Internet DRAFT - draft-dew-cfrg-signature-key-blinding
draft-dew-cfrg-signature-key-blinding
WG Working Group F. Denis
Internet-Draft Fastly Inc.
Intended status: Informational E. Eaton
Expires: 4 November 2022 University of Waterloo
C. A. Wood
Cloudflare, Inc.
3 May 2022
Key Blinding for Signature Schemes
draft-dew-cfrg-signature-key-blinding-02
Abstract
This document describes extensions to existing digital signature
schemes for key blinding. The core property of signing with key
blinding is that a blinded public key and all signatures produced
using the blinded key pair are independent of the unblinded key pair.
Moreover, signatures produced using blinded key pairs are
indistinguishable from signatures produced using unblinded key pairs.
This functionality has a variety of applications, including Tor onion
services and privacy-preserving airdrop for bootstrapping
cryptocurrency systems.
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://chris-
wood.github.io/draft-dew-cfrg-signature-key-blinding/draft-dew-cfrg-
signature-key-blinding.html. Status information for this document
may be found at https://datatracker.ietf.org/doc/draft-dew-cfrg-
signature-key-blinding/.
Discussion of this document takes place on the CFRG Working Group
mailing list (mailto:cfrg@irtf.org), which is archived at
https://mailarchive.ietf.org/arch/browse/cfrg/.
Source for this draft and an issue tracker can be found at
https://github.com/chris-wood/draft-dew-cfrg-signature-key-blinding.
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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document authors. All rights reserved.
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Table of Contents
1. Introduction . . . . . . . . . . . . . . . . . . . . . . . . 3
1.1. DISCLAIMER . . . . . . . . . . . . . . . . . . . . . . . 4
2. Conventions and Definitions . . . . . . . . . . . . . . . . . 4
3. Key Blinding . . . . . . . . . . . . . . . . . . . . . . . . 5
4. Ed25519ph, Ed25519ctx, and Ed25519 . . . . . . . . . . . . . 6
4.1. BlindPublicKey and UnblindPublicKey . . . . . . . . . . . 6
4.2. BlindKeySign . . . . . . . . . . . . . . . . . . . . . . 6
5. Ed448ph and Ed448 . . . . . . . . . . . . . . . . . . . . . . 7
5.1. BlindPublicKey and UnblindPublicKey . . . . . . . . . . . 7
5.2. BlindKeySign . . . . . . . . . . . . . . . . . . . . . . 7
6. ECDSA . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8
6.1. BlindPublicKey and UnblindPublicKey . . . . . . . . . . . 8
6.2. BlindKeySign . . . . . . . . . . . . . . . . . . . . . . 9
7. Security Considerations . . . . . . . . . . . . . . . . . . . 9
8. IANA Considerations . . . . . . . . . . . . . . . . . . . . . 10
9. Test Vectors . . . . . . . . . . . . . . . . . . . . . . . . 10
9.1. Ed25519 Test Vectors . . . . . . . . . . . . . . . . . . 10
9.2. ECDSA(P-384, SHA-384) Test Vectors . . . . . . . . . . . 10
10. References . . . . . . . . . . . . . . . . . . . . . . . . . 11
10.1. Normative References . . . . . . . . . . . . . . . . . . 11
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10.2. Informative References . . . . . . . . . . . . . . . . . 11
Acknowledgments . . . . . . . . . . . . . . . . . . . . . . . . . 12
Authors' Addresses . . . . . . . . . . . . . . . . . . . . . . . 12
1. Introduction
Digital signature schemes allow a signer to sign a message using a
private signing key and produce a digital signature such that anyone
can verify the digital signature over the message with the public
verification key corresponding to the signing key. Digital signature
schemes typically consist of three functions:
* KeyGen: A function for generating a private signing key skS and
the corresponding public verification key pkS.
* Sign(skS, msg): A function for signing an input message msg using
a private signing key skS, producing a digital signature sig.
