Network Working Group                                         C. Cremers
Internet-Draft                                                L. Garratt
Intended status: Informational                      University of Oxford
Expires: January 16, 2019                                  S. Smyshlyaev
                                                             N. Sullivan
                                                                 C. Wood
                                                              Apple Inc.
                                                           July 15, 2018

             Randomness Improvements for Security Protocols


   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
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   This Internet-Draft will expire on January 16, 2019.

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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
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   ( in effect on the date of
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   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 . . . . . . . . . . . . . . . . . . . . .   5
   6.  Security Considerations . . . . . . . . . . . . . . . . . . .   5
   7.  Comparison to RFC 6979  . . . . . . . . . . . . . . . . . . .   6
   8.  Normative References  . . . . . . . . . . . . . . . . . . . .   6
   Authors' Addresses  . . . . . . . . . . . . . . . . . . . . . . .   7

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.

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   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.
   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

   2.  An adversary Adv with full control of a (potentially broken)
       CSPRNG and able to observe all outputs of the proposed
       construction, does not obtain any non-negligible advantage in
       leaking the private key, modulo side channel attacks.

   3.  If the CSPRNG is broken or controlled by adversary Adv, the
       output of the proposed construction remains indistinguishable
       from random provided the private key remains unknown to Adv.

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 G(n) be an algorithm that generates n random bytes from raw
   entropy, i.e., the output of a CSPRNG.  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 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 length L suitable for
   cryptographic use.  Let Expand(k, info, n) be a randomness extractor,
   e.g., HKDF-Expand [RFC5869], that takes as input a pseudorandom key k
   of length L, info string, and output length n, and produces output of
   length n.  Finally, let tag1 be a fixed, context-dependent string,
   and let tag2 be a dynamically changing string.

   The construction works as follows.  Instead of using x = G(n) when
   randomness is needed, use:

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          x = Expand(Extract(G(L), H(Sig(sk, tag1))), 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 3 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 length n.  Thus, the security of this
   construction depends upon the secrecy of H(Sig(sk, tag1)) and G(n).
   If the signature is leaked, then security reduces to the scenario
   wherein randomness is expanded directly from G(n).

   Also, in systems where signature computations are expensive, 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.

   Sig(sk, tag1) should only be computed once for the lifetime of the
   randomness wrapper, and 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], 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

3.  Tag Generation

   Both tags SHOULD 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.

   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

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   to TLS, one simply replaces the "private" PRNG, i.e., the PRNG that
   generates private values, such as key shares, with:

   HKDF-Expand(HKDF-Extract(G(L), H(Sig(sk, tag1))), tag2, n)

   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.

   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 NOT use randomness from entropy sources with dubious randomness
   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, 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
   analyzing protocols specifically.  However, this construction is
   generic so the analyses of many protocols will still hold even if
   this proposed construction is incorporated.

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7.  Comparison to RFC 6979

   The construction proposed herein has similarities with that of RFC
   6979 [RFC6979]: both of them use private keys to seed a DRBG.
   Section 3.3 of RFC 6979 recommends 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
   provided herein is similar, with such difference that a key derived
   from G(x) 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 which requires entropy sources according to RFC 6979
   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 of RFC 6979 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.

8.  Normative References

              Yilek, Scott, et al, ., "When private keys are public -
              Results from the 2008 Debian OpenSSL vulnerability", n.d.,

   [DualEC]   Bernstein, Daniel et al, ., "Dual EC - A standardized back
              door", n.d., <

   [NAXOS]    LaMacchia, Brian et al, ., "Stronger Security of
              Authenticated Key Exchange", n.d.,

   [RFC2104]  Krawczyk, H., Bellare, M., and R. Canetti, "HMAC: Keyed-
              Hashing for Message Authentication", RFC 2104,
              DOI 10.17487/RFC2104, February 1997,

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   [RFC5869]  Krawczyk, H. and P. Eronen, "HMAC-based Extract-and-Expand
              Key Derivation Function (HKDF)", RFC 5869,
              DOI 10.17487/RFC5869, May 2010,

   [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, <>.

              "Recommendation for Random Number Generation Using
              Deterministic Random Bit Generators (Revised), NIST
              Special Publication 800-90A, January 2012.", n.d.,
              <National Institute of Standards and Technology>.

   [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..

   [X962]     "Public Key Cryptography for the Financial Services
              Industry -- The Elliptic Curve Digital Signature Algorithm
              (ECDSA), ANSI X9.62-2005, November 2005.", n.d., <American
              National Standards Institute>.

Authors' Addresses

   Cas Cremers
   University of Oxford
   Wolfson Building, Parks Road


   Luke Garratt
   University of Oxford
   Wolfson Building, Parks Road


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   Stanislav Smyshlyaev
   18, Suschevsky val
   Russian Federation


   Nick Sullivan
   101 Townsend St
   San Francisco
   United States of America


   Christopher A. Wood
   Apple Inc.
   One Apple Park Way
   Cupertino, California 95014
   United States of America


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