Network Working Group                                         C. Cremers
Internet-Draft                                                L. Garratt
Intended status: Informational                      University of Oxford
Expires: April 24, 2019                                    S. Smyshlyaev
                                                             N. Sullivan
                                                                 C. Wood
                                                              Apple Inc.
                                                        October 21, 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.  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 participants to
   augment their CSPRNGs using long-term private keys.  This improves
   randomness from broken or otherwise subverted CSPRNGs.

Status of This Memo

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   Internet-Drafts are working documents of the Internet Engineering
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   This Internet-Draft will expire on April 24, 2019.

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Copyright Notice

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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  . . . . . . . . . . . . . . . . . . . . .   5
   5.  IANA Considerations . . . . . . . . . . . . . . . . . . . . .   5
   6.  Security Considerations . . . . . . . . . . . . . . . . . . .   5
   7.  Comparison to RFC 6979  . . . . . . . . . . . . . . . . . . .   6
   8.  Normative References  . . . . . . . . . . . . . . . . . . . .   7
   Authors' Addresses  . . . . . . . . . . . . . . . . . . . . . . .   8

1.  Introduction

   Randomness is a crucial ingredient for TLS and related transport
   security protocols.  TLS in particular uses random number generators
   (generally speaking, CSPRNGs) to generate several values: session
   IDs, 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 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 randomness 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
   random value x is replaced by H(x, sk), where sk is the sender's

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   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.

   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 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 output of a CSPRNG.  When properly instantiated, x
   should be indistinguishable from a random string of x bytes.
   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 randomness.

   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 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 n bytes.

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   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 G(n) when
   randomness is needed, use G'(n), where

          G'(n) = 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 n bytes.  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 of G'(n) reduces to the
   scenario wherein randomness is expanded directly from G(n).

   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 and
   Expand functions) can be implemented either inside or outside the

   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.  To achieve this, tag1 may have the format that
   is not supported (or explicitly forbidden) by other applications
   using sk.

   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 generation.

   In systems where signature computations are expensive, G'(n) may be
   precomputed and pooled.  This is possible since the construction
   depends solely upon the CSPRNG output and private key.

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:

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   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.  To provide
      security in the cases of usage of CSPRNGs in virtual environments,
      it is RECOMMENDED to 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).  It
      is needed to address the problem of CSPRNG state cloning (see
      [RY2010]}.  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 outputs of G(L) were to
      repeat.  It MUST be implemented such that its values never repeat.
      This means, in particular, that timestamp is guaranteed to change
      between two requests to CSPRNG (otherwise counters should be

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" CSPRNG G(n), i.e., the
   CSPRNG that generates private values, such as key shares, with:

   G'(n) = 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

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   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 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, 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.

   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]).  Thus tag1 SHOULD incorporate all
   available information about the environment, such as process
   attributes, virtual machine user information, etc.

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 [X9.62], 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 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

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   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",

   [DualEC]   Bernstein, Daniel et al, "Dual EC - A standardized

              McGrew, Anderson, Fluhrer, Shenefeil, "PRNG Failures and
              TLS Vulnerabilities in the Wild",

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

   [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, <>.

   [RY2010]   Ristenpart, Yilek, "When Good Randomness Goes Bad: Virtual
              Machine Reset Vulnerabilities and Hedging Deployed

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

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   [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.

Authors' Addresses

   Cas Cremers
   University of Oxford
   Wolfson Building, Parks Road


   Luke Garratt
   University of Oxford
   Wolfson Building, Parks Road


   Stanislav Smyshlyaev
   18, Suschevsky val
   Russian Federation


   Nick Sullivan
   101 Townsend St
   San Francisco
   United States of America


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


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