* Verify(pkS, msg, sig): A function for verifying the digital
signature sig over input message msg against a public verification
key pkS, yielding true if the signature is valid and false
otherwise.
In some applications, it's useful for a signer to produce digital
signatures using the same long-term private signing key such that a
verifier cannot link any two signatures to the same signer. In other
words, the signature produced is independent of the long-term
private-signing key, and the public verification key for verifying
the signature is independent of the long-term public verification
key. This type of functionality has a number of practical
applications, including, for example, in the Tor onion services
protocol [TORDIRECTORY] and privacy-preserving airdrop for
bootstrapping cryptocurrency systems [AIRDROP]. It is also necessary
for a variant of the Privacy Pass issuance protocol [RATELIMITED].
One way to accomplish this is by signing with a private key which is
a function of the long-term private signing key and a freshly chosen
blinding key, and similarly by producing a public verification key
which is a function of the long-term public verification key and same
blinding key. A signature scheme with this functionality is referred
to as signing with key blinding. A signature scheme with key
blinding extends a basic digital scheme with four new functions:
* BlindKeyGen: A function for generating a private blind key.
* BlindPublicKey(pkS, bk): Blind the public verification key pkS
using the private blinding key bk, yielding a blinded public key
pkR.
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* UnblindPublicKey(pkR, bk): Unblind the public verification key pkR
using the private blinding key bk.
* BlindKeySign(skS, bk, msg): Sign a message msg using the private
signing key skS with the private blind key bk.
A signature scheme with key blinding aims to achieve unforgeability
and unlinkability. Informally, unforgeability means that one cannot
produce a valid (message, signature) pair for any blinding key
without access to the private signing key. Similarly, unlinkability
means that one cannot distinguish between two signatures produced
from two separate key signing keys, and two signatures produced from
the same signing key but with different blinding keys.
This document describes extensions to EdDSA [RFC8032] and ECDSA
[ECDSA] to enable signing with key blinding. Security analysis of
these extensions is currently underway; see Section 7 for more
details.
This functionality is also possible with other signature schemes,
including some post-quantum signature schemes [ESS21], though such
extensions are not specified here.
1.1. DISCLAIMER
This document is a work in progress and is still undergoing security
analysis. As such, it MUST NOT be used for real world applications.
See Section 7 for additional information.
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.
The following terms are used throughout this document to describe the
blinding modification.
* G: The standard base point.
* sk: A signature scheme private key. For EdDSA, this is a a
randomly generated private seed of length 32 bytes or 57 bytes
according to [RFC8032], Section 5.1.5 or [RFC8032], Section 5.2.5,
respectively. For [ECDSA], sk is a random scalar in the prime-
order elliptic curve group.
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* pk(sk): The public key corresponding to the private key sk.
* concat(x0, ..., xN): Concatenation of byte strings. concat(0x01,
0x0203, 0x040506) = 0x010203040506.
* ScalarMult(pk, k): Multiply the public key pk by scalar k,
producing a new public key as a result.
* ModInverse(x, L): Compute the multiplicative inverse of x modulo
L.
In pseudocode descriptions below, integer multiplication of two
scalar values is denoted by the * operator. For example, the product
of two scalars x and y is denoted as x * y.
3. Key Blinding
At a high level, a signature scheme with key blinding allows signers
to blind their private signing key such that any signature produced
with a private signing key and blinding key is independent of the
private signing key. Similar to the signing key, the blinding key is
also a private key that remains secret. For example, the blind is a
32-byte or 57-byte random seed for Ed25519 or Ed448 variants,
respectively, whereas the blind for ECDSA over P-256 is a random
scalar in the P-256 group. Key blinding introduces four new
functionalities for the signature scheme:
* BlindKeyGen: A function for generating a private blind key.
* BlindPublicKey(pkS, bk): Blind the public verification key pkS
using the private blinding key bk, yielding a blinded public key
pkR.
