Network Working Group R. Barnes
Internet-Draft Cisco
Intended status: Informational K. Bhargavan
Expires: July 22, 2019 Inria
January 18, 2019
Hybrid Public Key Encryption
draft-barnes-cfrg-hpke-00
Abstract
This document describes a scheme for hybrid public-key encryption
(HPKE). This scheme provides authenticated public key encryption of
arbitrary-sized plaintexts for a recipient public key. HPKE works
for any Diffie-Hellman group and has a strong security proof. We
provide instantiations of the scheme using standard and efficient
primitives.
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the Trust Legal Provisions and are provided without warranty as
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Table of Contents
1. Introduction . . . . . . . . . . . . . . . . . . . . . . . . 2
2. Requirements Notation . . . . . . . . . . . . . . . . . . . . 3
3. Security Properties . . . . . . . . . . . . . . . . . . . . . 3
4. Notation . . . . . . . . . . . . . . . . . . . . . . . . . . 3
5. Hybrid Public Key Encryption . . . . . . . . . . . . . . . . 3
5.1. Key Encapsulation and Decapsulation . . . . . . . . . . . 4
5.2. Encryption and Decryption . . . . . . . . . . . . . . . . 5
6. Ciphersuites . . . . . . . . . . . . . . . . . . . . . . . . 6
7. Security Considerations . . . . . . . . . . . . . . . . . . . 8
8. IANA Considerations . . . . . . . . . . . . . . . . . . . . . 8
9. References . . . . . . . . . . . . . . . . . . . . . . . . . 8
9.1. Normative References . . . . . . . . . . . . . . . . . . 8
9.2. Informative References . . . . . . . . . . . . . . . . . 9
Appendix A. Possible TODOs . . . . . . . . . . . . . . . . . . . 9
Authors' Addresses . . . . . . . . . . . . . . . . . . . . . . . 10
1. Introduction
Hybrid public-key encryption (HPKE) is a substantially more efficient
solution than traditional public key encryption techniques such as
those based on RSA or ElGamal. Encrypted messages convey a single
ciphertext and authentication tag alongside a short public key, which
may be further compressed. The key size and computational complexity
of elliptic curve cryptographic primitives for authenticated
encryption therefore make it compelling for a variety of use case.
This type of public key encryption has many applications in practice,
for example, in PGP [RFC6637] and in the developing Messaging Layer
Security protocol [I-D.ietf-mls-protocol].
Currently, there are numerous competing and non-interoperable
standards and variants for hybrid encryption, including ANSI X9.63
[ANSI], IEEE 1363a [IEEE], ISO/IEC 18033-2 [ISO], and SECG SEC 1
[SECG]. Lack of a single standard makes selection and deployment of
a compatible, cross-platform and ecosystem solution difficult to
define. This document defines an HPKE scheme that provides a subset
of the functions provided by the collection of schemes above, but
specified with sufficient clarity that they can be interoperably
implemented and formally verified.
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2. Requirements Notation
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
BCP14 [RFC2119] [RFC8174] when, and only when, they appear in all
capitals, as shown here.
3. Security Properties
As a hybrid authentication encryption algorithm, we desire security
against (adaptive) chosen ciphertext attacks (IND-CCA2 secure). The
HPKE variants described in this document achieve this property under
the Random Oracle model assuming the gap Computational Diffie Hellman
(CDH) problem is hard [S01].
4. Notation
The following terms are used throughout this document to describe the
operations, roles, and behaviors of HPKE:
o Initiator (I): Sender of an encrypted message.
o Responder (R): Receiver of an encrypted message.
o Ephemeral (E): A fresh random value meant for one-time use.
o "||": Concatenation of octet strings, i.e., "0x01 || 0x02 =
0x0102".
