Internet Research Task Force (IRTF) C. Cremers
Request for Comments: 8937
Category: Informational L. Garratt
ISSN: 2070-1721 Cisco Meraki
Randomness Improvements for Security Protocols
Randomness is a crucial ingredient for Transport Layer Security (TLS)
and related security protocols. Weak or predictable
"cryptographically secure" pseudorandom number generators (CSPRNGs)
can be abused or exploited for malicious purposes. An initial
entropy source that seeds a CSPRNG might be weak or broken as well,
which can also lead to critical and systemic security problems. This
document describes a way for security protocol implementations to
augment their CSPRNGs using long-term private keys. This improves
randomness from broken or otherwise subverted CSPRNGs.
This document is a product of the Crypto Forum Research Group (CFRG)
in the IRTF.
Status of This Memo
This document is not an Internet Standards Track specification; it is
published for informational purposes.
This document is a product of the Internet Research Task Force
(IRTF). The IRTF publishes the results of Internet-related research
and development activities. These results might not be suitable for
deployment. This RFC represents the consensus of the Crypto Forum
Research Group of the Internet Research Task Force (IRTF). Documents
approved for publication by the IRSG are not a candidate for any
level of Internet Standard; see Section 2 of RFC 7841
Information about the current status of this document, any errata,
and how to provide feedback on it may be obtained at https://www.rfc-editor.org/info/rfc8937
Copyright (c) 2020 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
) 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.
Table of Contents 1.
Conventions Used in This Document 3.
Randomness Wrapper 4.
Tag Generation 5.
Application to TLS 6.
Implementation Guidance 7.
IANA Considerations 8.
Security Considerations 9.
Comparison to RFC 6979 10.
Normative References 10.2.
Secure and properly implemented random number generators, or
"cryptographically secure" pseudorandom number generators (CSPRNGs),
should produce output that is indistinguishable from a random string
of the same length. CSPRNGs are critical building blocks for TLS and
related transport security protocols. TLS in particular uses CSPRNGs
to generate several values, such as ephemeral key shares and
ClientHello and ServerHello random values. CSPRNG failures, such as
the Debian bug described in [DebianBug], can lead to insecure TLS
connections. CSPRNGs may also be intentionally weakened to cause
harm [DualEC]. Initial entropy sources can also be weak or broken,
and that would lead to insecurity of all CSPRNG instances seeded with
them. In such cases where CSPRNGs are poorly implemented or
insecure, an adversary, Adv, may be able to distinguish its output
from a random string or predict its output and recover secret key
material used to 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 randomness where needed, e.g., in
generating ephemeral key shares, a function of a party's long-term
private key is mixed into the entropy pool. In the NAXOS key
exchange protocol, raw random value x is replaced by H(x, sk), where
sk is the sender's private key. Unfortunately, as private keys are
often isolated in Hardware Security Modules (HSMs), direct access to
compute H(x, sk) is impossible. Moreover, some HSM APIs may only
offer the option to sign messages using a private key, yet offer no
other operations involving that key. An alternate, yet functionally
equivalent construction, is needed.
The approach described herein replaces the NAXOS hash with a keyed
hash, or pseudorandom function (PRF), where the key is derived from a
raw random value and a private key signature. Implementations SHOULD
apply this technique a) when indirect access to a private key is
available and CSPRNG randomness guarantees are dubious or b) to
provide stronger guarantees about possible future issues with the
randomness. Roughly, the security properties provided by the
proposed construction are as follows: 1.
If the CSPRNG works fine (that is, in a certain adversary model,
the CSPRNG output is indistinguishable from a truly random
sequence), then the output of the proposed construction is also
indistinguishable from a truly random sequence in that adversary
Adv with full control of a (potentially broken) CSPRNG and
ability to observe all outputs of the proposed construction does
not obtain any non-negligible advantage in leaking the private
key (in the absence of side channel attacks). 3.
If the CSPRNG is broken or controlled by Adv, the output of the
proposed construction remains indistinguishable from random,
provided that the private key remains unknown to Adv.
This document represents the consensus of the Crypto Forum Research
2. Conventions Used in This Document
The key words "MUST
", "MUST NOT
", "SHALL NOT
", "SHOULD NOT
", "NOT RECOMMENDED
" in this document are to be interpreted as described in
BCP 14 [RFC2119
] when, and only when, they appear in all
capitals, as shown here.