* UnblindPublicKey(pkR, bk): Unblind the public verification key pkR
using the private blinding key bk.
* BlindKeySign(skS, bk, msg): Sign a message msg using the private
signing key skS with the private blind key bk.
For a given bk produced from BlindKeyGen, correctness requires the
following equivalence to hold:
UnblindPublicKey(BlindPublicKey(pkS, bk), bk) = pkS
Security requires that signatures produced using BlindKeySign are
unlinkable from signatures produced using the standard signature
generation function with the same private key.
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4. Ed25519ph, Ed25519ctx, and Ed25519
This section describes implementations of BlindPublicKey,
UnblindPublicKey, and BlindKeySign as modifications of routines in
[RFC8032], Section 5.1. BlindKeyGen invokes the key generation
routine specified in [RFC8032], Section 5.1.5 and outputs only the
private key.
4.1. BlindPublicKey and UnblindPublicKey
BlindPublicKey transforms a private blind bk into a scalar for the
edwards25519 group and then multiplies the target key by this scalar.
UnblindPublicKey performs essentially the same steps except that it
multiplies the target public key by the multiplicative inverse of the
scalar, where the inverse is computed using the order of the group L,
described in [RFC8032], Section 5.1.
More specifically, BlindPublicKey(pk, bk) works as follows.
1. Hash the 32-byte private key bk using SHA-512, storing the digest
in a 64-octet large buffer, denoted b. Interpret the lower 32
bytes buffer as a little-endian integer, forming a secret scalar
s. Note that this explicitly skips the buffer pruning step in
[RFC8032], Section 5.1.
2. Perform a scalar multiplication ScalarMult(pk, s), and output the
encoding of the resulting point as the public key.
UnblindPublicKey(pkR, bk) works as follows.
1. Compute the secret scalar s from bk as in BlindPublicKey.
2. Compute the sInv = ModInverse(s, L), where L is as defined in
[RFC8032], Section 5.1.
3. Perform a scalar multiplication ScalarMult(pk, sInv), and output
the encoding of the resulting point as the public key.
4.2. BlindKeySign
BlindKeySign transforms a private key bk into a scalar for the
edwards25519 group and a message prefix to blind both the signing
scalar and the prefix of the message used in the signature generation
routine.
More specifically, BlindKeySign(skS, bk, msg) works as follows:
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1. Hash the private key skS, 32 octets, using SHA-512. Let h denote
the resulting digest. Construct the secret scalar s1 from the
first half of the digest, and the corresponding public key A1, as
described in [RFC8032], Section 5.1.5. Let prefix1 denote the
second half of the hash digest, h[32],...,h[63].
2. Hash the 32-byte private key bk using SHA-512, storing the digest
in a 64-octet large buffer, denoted b. Interpret the lower 32
bytes buffer as a little-endian integer, forming a secret scalar
s2. Let prefix2 denote the second half of the hash digest,
b[32],...,b[63].
3. Compute the signing scalar s = s1 * s2 (mod L) and the signing
public key A = ScalarMult(G, s).
4. Compute the signing prefix as concat(prefix1, prefix2).
5. Run the rest of the Sign procedure in [RFC8032], Section 5.1.6
from step (2) onwards using the modified scalar s, public key A,
and string prefix.
5. Ed448ph and Ed448
This section describes implementations of BlindPublicKey,
UnblindPublicKey, and BlindKeySign as modifications of routines in
[RFC8032], Section 5.2. BlindKeyGen invokes the key generation
routine specified in [RFC8032], Section 5.1.5 and outputs only the
private key.
5.1. BlindPublicKey and UnblindPublicKey
BlindPublicKey and UnblindPublicKey for Ed448ph and Ed448 are
implemented just as these routines are for Ed25519ph, Ed25519ctx, and
Ed25519, except that SHAKE256 is used instead of SHA-512 for hashing
the secret blind to a 114-byte buffer (and using the lower 57-bytes
for the secret), and the order of the edwards448 group L is as
defined in [RFC8032], Section 5.2.1.
