Joseph Ashwood writes, regarding unauthenticated DH:
> I would actually recommend sending all the public data. This does not take 
> significant additional space and allows more verification to be performed. I 
> would also suggest looking at what exactly the goal is. As written this 
> provides no authentication just privacy, and if b uses the same private key 
> to generate multiple yb the value of b will slowly leak.

I'm not familiar with this last claim, that the value of b's private key
(presuming that is what you mean) would slowly leak if it were reused for
many DH exchanges. Can you explain what you mean? Are you talking about
Lim&Lee style attacks where the recipient does not check the parameters
for validity? In that case I would say the private exponent would leak
quickly rather than slowly. But if the parameters are checked, I don't
see how that would leak a reused exponent.

> You can then use the gpb trio for DSA, leveraging the key set for more 
> capabilities.

Presuming here you mean (g,p,q) as suitable for reuse. This raises the
question, is the same set of (g,p,q) parameters suitable for use in both
DH exchange and DSA signatures?

>From the security engineering perspective, I'd suggest that the goals and
threat models for encryption vs signatures are different enough that one
would prefer different parameters for the two. For DSA signatures, we'd
like small subgroups, since the subgroup size determines the signature
size. This constraint is not present with DH encryption, where a large
subgroup will work as well as a small one. Large subgroups can then
support larger private exponents in the DH exchange.

Now it may be argued that large subgroups do not actually increase
security in the DH exchange, because index calculus methods are
independent of subgroup size. In fact, parameters for DSA signatures
are typically chosen so that subgroup based methods such as Shanks that
take sqrt(q) cost are balanced against estimates of index calculus
work to break p. However, this balancing is inherently uncertain and
it's possible that p-based attacks will turn out to be harder than ones
based on q. Hence one would prefer to use a larger q to provide a margin
of safety if the costs are not too high. While there is a computational
cost to using a larger subgroup for DH exchange, there is no data cost,
while for DSA there are both computational and data costs. Therefore the
tradeoffs for DH would tend to be different than for DSA, and a larger
q would be preferred for DH, all else equal. In fact it is rather common
in DH parameter sets to use Sophie-Germain primes for q.

We may also consider that breaking encryption keys is a passive
attack which can be mounted over a larger period of time (potentially
providing useful information even years after the keys were retired)
and is largely undetectable; while breaking signatures, to be useful,
must be performed actively, carries risks of detection, and must be
completed within a limited time frame. All these considerations motivate
using larger parameter sets for DH encryption than for DSA signatures.

Hal Finney

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