Network Working Group                                         C. Cremers
Internet-Draft                                                L. Garratt
Intended status: Informational                      University of Oxford
Expires: September 2, 2018                                 S. Smyshlyaev
                                                             N. Sullivan
                                                                 C. Wood
                                                              Apple Inc.
                                                          March 01, 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

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   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 September 2, 2018.

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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 . . . . . . . . . . . . . . . . . . . . .   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.

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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.

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.

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   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.

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   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

              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,

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

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   [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, <>.

   [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


   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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