5.2. BlindKeySign
BlindKeySign for Ed448ph and Ed448 is implemented just as this
routine for Ed25519ph, Ed25519ctx, and Ed25519, except in how the
scalars (s1, s2), public keys (A1, A2), and message strings (prefix1,
prefix2) are computed. More specifically, BlindKeySign(skS, bk, msg)
works as follows:
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1. Hash the private key skS, 57 octets, using SHAKE256(skS, 117).
Let h denote the resulting digest. Construct the secret scalar
s1 from the first half of the digest, and the corresponding
public key A1, as described in [RFC8032], Section 5.2.5. Let
prefix1 denote the second half of the hash digest,
h[57],...,h[113].
2. Perform the same routine to transform the secret blind bk into a
secret scalar s2, public key A2, and prefix2.
3. Compute the signing scalar s = s1 * s2 (mod L) and the signing
public key A = ScalarMult(A1, s2).
4. Compute the signing prefix as concat(prefix1, prefix2).
5. Run the rest of the Sign procedure in [RFC8032], Section 5.2.6
from step (2) onwards using the modified scalar s, public key A,
and string prefix.
6. ECDSA
[[DISCLAIMER: Multiplicative blinding for ECDSA is known to be NOT be
SUF-CMA-secure in the presence of an adversary that controls the
blinding value. [MSMHI15] describes this in the context of related-
key attacks. This variant may likely be removed in followup versions
of this document based on further analysis.]]
This section describes implementations of BlindPublicKey,
UnblindPublicKey, and BlindKeySign as functions implemented on top of
an existing [ECDSA] implementation. BlindKeyGen invokes the key
generation routine specified in [ECDSA] and outputs only the private
key. In the descriptions below, let p be the order of the
corresponding elliptic curve group used for ECDSA. For example, for
P-256, p = 1157920892103562487626974469494075735299969552241357603424
22259061068512044369.
6.1. BlindPublicKey and UnblindPublicKey
BlindPublicKey multiplies the public key pkS by an augmented private
key bk yielding a new public key pkR. UnblindPublicKey inverts this
process by multiplying the input public key by the multiplicative
inverse of the augmented bk. Augmentation here maps the private key
bk to another scalar using hash_to_field as defined in Section 5 of
[H2C], with DST set to "ECDSA Key Blind", L set to the value
corresponding to the target curve, e.g., 48 for P-256 and 72 for
P-384, expand_message_xmd with a hash function matching that used for
the corresponding digital signature algorithm, and prime modulus
equal to the order p of the corresponding curve. Letting
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HashToScalar denote this augmentation process, BlindPublicKey and
UnblindPublicKey are then implemented as follows:
BlindPublicKey(pk, bk) = ScalarMult(pk, HashToScalar(bk))
UnblindPublicKey(pk, bk) = ScalarMult(pk, ModInverse(HashToScalar(bk), p))
6.2. BlindKeySign
BlindKeySign transforms the signing key skS by the private key bk
into a new signing key, skR, and then invokes the existing ECDSA
signing procedure. More specifically, skR = skS * HashToScalar(bk)
(mod p).
7. Security Considerations
The signature scheme extensions in this document aim to achieve
unforgeability and unlinkability. Informally, unforgeability means
that one cannot produce a valid (message, signature) pair for any
blinding key without access to the private signing key. Similarly,
unlinkability means that one cannot distinguish between two
signatures produced from two separate key signing keys, and two
signatures produced from the same signing key but with different
blinds. Security analysis of the extensions in this document with
respect to these two properties is currently underway.
Preliminary analysis has been done for a variant of these extensions
used for identity key blinding routine used in Tor's Hidden Service
feature [TORBLINDING]. For EdDSA, further analysis is needed to
ensure this is compliant with the signature algorithm described in
[RFC8032].