5. Hybrid Public Key Encryption
HPKE takes as input a recipient public key "pkR" and plaintext "pt"
and produces, as output, an ephemeral public key "pkE" and ciphertext
"ct". The ciphertext is encrypted such that only the owner of the
private key associated with "pkR" can decrypt the ciphertext "ct" to
recover the plaintext "pt". In the algorithms defined below, we also
allow the inclusion of Additional Authenticated Data (AAD) which is
authenticated, but not encrypted (as with an AEAD encryption
algorithm).
HPKE variants rely on the following primitives:
o A Diffie-Hellman scheme:
* GenerateKeyPair(): Generate an ephemeral key pair "(sk, pk)"
for the DH group in use
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* DH(sk, pk): Perform a non-interactive DH exchange using the
private key sk and public key pk to produce a shared secret
* Marshal(pk): Produce a fixed-length octet string encoding the
public key "pk"
o A Key Derivation Function:
* Extract(salt, IKM): Extract a pseudorandom key of fixed length
from input keying material "IKM" and an optional octet string
"salt"
* Expand(PRK, info, L): Expand a pseudorandom key "PRK" using
optional string "info" into "L" bytes of output keying material
* Nh: The output size of the Extract function
o An AEAD encryption algorithm [RFC5116]:
* Seal(key, nonce, aad, pt): Encrypt and authenticate plaintext
"pt" with associated data "aad" using secret key "key" and
nonce "nonce", yielding ciphertext and tag "ct"
* Open(key, nonce, aad, ct): Decrypt ciphertext "ct" using
associated data "aad" with secret key "key" and nonce "nonce",
returning plaintext message "pt" or an error
* Nk: The length in octets of a key for this algorithm
* Nn: The length in octets of a nonce for this algorithm
A set of concrete instantiations of these primitives is provided in
Section 6. Ciphersuite values are one octet long.
In the algorithms that follow, let "Nk" be the length in bytes of a
symmetric key suitable for encryption and decryption with the AEAD
scheme in use, and let "Nn" be the length of a in bytes of a suitable
nonce.
5.1. Key Encapsulation and Decapsulation
HPKE uses DH to generate an ephemeral secret that is shared between
the sender and the receiver, then uses this secret to generate one or
more (key, nonce) pairs for use with an Authenticated Encryption with
Associated Data (AEAD) algorithm.
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In the below algorithms, the various functions and variables specific
to the underlying primitives (Expand, Nn, etc.) are understood to be
in the context of the specified ciphersuite.
The SetupI() procedure takes as input a ciphersuite (see Section 6),
peer public key, and info string and generates a shared secret value
and a public key that the receiver can use to recover shared secret.
Input: ciphersuite, pkR, info
1. (skE, pkE) = GenerateKeyPair()
2. zz = DH(skE, pkR)
3. secret = Extract(0^Nh, zz)
4. context = ciphersuite || Marshal(pkE) || Marshal(pkR) || info
6. keyIR = Expand(secret, "hpke key" || context, Nk)
8. nonceIR = Expand(secret, "hpke nonce" || context, Nn)
Output: pkE, keyIR, nonceIR
In step 3, the octet string "0^Nh" is the all-zero octet string of
length "Nh". Note that step 4 includes the recipient public key in
the key derivation step so that the derived key is bound to the
recipient.
The SetupR() procedure takes as input a ciphersuite, encapsulated
secret, secret key, and info string to produce a shared secret.
