Transport Layer Security J. Preuß Mattsson
Internet-Draft Ericsson
Intended status: Standards Track 19 January 2023
Expires: 23 July 2023
Compact ECDHE and ECDSA Encodings for TLS 1.3
draft-mattsson-tls-compact-ecc-03
Abstract
The encodings used in the ECDHE groups secp256r1, secp384r1, and
secp521r1 and the ECDSA signature algorithms ecdsa_secp256r1_sha256,
ecdsa_secp384r1_sha384, and ecdsa_secp521r1_sha512 have significant
overhead and the ECDSA encoding produces variable-length signatures.
This document defines new optimal fixed-length encodings and
registers new ECDHE groups and ECDSA signature algorithms using these
new encodings. The new encodings reduce the size of the ECDHE groups
with 33, 49, and 67 bytes and the ECDSA algorithms with an average of
7 bytes. These new encodings also work in DTLS 1.3 and are
especially useful in cTLS.
About This Document
This note is to be removed before publishing as an RFC.
The latest revision of this draft can be found at
https://emanjon.github.io/draft-mattsson-tls-compact-ecc/draft-
mattsson-tls-compact-ecc.html. Status information for this document
may be found at https://datatracker.ietf.org/doc/draft-mattsson-tls-
compact-ecc/.
Discussion of this document takes place on the Transport Layer
Security Working Group mailing list (mailto:tls@ietf.org), which is
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at https://www.ietf.org/mailman/listinfo/tls/.
Source for this draft and an issue tracker can be found at
https://github.com/emanjon/draft-mattsson-tls-compact-ecc.
Status of This Memo
This Internet-Draft is submitted in full conformance with the
provisions of BCP 78 and BCP 79.
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Table of Contents
1. Introduction . . . . . . . . . . . . . . . . . . . . . . . . 3
2. Conventions and Definitions . . . . . . . . . . . . . . . . . 3
3. Compact ECDHE Encoding . . . . . . . . . . . . . . . . . . . 3
3.1. Example Compact ECDHE Encoding . . . . . . . . . . . . . 4
3.2. Implementation Considerations for Compact
Representation . . . . . . . . . . . . . . . . . . . . . 5
4. Compact ECDSA Encoding . . . . . . . . . . . . . . . . . . . 6
4.1. Example Compact ECDSA Encoding . . . . . . . . . . . . . 6
5. Security Considerations . . . . . . . . . . . . . . . . . . . 7
6. IANA Considerations . . . . . . . . . . . . . . . . . . . . . 7
7. References . . . . . . . . . . . . . . . . . . . . . . . . . 7
7.1. Normative References . . . . . . . . . . . . . . . . . . 7
7.2. Informative References . . . . . . . . . . . . . . . . . 8
Acknowledgments . . . . . . . . . . . . . . . . . . . . . . . . . 9
Author's Address . . . . . . . . . . . . . . . . . . . . . . . . 9
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1. Introduction
The encodings used in the ECDHE groups secp256r1, secp384r1, and
secp521r1 and the ECDSA signature algorithms ecdsa_secp256r1_sha256,
ecdsa_secp384r1_sha384, and ecdsa_secp521r1_sha512 have significant
overhead and the ECDSA encodings produces variable-length signatures.
This document defines new optimal fixed-length encodings and
registers new ECDHE groups and ECDSA signature algorithms using these
new encodings. The new encodings reduce the size of the ECDHE groups
with 33, 49, and 67 bytes and the ECDSA algorithms with an average of
7 bytes. These new encodings also work in DTLS 1.3 [RFC9147] and are
especially useful in cTLS [I-D.ietf-tls-ctls]. When secp256r1 and
ecdsa_secp256r1_sha256 are used as a replacement for the the old
encdodings they reduce the size of the TLS handshake with on average
80 bytes. The new encodings have the same security properties and
requirements as the old encodings.
2. Conventions and Definitions
The key words "MUST", "MUST NOT", "REQUIRED", "SHALL", "SHALL NOT",
"SHOULD", "SHOULD NOT", "RECOMMENDED", "NOT RECOMMENDED", "MAY", and
"OPTIONAL" in this document are to be interpreted as described in
BCP 14 [RFC2119] [RFC8174] when, and only when, they appear in all
capitals, as shown here.
3. Compact ECDHE Encoding
The encoding specified in [RFC8446] of the ECDHE groups secp256r1,
secp384r1, and secp521r1 [RFC8422] have significant overhead. This
document specifies a new optimal fixed-length encoding for the
groups. The new encoding is defined as a compression of the
UncompressedPointRepresentation structure. Given a
UncompressedPointRepresentation structure [RFC8446]
struct {
uint8 legacy_form = 4;
opaque X[coordinate_length];
opaque Y[coordinate_length];
} UncompressedPointRepresentation;
the legacy_form and Y field are omitted to create a
CompactRepresentation structure.
struct {
opaque X[coordinate_length];
} CompactRepresentation;
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The resulting groups are called secp256r1_compact, secp384r1_compact,
and secp521r1_compact. The new encodings have CompactRepresentation
structures of length 32, 48, and 66 bytes, and reduce the size with
33, 49, and 67 bytes respectively. For secp256r1_compact,
secp384r1_compact, and secp521r1_compact the opaque key_exchange
field contains the serialized value of the CompactRepresentation
struct.
