Network Working Group C. Cremers
Internet-Draft L. Garratt
Intended status: Informational University of Oxford
Expires: September 2, 2018 S. Smyshlyaev
CryptoPro
N. Sullivan
Cloudflare
C. Wood
Apple Inc.
March 01, 2018
Randomness Improvements for Security Protocols
draft-cremers-cfrg-randomness-improvements-00
Abstract
Randomness is a crucial ingredient for TLS and related security
protocols. Weak or predictable "cryptographically-strong"
pseudorandom number generators (CSPRNGs) can be abused or exploited
for malicious purposes. The Dual EC random number backdoor and
Debian bugs are relevant examples of this problem. This document
describes a way for security protocol participants to mix their long-
term private key into the entropy pool(s) from which random values
are derived. This augments and improves randomness from broken or
otherwise subverted CSPRNGs.
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 September 2, 2018.
Cremers, et al. Expires September 2, 2018 [Page 1]
Internet-Draft Randomness Improvements March 2018
Copyright Notice
Copyright (c) 2018 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.
Table of Contents
1. Introduction . . . . . . . . . . . . . . . . . . . . . . . . 2
2. Randomness Wrapper . . . . . . . . . . . . . . . . . . . . . 3
3. Tag Generation . . . . . . . . . . . . . . . . . . . . . . . 4
4. Application to TLS . . . . . . . . . . . . . . . . . . . . . 4
5. IANA Considerations . . . . . . . . . . . . . . . . . . . . . 4
6. Security Considerations . . . . . . . . . . . . . . . . . . . 4
7. Normative References . . . . . . . . . . . . . . . . . . . . 5
Authors' Addresses . . . . . . . . . . . . . . . . . . . . . . . 6
1. Introduction
Randomness is a crucial ingredient for TLS and related transport
security protocols. TLS in particular uses Random Number Generators
(RNGs) to generate several values: session IDs, ephemeral key shares,
and ClientHello and ServerHello random values. RNG failures such as
the Debian bug described in [DebianBug] can lead to insecure TLS
connections. RNGs may also be intentionally weakened to cause harm
[DualEC]. In such cases where RNGs are poorly implemented or
insecure, an adversary may be able to predict its output and recover
secret Diffie-Hellman key shares that protect the connection.
This document proposes an improvement to randomness generation in
security protocols inspired by the "NAXOS trick" [NAXOS].
Specifically, instead of using raw entropy where needed, e.g., in
generating ephemeral key shares, a party's long-term private key is
mixed into the entropy pool. In the NAXOS key exchange protocol, raw
entropy output x is replaced by H(x, sk), where sk is the sender's
private key. Unfortunately, as private keys are often isolated in
HSMs, direct access to compute H(x, sk) is impossible. An alternate
yet functionally equivalent construction is needed.
Cremers, et al. Expires September 2, 2018 [Page 2]
Internet-Draft Randomness Improvements March 2018
The approach described herein replaces the NAXOS hash with a keyed
hash, or pseudorandom function (PRF), where the key is derived from
raw entropy output and a private key signature. Implementations
SHOULD apply this technique when indirect access to a private key is
available and CSPRNG randomness guarantees are dubious, or to provide
stronger guarantees about possible future issues with the randomness.
2. Randomness Wrapper
Let x be the raw entropy output of a CSPRNG. When properly
instantiated, x should be indistinguishable from a random string of
length |x|. However, as previously discussed, this is not always
true. To mitigate this problem, we propose an approach for wrapping
the CSPRNG output with a construction that artificially injects
randomness into a value that may be lacking entropy.
Let PRF(k, m) be a cryptographic pseudorandom function, e.g., HMAC
[RFC2104], that takes as input a key k of length L and message m and
produces an output of length M. For example, when using HMAC with
SHA256, L and M are 256 bits. Let Sig(sk, m) be a function that
computes a signature of message m given private key sk. Let G be an
algorithm that generates random numbers from raw entropy, i.e., the
output of a CSPRNG. Let tag be a fixed, context-dependent string.
Let KDF be a key derivation function, e.g., HKDF-Extract [RFC5869]
(with first argument set to nil), that extracts a key of length L
suitable for cryptographic use. Lastly, let H be a cryptographic
hash function that produces output of length M.
The construction works as follows: instead of using x when randomness
is needed, use:
PRF(KDF(G(x) || H(Sig(sk, tag1))), tag2)
Functionally, this computes the PRF of a string (tag2) with a key
derived from the CSPRNG output and signature over a fixed string
(tag1). See Section 3 for details about how "tag1" and "tag2" should
be generated. The PRF behaves in a manner that is indistinguishable
from a truly random function from {0, 1}^L to {0, 1}^M assuming the
key is selected at random. Thus, the security of this construction
depends upon the secrecy of H(Sig(sk, tag1)) and G(x). If the
signature is leaked, then security reduces to the scenario wherein
the PRF provides only a wrapper to G(x).
In systems where signature computations are not cheap, these values
may be precomputed in anticipation of future randomness requests.
This is possible since the construction depends solely upon the
CSPRNG output and private key.
Cremers, et al. Expires September 2, 2018 [Page 3]
Internet-Draft Randomness Improvements March 2018
Sig(sk, tag1) MUST NOT be used or exposed beyond its role in this
computation. Moreover, Sig MUST be a deterministic signature
function, e.g., deterministic ECDSA [RFC6979].
