F575D4F42
- y_Z = 0DF213417EBE4D8E40A5F76F66C56470C489A3478D146DECF6DF0D94BAE9E598157290F8756066975F1DB34B2324B7BD

Curve brainpoolP512r1

- dA = 16302FF0DBBB5A8D733DAB7141C1B45ACBC8715939677F6A56850A38BD87BD59B09E80279609FF333EB9D4C061231FB26F92EEB04982A5F1D1764CAD57665422
- x_qA = 0A420517E406AAC0ACDCE90FCD71487718D3B953EFD7FBEC5F7F27E28C6149999397E91E029E06457DB2D3E640668B392C2A7E737A7F0BF04436D11640FD09FD
- y_qA = 72E6882E8DB28AAD36237CD25D580DB23783961C8DC52DFA2EC138AD472A0FCEF3887CF62B623B2A87DE5C588301EA3E5FC269B373B60724F5E82A6AD147FDE7
- dB = 230E18E1BCC88A362FA54E4EA3902009292F7F8033624FD471B5D8ACE49D12CFABBC19963DAB8E2F1EBA00BFFB29E4D72D13F2224562F405CB80503666B25429
- x_qB = 9D45F66DE5D67E2E6DB6E93A59CE0BB48106097FF78A081DE781CDB31FCE8CCBAAEA8DD4320C4119F1E9CD437A2EAB3731FA9668AB268D871DEDA55A5473199F
- y_qB = 2FDC313095BCDD5FB3A91636F07A959C8E86B5636A1E930E8396049CB481961D365CC11453A06C719835475B12CB52FC3C383BCE35E27EF194512B71876285FA
- x_Z = A7927098655F1F9976FA50A9D566865DC530331846381C87256BAF3226244B76D36403C024D7BBF0AA0803EAFF405D3D24F11A9B5C0BEF679FE1454B21C4CD1F
- y_Z = 7DB71C3DEF63212841C463E881BDCF055523BD368240E6C3143BD8DEF8B3B3223B95E0F53082FF5E412F4222537A43DF1C6D25729DDB51620A832BE6A26680A2

Leonie Bruckert
secunet Security Networks
Ammonstr. 74
01067 Dresden,
Germany
Phone: +49 201 5454 3819
EMail: leonie.bruckert@secunet.com

Johannes Merkle
secunet Security Networks
Mergenthaler Allee 77
65760 Eschborn,
Germany
Phone: +49 201 5454 3091
EMail: johannes.merkle@secunet.com

Manfred Lochter
BSI
Postfach 200363
53133 Bonn,
Germany
Phone: +49 228 9582 5643
EMail: manfred.lochter@bsi.bund.de