+=======+===================+=============+=================+
| Value | Description | Recommended | Reference |
+=======+===================+=============+=================+
| TBD1 | secp256r1_compact | Y | [This-Document] |
+-------+-------------------+-------------+-----------------+
| TBD2 | secp384r1_compact | Y | [This-Document] |
+-------+-------------------+-------------+-----------------+
| TBD3 | secp521r1_compact | Y | [This-Document] |
+-------+-------------------+-------------+-----------------+
Table 1: Compact ECDHE Groups
The difference between compact representation [RFC6090] and point
compression [SECG]) is that point compression also communicates the
sign bit of the y-coordinate along with the x-coordinate while
compact representation only transmits the x-coordinate.
3.1. Example Compact ECDHE Encoding
The following shows an example compact ECDHE encoding. Figure 1
shows a 65 bytes ecdsa_secp256r1_sha256
UncompressedPointRepresentation structure.
04 A6 DA 73 92 EC 59 1E 17 AB FD 53 59 64 B9 98
94 D1 3B EF B2 21 B3 DE F2 EB E3 83 0E AC 8F 01
51 81 26 77 C4 D6 D2 23 7E 85 CF 01 D6 91 0C FB
83 95 4E 76 BA 73 52 83 05 34 15 98 97 E8 06 57
80
Figure 1: secp256r1
Figure 2 shows the 32 bytes secp256r1_compact CompactRepresentation
structure encoding of the same key share.
A6 DA 73 92 EC 59 1E 17 AB FD 53 59 64 B9 98 94
D1 3B EF B2 21 B3 DE F2 EB E3 83 0E AC 8F 01 51
Figure 2: secp256r1_compact
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3.2. Implementation Considerations for Compact Representation
For compatibility with APIs a compressed y-coordinate might be
required. For validation or for compatibility with APIs that do not
support the full [SECG] format an uncompressed y-coordinate might be
required (using the notation in [SECG]):
* If a compressed y-coordinate is required, then the value ~yp set
to zero can be used. The compact representation described above
can in such a case be transformed into the SECG point compressed
format by prepending X with the single byte 0x02 (i.e., M =
0x02 || X).
* If an uncompressed y-coordinate is required, then a y-coordinate
has to be calculated following Section 2.3.4 of [SECG] or
Appendix C of [RFC6090]. Any of the square roots (see [SECG] or
[RFC6090]) can be used. The uncompressed SECG format is M =
0x04 || X || Y.
For example: The curve P-256 has the parameters (using the notation
in [RFC6090])
* p = 2^256 - 2^224 + 2^192 + 2^96 - 1
* a = -3
* b = 410583637251521421293261297800472684091144410159937255
54835256314039467401291
Given an example x:
* x = 115792089183396302095546807154740558443406795108653336
398970697772788799766525
we can calculate y as the square root w = (x^3 + a ⋅ x + b)^((p +
1)/4) (mod p)
* y = 834387180070192806820075864918626005281451259964015754
16632522940595860276856
Note that this does not guarantee that (x, y) is on the correct
elliptic curve. A full validation according to Section 5.6.2.3.3 of
[SP-800-56A] is done by also checking that 0 ≤ x < p and that y^2 ≡
x^3 + a ⋅ x + b (mod p). The implementation MUST perform public-key
validation.
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4. Compact ECDSA Encoding
The variable-length encoding of the ECDSA signature algorithms
ecdsa_secp256r1_sha256, ecdsa_secp384r1_sha384, and
ecdsa_secp521r1_sha512 specified in [RFC8446] have significant
overhead.
This document specifies a new optimal fixed-length encoding for the
algorithms. The new encoding is defined as a compression of the DER-
encoded ECDSA-Sig-Value structure. Given a DER-encoded ECDSA-Sig-
Value structure [RFC8422]
Ecdsa-Sig-Value ::= SEQUENCE {
r INTEGER,
s INTEGER
}
the SEQUENCE type, INTEGER type, and length fields are omitted and if
necessary the two INTEGER value fields are truncated (at most a
single zero byte) or left padded with zeroes to the fixed length L.
For secp256r1, secp384r1, and secp521r1, L is 32, 48, and 66 bytes
respectively. The resulting signatures are called
ecdsa_secp256r1_sha256_compact, ecdsa_secp384r1_sha384_compact, and
ecdsa_secp521r1_sha512_compact and has length 64, 96, and 132 bytes
respectively. The new encodings reduce the size of the signatures
with an average of 7 bytes. For secp256r1_compact,
secp384r1_compact, and secp521r1_compact the opaque signature field
contains the compressed Ecdsa-Sig-Value.