The constructions in this document assume that both the signing and
blinding keys are private, and, as such, not controlled by an
attacker. [MSMHI15] demonstrate that ECDSA with attacker-controlled
multiplicative blinding for producing related keys can be abused to
produce forgeries. In particular, if an attacker can control the
private blinding key used in BlindKeySign, they can construct a
forgery over a different message that validates under a different
public key. One mitigation to this problem is to change BlindKeySign
such that the signature is computed over the input message as well as
the blind public key. However, this would require verifiers to treat
both the blind public key and message as input to their verification
interface. The construction in Section 6 does not require this
change. However, further analysis is needed to determine whether or
not this construction is safe.
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8. IANA Considerations
This document has no IANA actions.
9. Test Vectors
This section contains test vectors for a subset of the signature
schemes covered in this document.
9.1. Ed25519 Test Vectors
This section contains test vectors for Ed25519 as described in
[RFC8032]. Each test vector lists the private key and blind seeds,
denoted skS and bk and encoded as hexadecimal strings, along with the
public key pkS corresponding to skS encoded has hexadecimal strings
according to [RFC8032], Section 5.1.2. Each test vector also
includes the blinded public key pkR computed from skS and bk, denoted
pkR and encoded has a hexadecimal string. Finally, each vector
includes the message and signature values, each encoded as
hexadecimal strings.
// Randomly generated private key and blind seed
skS: 875532ab039b0a154161c284e19c74afa28d5bf5454e99284bbcffaa71eebf45
pkS: 3b5983605b277cd44918410eb246bb52d83adfc806ccaa91a60b5b2011bc5973
bk: c461e8595f0ac41d374f878613206704978115a226f60470ffd566e9e6ae73bf
pkR: e52bbb204e72a816854ac82c7e244e13a8fcc3217cfdeb90c8a5a927e741a20f
message: 68656c6c6f20776f726c64
signature: f35d2027f14250c07b3b353359362ec31e13076a547c749a981d0135fce06
7a361ad6522849e6ed9f61d93b0f76428129b9eb3f9c3cd0bfa1bc2a086a5eebd09
// Randomly generated private key seed and zero blind seed
skS: f3348942e77a83943a6330d372e7531bb52203c2163a728038388ea110d1c871
pkS: ada4f42be4b8fa93ddc7b41ca434239a940b4b18d314fe04d5be0b317a861ddf
bk: 0000000000000000000000000000000000000000000000000000000000000000
pkR: 7b8dcabbdfce4f8ad57f38f014abc4a51ac051a4b77b345da45ee2725d9327d0
message: 68656c6c6f20776f726c64
signature: b38b9d67cb4182e91a86b2eb0591e04c10471c1866202dd1b3b076fb86a61
c7c4ab5d626e5c5d547a584ca85d44839c13f6c976ece0dcba53d82601e6737a400
9.2. ECDSA(P-384, SHA-384) Test Vectors
This section contains test vectors for ECDSA with P-384 and SHA-384,
as described in [ECDSA]. Each test vector lists the signing and
blinding keys, denoted skS and bk, each serialized as a big-endian
integers and encoded as hexadecimal strings. Each test vector also
blinded public key pkR, encoded as compressed elliptic curve points
according to [ECDSA]. Finally, each vector lists message and
signature values, where the message is encoded as a hexadecimal
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string, and the signature value is serialized as the concatenation of
scalars (r, s) and encoded as a hexadecimal string.