3. Randomness Wrapper
The output of a properly instantiated CSPRNG should be
indistinguishable from a random string of the same length. 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 mixes secret data into a value that may be lacking
Let G(n) be an algorithm that generates n random bytes, i.e., the
output of a CSPRNG. Define an augmented CSPRNG G' as follows. Let
Sig(sk, m) be a function that computes a signature of message m given
private key sk. Let H be a cryptographic hash function that produces
output of length M. Let Extract(salt, IKM) be a randomness
extraction function, e.g., HKDF-Extract [RFC5869
], which accepts a
salt and input keying material (IKM) parameter and produces a
pseudorandom key of L bytes suitable for cryptographic use. It must
be a secure PRF (for salt as a key of length M) and preserve
uniformness of IKM (for details, see [SecAnalysis]). L SHOULD
fixed length. Let Expand(k, info, n) be a variable-length output
PRF, e.g., HKDF-Expand [RFC5869
], that takes as input a pseudorandom
key k of L bytes, info string, and output length n, and produces
output of n bytes. Finally, let tag1 be a fixed, context-dependent
string, and let tag2 be a dynamically changing string (e.g., a
counter) of L' bytes. We require that L >= n - L' for each value of
The construction works as follows. Instead of using G(n) when
randomness is needed, use G'(n), where
G'(n) = Expand(Extract(H(Sig(sk, tag1)), G(L)), tag2, n)
Functionally, this expands n random bytes from a key derived from the
CSPRNG output and signature over a fixed string (tag1). See Section 4
for details about how "tag1" and "tag2" should be generated
and used per invocation of the randomness wrapper. Expand()
generates a string that is computationally indistinguishable from a
truly random string of n bytes. Thus, the security of this
construction depends upon the secrecy of H(Sig(sk, tag1)) and G(L).
If the signature is leaked, then security of G'(n) reduces to the
scenario wherein randomness is expanded directly from G(L).
If a private key sk is stored and used inside an HSM, then the
signature calculation is implemented inside it, while all other
operations (including calculation of a hash function, Extract
function, and Expand function) can be implemented either inside or
outside the HSM.
Sig(sk, tag1) need only be computed once for the lifetime of the
randomness wrapper and MUST NOT
be used or exposed beyond its role in
this computation. Additional recommendations for tag1 are given in
the following section.
be a deterministic signature function, e.g., deterministic
Elliptic Curve Digital Signature Algorithm (ECDSA) [RFC6979
], or use
an independent (and completely reliable) entropy source, e.g., if Sig
is implemented in an HSM with its own internal trusted entropy source
for signature generation.
Because Sig(sk, tag1) can be cached, the relative cost of using G'(n)
instead of G(n) tends to be negligible with respect to cryptographic
operations in protocols such as TLS (the relatively inexpensive
computational cost of HKDF-Extract and HKDF-Expand dominates when
comparing G' to G). A description of the performance experiments and
their results can be found in [SecAnalysis].
Moreover, the values of G'(n) may be precomputed and pooled. This is
possible since the construction depends solely upon the CSPRNG output
and private key.
4. Tag Generation
Both tags MUST
be generated such that they never collide with another
contender 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.
tag construction procedure is as follows:
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 Media Access Control
(MAC) address. To provide security in the cases of usage of
CSPRNGs in virtual environments, it is RECOMMENDED
incorporate all available information specific to the process
that would ensure the uniqueness of each tag1 value among
different instances of virtual machines (including ones that
were cloned or recovered from snapshots). This is needed to
address the problem of CSPRNG state cloning (see [RY2010]).
See Section 5
for example protocol information that can be
used in the context of TLS 1.3. If sk could be used for other
purposes, then selecting a value for tag1 that is different
than the form allowed by those other uses ensures that the
signature is not exposed.
tag2: A nonce, that is, a value that is unique for each use of the
same combination of G(L), tag1, and sk values. The tag2 value
can be implemented using a counter or a timer, provided that
the timer is guaranteed to be different for each invocation of
5. 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" CSPRNG G(n), i.e., the
CSPRNG that generates private values, such as key shares, with
G'(n) = HKDF-Expand(HKDF-Extract(H(Sig(sk, tag1)), G(L)), tag2, n)
6. Implementation Guidance
Recall that the wrapper defined in Section 3
requires L >= n - L',
where L is the Extract output length and n is the desired amount of
randomness. Some applications may require n to exceed this bound.
Wrapper implementations can support this use case by invoking G'
multiple times and concatenating the results.
7. IANA Considerations
This document has no IANA actions.
8. Security Considerations
A security analysis was performed in [SecAnalysis]. Generally
speaking, the following security theorem has been proven: if Adv
learns only one of the signature or the usual randomness generated on
one particular instance, then, under the security assumptions on our
primitives, the wrapper construction should output randomness that is
indistinguishable from a random string.
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. Hence, it is recommended to generate a
key specifically for the purposes of the defined construction and not
to use it another way.