Input: ciphersuite, pkE, skR, info
1. zz = DH(skR, pkE)
2. secret = Extract(0^Nh, zz)
3. context = ciphersuite || Marshal(pkE) || Marshal(pkR) || info
4. keyIR = Expand(secret, "hpke key" || context, Nk)
5. nonceIR = Expand(secret, "hpke nonce" || context, Nn)
Output: keyIR, nonceIR
5.2. Encryption and Decryption
HPKE encryption "Encrypt()" and decryption "Decrypt()" are single-
shot so shared secrets are never re-used. "Encrypt()" takes as input
plaintext "pt" and associated data "ad" to encrypt, along with the
ciphersuite, Responder public key, and an info string, and produces a
ciphertext "ct" and encapsulated ephemeral key "secretIR", as
follows:
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Input: ciphersuite, pkR, info, ad, pt
1. pkE, keyIR, nonceIR = SetupI(ciphersuite, pkR, info)
2. ct = Seal(keyIR, nonceIR, ad, pt)
Output: ct, pkE
Decryption "Decrypt()" mirrors encryption, as follows:
Input: ciphersuite, skR, pkE, info, ad, ct
1. keyIR, nonceIR = Decap(ciphersuite, pkE, pkR, info)
2. pt = Open(keyIR, nonceIR, ad, ct)
Output: pt
6. Ciphersuites
The HPKE variants as presented will function correctly for any
combination of primitives that provides the functions described
above. In this section, we provide specific instantiations of these
primitives for standard groups, including: Curve25519, Curve448
[RFC7748], and the NIST curves (P-256, P-384, P-512).
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+-------------------------+---------+----------+-------------+------+
| Configuration | DH | KDF | AEAD | Valu |
| | Group | | | e |
+-------------------------+---------+----------+-------------+------+
| X25519-HKDF-SHA256-AES- | Curve25 | HKDF- | AES-GCM-128 | 0x01 |
| GCM-128 | 519 | SHA256 | | |
| | | | | |
| X25519-HKDF- | Curve25 | HKDF- | ChaCha20Pol | 0x02 |
| SHA256-ChaCha20Poly1305 | 519 | SHA256 | y1305 | |
| | | | | |
| X448-HKDF-SHA512-AES- | Curve44 | HKDF- | AES-GCM-256 | 0x03 |
| GCM-256 | 8 | SHA512 | | |
| | | | | |
| X448-HKDF- | Curve44 | HKDF- | ChaCha20Pol | 0x04 |
| SHA512-ChaCha20Poly1305 | 8 | SHA512 | y1305 | |
| | | | | |
| P256-HKDF-SHA256-AES- | P-256 | HKDF- | AES-GCM-128 | 0x05 |
| GCM-128 | | SHA256 | | |
| | | | | |
| P256-HKDF- | P-256 | HKDF- | ChaCha20Pol | 0x06 |
| SHA256-ChaCha20Poly1305 | | SHA256 | y1305 | |
| | | | | |
| P521-HKDF-SHA512-AES- | P-521 | HKDF- | AES-GCM-256 | 0x07 |
| GCM-256 | | SHA512 | | |
| | | | | |
| P521-HKDF- | P-521 | HKDF- | ChaCha20Pol | 0x08 |
| SHA512-ChaCha20Poly1305 | | SHA512 | y1305 | |
+-------------------------+---------+----------+-------------+------+
For the NIST curves P-256 and P-521, the Marshal function of the DH
scheme produces the normal (non-compressed) representation of the
public key, according to [SECG]. When these curves are used, the
recipient of an HPKE ciphertext MUST validate that the ephemeral
public key "pkE" is on the curve. The relevant validation procedures
are defined in [keyagreement]
For the CFRG curves Curve25519 and Curve448, the Marshal function is
the identity function, since these curves already use fixed-length
octet strings for public keys.
The values "Nk" and "Nn" for the AEAD algorithms referenced above are
as follows:
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+------------------+----+----+
| AEAD | Nk | Nn |
+------------------+----+----+
| AES-GCM-128 | 16 | 12 |
| | | |
| AES-GCM-256 | 32 | 12 |
| | | |
| ChaCha20Poly1305 | 32 | 12 |
+------------------+----+----+
7. Security Considerations
[[ TODO ]]
8. IANA Considerations
[[ OPEN ISSUE: Should the above table be in an IANA registry? ]]
9. References
9.1. Normative References
[ANSI] "Public Key Cryptography for the Financial Services
Industry -- Key Agreement and Key Transport Using Elliptic
Curve Cryptography", n.d..