// Randomly generated signing and blind private keys
skS: 0e1e4fcc2726e36c5a24be3d30dc6f52d61e6614f5c57a1ec7b829d8adb7c85f456
c30c652d9cd1653cef4ce4da9008d
pkS: 03c66e61f5e12c35568928d9a0ffbc145ee9679e17afea3fba899ed3f878f9e82a8
859ce784d9ff43fea2bc8e726468dd3
bk: 865b6b7fc146d0f488854932c93128c3ab3572b7137c4682cb28a2d55f7598df467
e890984a687b22c8bc60a986f6a28
pkR: 038defb9b698b91ee7f3985e54b57b519be237ced2f6f79408558ff7485bf2d60a2
4dc986b9145e422ea765b56de7c5956
message: 68656c6c6f20776f726c64
signature: 5e5643a8c22b274ec5f776e63ed23ff182c8c87642e35bd5a5f7455ae1a19
a9956795df33e2f8b30150904ef6ba5e7ee4f18cef026f594b4d21fc157552ce3cf6d7ef
c3226b8d8194fc93df1c7f5facafc96daab7c5a0d840fbd3b9342f2ddad
10. References
10.1. Normative References
[ECDSA] American National Standards Institute, "Public Key
Cryptography for the Financial Services Industry - The
Elliptic Curve Digital Signature Algorithm (ECDSA)",
ANSI ANS X9.62-2005, November 2005.
[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/rfc/rfc2119>.
[RFC8032] Josefsson, S. and I. Liusvaara, "Edwards-Curve Digital
Signature Algorithm (EdDSA)", RFC 8032,
DOI 10.17487/RFC8032, January 2017,
<https://www.rfc-editor.org/rfc/rfc8032>.
[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/rfc/rfc8174>.
10.2. Informative References
[AIRDROP] Wahby, R. S., Boneh, D., Jeffrey, C., and J. Poon, "An
airdrop that preserves recipient privacy", n.d.,
<https://eprint.iacr.org/2020/676.pdf>.
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[ESS21] Eaton, E., Stebila, D., and R. Stracovsky, "Post-Quantum
Key-Blinding for Authentication in Anonymity Networks",
2021, <https://eprint.iacr.org/2021/963>.
[H2C] Faz-Hernandez, A., Scott, S., Sullivan, N., Wahby, R. S.,
and C. A. Wood, "Hashing to Elliptic Curves", Work in
Progress, Internet-Draft, draft-irtf-cfrg-hash-to-curve-
14, 18 February 2022,
<https://datatracker.ietf.org/doc/html/draft-irtf-cfrg-
hash-to-curve-14>.
[MSMHI15] Morita, H., Schuldt, J., Matsuda, T., Hanaoka, G., and T.
Iwata, "On the Security of the Schnorr Signature Scheme
and DSA Against Related-Key Attacks", Information Security
and Cryptology - ICISC 2015 pp. 20-35,
DOI 10.1007/978-3-319-30840-1_2, 2016,
<https://doi.org/10.1007/978-3-319-30840-1_2>.
[RATELIMITED]
Hendrickson, S., Iyengar, J., Pauly, T., Valdez, S., and
C. A. Wood, "Rate-Limited Token Issuance Protocol", Work
in Progress, Internet-Draft, draft-privacypass-rate-limit-
tokens-02, 2 May 2022,
<https://datatracker.ietf.org/doc/html/draft-privacypass-
rate-limit-tokens-02>.
[TORBLINDING]
Hopper, N., "Proving Security of Tor’s Hidden Service
Identity Blinding Protocol", 2013,
<https://www-users.cse.umn.edu/~hoppernj/basic-proof.pdf>.
[TORDIRECTORY]
"Tor directory protocol, version 3", n.d.,
<https://gitweb.torproject.org/torspec.git/tree/dir-
spec.txt>.
Acknowledgments
The authors would like to thank Dennis Jackson for helpful
discussions that informed the development of this draft.
Authors' Addresses
Frank Denis
Fastly Inc.
475 Brannan St
San Francisco,
United States of America
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Internet-Draft Key Blinding for Signature Schemes May 2022
Email: fde@00f.net
Edward Eaton
University of Waterloo
200 University Av West
Waterloo
Canada
Email: ted@eeaton.ca
Christopher A. Wood
Cloudflare, Inc.
101 Townsend St
San Francisco,
United States of America
Email: caw@heapingbits.net
Denis, et al. Expires 4 November 2022 [Page 13]