3. Tag Generation
Both tags SHOULD be generated such that they never collide with
another accessor or owner of the private key. This can happen if,
for example, one HSM with a private key is used from several servers,
or if virtual machines are cloned.
To mitigate collisions, tag strings SHOULD be constructed as follows:
o tag1: Constant string bound to a specific device and protocol in
use. This allows caching of Sig(sk, tag1). Device specific
information may include, for example, a MAC address. See
Section 4 for example protocol information that can be used in the
context of TLS 1.3.
o tag2: Non-constant string that includes a timestamp or counter.
This ensures change over time even if randomness were to repeat.
4. Application to TLS
The PRF randomness wrapper can be applied to any protocol wherein a
party has a long-term private key and also generates randomness.
This is true of most TLS servers. Thus, to apply this construction
to TLS, one simply replaces the "private" PRNG, i.e., the PRNG that
generates private values, such as key shares, with:
HMAC(HKDF-Extract(nil, G(x) || Sig(sk, tag1)), tag2)
Moreover, we fix tag1 to protocol-specific information such as "TLS
1.3 Additional Entropy" for TLS 1.3. Older variants use similarly
constructed strings.
5. IANA Considerations
This document makes no request to IANA.
6. Security Considerations
A security analysis was performed by two authors of this document.
Generally speaking, security depends on keeping the private key
secret. If this secret is compromised, the scheme reduces to the
scenario wherein the PRF provides only an outer wrapper on usual
CSPRNG generation.
Cremers, et al. Expires September 2, 2018 [Page 4]
Internet-Draft Randomness Improvements March 2018
The main reason one might expect the signature to be exposed is via a
side-channel attack. It is therefore prudent when implementing this
construction to take into consideration the extra long-term key
operation if equipment is used in a hostile environment when such
considerations are necessary.
The signature in the construction as well as in the protocol itself
MUST be deterministic: if the signatures are probabilistic, then with
weak entropy, our construction does not help and the signatures are
still vulnerable due to repeat randomness attacks. In such an
attack, the adversary might be able to recover the long-term key used
in the signature.
Under these conditions, applying this construction should never yield
worse security guarantees than not applying it assuming that applying
the PRF does not reduce entropy. We believe there is always merit in
analysing protocols specifically. However, this construction is
generic so the analyses of many protocols will still hold even if
this proposed construction is incorporated.
7. Normative References
[DebianBug]
Yilek, Scott, et al, ., "When private keys are public -
Results from the 2008 Debian OpenSSL vulnerability", n.d.,
<https://pdfs.semanticscholar.org/fcf9/
fe0946c20e936b507c023bbf89160cc995b9.pdf>.
[DualEC] Bernstein, Daniel et al, ., "Dual EC - A standardized back
door", n.d., <https://projectbullrun.org/dual-
ec/documents/dual-ec-20150731.pdf>.
[NAXOS] LaMacchia, Brian et al, ., "Stronger Security of
Authenticated Key Exchange", n.d.,
<https://www.microsoft.com/en-us/research/wp-
content/uploads/2016/02/strongake-submitted.pdf>.
[RFC2104] Krawczyk, H., Bellare, M., and R. Canetti, "HMAC: Keyed-
Hashing for Message Authentication", RFC 2104,
DOI 10.17487/RFC2104, February 1997,
<https://www.rfc-editor.org/info/rfc2104>.
[RFC5869] Krawczyk, H. and P. Eronen, "HMAC-based Extract-and-Expand
Key Derivation Function (HKDF)", RFC 5869,
DOI 10.17487/RFC5869, May 2010,
<https://www.rfc-editor.org/info/rfc5869>.
Cremers, et al. Expires September 2, 2018 [Page 5]
Internet-Draft Randomness Improvements March 2018
[RFC6979] Pornin, T., "Deterministic Usage of the Digital Signature
Algorithm (DSA) and Elliptic Curve Digital Signature
Algorithm (ECDSA)", RFC 6979, DOI 10.17487/RFC6979, August
2013, <https://www.rfc-editor.org/info/rfc6979>.
[X9.62] American National Standards Institute, ., "Public Key
Cryptography for the Financial Services Industry -- The
Elliptic Curve Digital Signature Algorithm (ECDSA). ANSI
X9.62-2005, November 2005.", n.d..
Authors' Addresses
Cas Cremers
University of Oxford
Wolfson Building, Parks Road
Oxford
England
Email: cas.cremers@cs.ox.ac.uk
Luke Garratt
University of Oxford
Wolfson Building, Parks Road
Oxford
England
Email: luke.garratt@cs.ox.ac.uk
Stanislav Smyshlyaev
CryptoPro
18, Suschevsky val
Moscow
Russian Federation
Email: svs@cryptopro.ru
Nick Sullivan
Cloudflare
101 Townsend St
San Francisco
United States of America
Email: nick@cloudflare.com
Cremers, et al. Expires September 2, 2018 [Page 6]
Internet-Draft Randomness Improvements March 2018
Christopher A. Wood
Apple Inc.
One Apple Park Way
Cupertino, California 95014
United States of America
Email: cawood@apple.com
Cremers, et al. Expires September 2, 2018 [Page 7]