[IEEE] "IEEE 1363a, Standard Specifications for Public Key
Cryptography - Amendment 1 -- Additional Techniques",
n.d..
[ISO] "ISO/IEC 18033-2, Information Technology - Security
Techniques - Encryption Algorithms - Part 2 -- Asymmetric
Ciphers", n.d..
[keyagreement]
Barker, E., Chen, L., Roginsky, A., and M. Smid,
"Recommendation for Pair-Wise Key Establishment Schemes
Using Discrete Logarithm Cryptography", National Institute
of Standards and Technology report,
DOI 10.6028/nist.sp.800-56ar2, May 2013.
[MAEA10] "A Comparison of the Standardized Versions of ECIES",
n.d., <http://sceweb.sce.uhcl.edu/yang/teaching/
csci5234WebSecurityFall2011/Chaum-blind-signatures.PDF>.
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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,
<https://www.rfc-editor.org/info/rfc2119>.
[RFC5116] McGrew, D., "An Interface and Algorithms for Authenticated
Encryption", RFC 5116, DOI 10.17487/RFC5116, January 2008,
<https://www.rfc-editor.org/info/rfc5116>.
[RFC7748] Langley, A., Hamburg, M., and S. Turner, "Elliptic Curves
for Security", RFC 7748, DOI 10.17487/RFC7748, January
2016, <https://www.rfc-editor.org/info/rfc7748>.
[RFC8174] Leiba, B., "Ambiguity of Uppercase vs Lowercase in RFC
2119 Key Words", BCP 14, RFC 8174, DOI 10.17487/RFC8174,
May 2017, <https://www.rfc-editor.org/info/rfc8174>.
[S01] "A Proposal for an ISO Standard for Public Key Encryption
(verison 2.1)", n.d.,
<http://www.shoup.net/papers/iso-2_1.pdf>.
[SECG] "Elliptic Curve Cryptography, Standards for Efficient
Cryptography Group, ver. 2", n.d.,
<http://www.secg.org/download/aid-780/sec1-v2.pdf>.
9.2. Informative References
[I-D.ietf-mls-protocol]
Barnes, R., Millican, J., Omara, E., Cohn-Gordon, K., and
R. Robert, "The Messaging Layer Security (MLS) Protocol",
draft-ietf-mls-protocol-03 (work in progress), January
2019.
[RFC6637] Jivsov, A., "Elliptic Curve Cryptography (ECC) in
OpenPGP", RFC 6637, DOI 10.17487/RFC6637, June 2012,
<https://www.rfc-editor.org/info/rfc6637>.
Appendix A. Possible TODOs
The following extensions to the basic HPKE functions defined above
might be worth specifying:
o Use of general KEM - It could be useful to define the routines in
this document in terms of a general KEM, as opposed to just DH.
For example, there are currently more post-quantum KEM proposals
than DH proposals.
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o Sender authentication - It is possible to enable a degree of
sender authentication by mixing in a long-term key for the sender
of a ciphertext as well as the recipient. This is done, for
example, in the libnacl "box" function.
o PSK authentication - A pre-shared key could be folded into the key
schedule as another form of authentication.
o Streaming (multi-message) encryption - In many use cases, it is
useful to amortize the cost of the DH operation over several AEAD
encryptions.
o Multiple recipients - It might be possible to add some
simplifications / assurances for the case where the same value is
being encrypted to multiple recipients.
o Test vectors - Obviously, we can provide decryption test vectors
in this document. In order to provide known-answer tests, we
would have to introduce a non-secure deterministic mode where the
ephemeral key pair is derived from the inputs. And to do that
safely, we would need to augment the decrypt function to detect
the deterministic mode and fail.
o A reference implementation in hacspec or similar
Authors' Addresses
Richard L. Barnes
Cisco
Email: rlb@ipv.sx
Karthik Bhargavan
Inria
Email: karthikeyan.bhargavan@inria.fr
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