The signature in the construction, as well as in the protocol itself, MUST NOT
use randomness from entropy sources with dubious security
guarantees. Thus, the signature scheme MUST
either use a reliable
entropy source (independent from the CSPRNG that is being improved
with the proposed construction) or be deterministic; if the
signatures are probabilistic and use weak entropy, our construction
does not help, and the signatures are still vulnerable due to repeat
randomness attacks. In such an attack, Adv 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 analyzing protocols specifically. However, this
construction is generic so the analyses of many protocols will still
hold even if this proposed construction is incorporated.
The proposed construction cannot provide any guarantees of security
if the CSPRNG state is cloned due to the virtual machine snapshots or
process forking (see [MAFS2017]). It is RECOMMENDED
incorporate all available information about the environment, such as
process attributes, virtual machine user information, etc.
9. Comparison to RFC 6979
The construction proposed herein has similarities with that of
]; both of them use private keys to seed a deterministic
random number generator. Section 3.3 of [RFC6979
deterministically instantiating an instance of the HMAC_DRBG
pseudorandom number generator, described in [SP80090A] and Annex D of
[X962], using the private key sk as the entropy_input parameter and
H(m) as the nonce. The construction G'(n) provided herein is
similar, with such difference that a key derived from G(n) and
H(Sig(sk, tag1)) is used as the entropy input and tag2 is the nonce.
However, the semantics and the security properties obtained by using
these two constructions are different. The proposed construction
aims to improve CSPRNG usage such that certain trusted randomness
would remain even if the CSPRNG is completely broken. Using a
signature scheme that requires entropy sources according to [RFC6979
is intended for different purposes and does not assume possession of
any entropy source -- even an unstable one. For example, if in a
certain system all private key operations are performed within an
HSM, then the differences will manifest as follows: the HMAC_DRBG
construction described in [RFC6979
] may be implemented inside the HSM
for the sake of signature generation, while the proposed construction
would assume calling the signature implemented in the HSM.
10.1. Normative References
] Bradner, S., "Key words for use in RFCs to Indicate
Requirement Levels", BCP 14, RFC 2119
, March 1997,
] Krawczyk, H. and P. Eronen, "HMAC-based Extract-and-Expand
Key Derivation Function (HKDF)", RFC 5869
, May 2010,
] Pornin, T., "Deterministic Usage of the Digital Signature
Algorithm (DSA) and Elliptic Curve Digital Signature
Algorithm (ECDSA)", RFC 6979
, DOI 10.17487/RFC6979
] 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
10.2. Informative References
Yilek, S., Rescorla, E., Shacham, H., Enright, B., and S.
Savage, "When private keys are public: results from the
2008 Debian OpenSSL vulnerability", ICM '09,
DOI 10.1145/1644893.1644896, November 2009,
[DualEC] Bernstein, D., Lange, T., and R. Niederhagen, "Dual EC: A
Standardized Back Door", DOI 10.1007/978-3-662-49301-4_17,
March 2016, <https://projectbullrun.org/dual-ec/documents/
[MAFS2017] McGrew, D., Anderson, B., Fluhrer, S., and C. Schenefiel,
"PRNG Failures and TLS Vulnerabilities in the Wild",
[NAXOS] LaMacchia, B., Lauter, K., and A. Mityagin, "Stronger
Security of Authenticated Key Exchange",
DOI 10.1007/978-3-540-75670-5_1, November 2007,
[RY2010] Ristenpart, T. and S. Yilek, "When Good Randomness Goes
Bad: Virtual Machine Reset Vulnerabilities and Hedging
Deployed Cryptography", January 2010,
Akhmetzyanova, L., Cremers, C., Garratt, L., Smyshlyaev,
S., and N. Sullivan, "Limiting the impact of unreliable
randomness in deployed security protocols",
DOI 10.1109/CSF49147.2020.00027, IEEE 33rd Computer
Security Foundations Symposium (CSF), Boston, MA, USA, pp.
[SP80090A] National Institute of Standards and Technology,
"Recommendation for Random Number Generation Using
Deterministic Random Bit Generators, Special Publication
800-90A Revision 1", DOI 10.6028/NIST.SP.800-90Ar1, June
[X962] American National Standard for Financial Services (ANSI),
"Public Key Cryptography for the Financial Services
Industry, The Elliptic Curve Digital Signature Algorithm
(ECDSA)", ANSI X9.62, November 2005,
We thank Liliya Akhmetzyanova for her deep involvement in the
security assessment in [SecAnalysis]. We thank John Mattsson, Martin
Thomson, and Rich Salz for their careful readings and useful
Saarland Informatics Campus
500 Terry A Francois Blvd
United States of America
18, Suschevsky val
101 Townsend St
United States of America
Christopher A. Wood
101 Townsend St
United States of America