+=====+================================+===========+===============+
|Value| Description |Recommended|Reference |
+=====+================================+===========+===============+
| TBD4| ecdsa_secp256r1_sha256_compact | Y|[This-Document]|
+-----+--------------------------------+-----------+---------------+
| TBD5| ecdsa_secp384r1_sha384_compact | Y|[This-Document]|
+-----+--------------------------------+-----------+---------------+
| TBD6| ecdsa_secp521r1_sha512_compact | Y|[This-Document]|
+-----+--------------------------------+-----------+---------------+
Table 2: Compact ECDSA Signature Algorithms
4.1. Example Compact ECDSA Encoding
The following shows an example compact ECDSA encoding. Figure 3
shows a 71 bytes DER encoded ecdsa_secp256r1_sha256 ECDSA-Sig-Value
structure. The values on the left are the ASN.1 tag (in hexadecimal)
and the length (in decimal).
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30 69: SEQUENCE {
02 33: INTEGER
00 D7 A4 D3 4B D5 4F 55 FE E1 A8 96 25 67 8C 3D
D5 E5 F6 0D AC 73 EC 94 0C 5C 7B 93 04 A0 20 84
A9
02 32: INTEGER
28 9F 59 5E D4 88 B9 AC 68 9A 3D 19 2B 1A 8B B3
8F 34 AF 78 74 C0 59 C9 80 6A 1F 38 26 93 53 E8
}
Figure 3: ecdsa_secp256r1_sha256
Figure 4 shows the 64 bytes ecdsa_secp256r1_sha256_compact encoding
of the same signature.
D7 A4 D3 4B D5 4F 55 FE E1 A8 96 25 67 8C 3D D5
E5 F6 0D AC 73 EC 94 0C 5C 7B 93 04 A0 20 84 A9
28 9F 59 5E D4 88 B9 AC 68 9A 3D 19 2B 1A 8B B3
8F 34 AF 78 74 C0 59 C9 80 6A 1F 38 26 93 53 E8
Figure 4: ecdsa_secp256r1_sha256_compact
5. Security Considerations
The new encodings are just encodings and have the same security
properties and security requirements as the old encodings. Compact
representation of a ECDHE key share produces the same shared secret
as the uncompressed encoding and does not change any requirements on
point validation, the peers MUST validate each other's public key
shares.
6. IANA Considerations
IANA is requested to update the TLS Supported Groups registry
[RFC8447] under the Transport Layer Security (TLS) Parameters heading
with the contents of Table 1.
IANA is requested to update the TLS SignatureScheme registry
[RFC8447] under the Transport Layer Security (TLS) Parameters heading
with the contents of Table 2.
7. References
7.1. Normative References
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[RFC2119] Bradner, S., "Key words for use in RFCs to Indicate
Requirement Levels", BCP 14, RFC 2119,
DOI 10.17487/RFC2119, March 1997,
.
[RFC8174] Leiba, B., "Ambiguity of Uppercase vs Lowercase in RFC
2119 Key Words", BCP 14, RFC 8174, DOI 10.17487/RFC8174,
May 2017, .
[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,
.
[RFC8447] Salowey, J. and S. Turner, "IANA Registry Updates for TLS
and DTLS", RFC 8447, DOI 10.17487/RFC8447, August 2018,
.
7.2. Informative References
[I-D.ietf-tls-ctls]
Rescorla, E., Barnes, R., Tschofenig, H., and B. M.
Schwartz, "Compact TLS 1.3", Work in Progress, Internet-
Draft, draft-ietf-tls-ctls-07, 3 January 2023,
.
[RFC6090] McGrew, D., Igoe, K., and M. Salter, "Fundamental Elliptic
Curve Cryptography Algorithms", RFC 6090,
DOI 10.17487/RFC6090, February 2011,
.
[RFC9147] Rescorla, E., Tschofenig, H., and N. Modadugu, "The
Datagram Transport Layer Security (DTLS) Protocol Version
1.3", RFC 9147, DOI 10.17487/RFC9147, April 2022,
.
[SECG] "Standards for Efficient Cryptography 1 (SEC 1)", May
2009, .
[SP-800-56A]
Barker, E., Chen, L., Roginsky, A., Vassilev, A., and R.
Davis, "Recommendation for Pair-Wise Key-Establishment
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Schemes Using Discrete Logarithm Cryptography",
NIST Special Publication 800-56A Revision 3, April 2018,
.
Acknowledgments
The authors want to thank Dan Brown, Scott Fluhrer, Erik Thormarker,
and Hannes Tschofenig for their valuable comments and feedback.
Author's Address
John Preuß Mattsson
Ericsson AB
SE-164 80 Stockholm
Sweden
Email: john.mattsson@ericsson.com
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