Network Working Group                                         C. Cramers
Internet-Draft                                                L. Garratt
Intended status: Informational                      University of Oxford
Expires: May 3, 2018                                         N. Sullivan
                                                        October 30, 2017

             Randomness Improvements for Security Protocols


   Randomness is a crucial ingredient for TLS and related transport
   security protocols.  Weak or predictable cryptographically-strong
   pseudorandom number generators (CSPRNGs) can be abused or exploited
   for malicious purposes.  See the Dual EC random number backdoor for a
   relevant example of this problem.  This document describes a way for
   security protocol participants to mix their long-term private key
   into the entropy pool from which random values are derived.  This may
   help mitigate problems that stem from broken CSPRNGs.

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   carefully, as they describe your rights and restrictions with respect
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Table of Contents

   1.  Introduction  . . . . . . . . . . . . . . . . . . . . . . . .   2
   2.  Randomness Wrapper  . . . . . . . . . . . . . . . . . . . . .   2
   3.  Application to TLS  . . . . . . . . . . . . . . . . . . . . .   3
   4.  IANA Considerations . . . . . . . . . . . . . . . . . . . . .   4
   5.  Security Considerations . . . . . . . . . . . . . . . . . . .   4
   6.  Normative References  . . . . . . . . . . . . . . . . . . . .   4
   Authors' Addresses  . . . . . . . . . . . . . . . . . . . . . . .   4

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
   but functionally equivalent construction is needed.

   The approach described herein replaces the NAXOS hash with the keyed
   hash, or PRF, wherein the key is derived from raw entropy output and
   a private key signature.

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 always true.
   To mitigate this problem, we propose an approach for wrapping the

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   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.
   Lastly, let KDF be a key derivation function, e.g., HKDF-Extract
   [RFC5869], that extracts a key of length L suitable for cryptographic

   The construction is simple: instead of using x when randomness is
   needed, use:

   PRF(KDF(G(x) || Sig(sk, tag)), tag)

   Functionally, this computes the PRF of a fixed string with a key
   derived from the CSPRNG output and signature over the fixed string.
   The PRF behaves like a truly random function from 2^L to 2^M assuming
   the key is selected at random.  Thus, the security of this
   construction depends on secrecy of Sig(sk, tag) and G(x).  If both
   are leaked, then the security reduces to the scenario wherein this
   wrapping construction is not applied.

   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.

3.  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, tag)), tag)

   Moreover, we fix tag as "TLS 1.3 Additional Entropy" for TLS 1.3.
   Older variants use similarly constructed strings.

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4.  IANA Considerations

   This document makes no request to IANA.

5.  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 random wrapper was not applied in the first

6.  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,

Authors' Addresses

   Cas Cremers
   University of Oxford
   Wolfson Building, Parks Road


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Internet-Draft           Randomness Improvements            October 2017

   Luke Garratt
   University of Oxford
   Wolfson Building, Parks Road


   Nick Sullivan
   101 Townsend St
   San Francisco
   United States of America


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