Re: [Cfrg] Static-DH oracles, strong-DH security

"Filippo Valsorda" <> Fri, 22 November 2019 06:57 UTC

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Date: Fri, 22 Nov 2019 01:55:44 -0500
From: "Filippo Valsorda" <>
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Subject: Re: [Cfrg] Static-DH oracles, strong-DH security
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Thank you Taylor for the great summary. I was asked to look into this
for ristretto255 and my results match yours.

2019-11-21 19:01 GMT-05:00 Taylor R Campbell <>et>:
> To be clear: I don't mean to suppose limiting adversaries to 2^64
> queries overall; rather, I mean to suppose limiting them to 2^64
> queries made _one after the other_ -- not in parallel.
> What matters is the _latency_ of a query, not the _bandwidth_ of the
> global Cloudflare network.  And I think it is quite reasonable to
> suppose limiting the latency of a query to at least a nanosecond:

I think it's even reasonable to assume a latency of 10 nanoseconds,
meaning 684245902131068969 queries would take two centuries, leaving the
only realistic attack at 2^118.

For a query to take 10ns, all of the following need to be true:

* Every bus in the path needs to have a minimum bandwidth of 25.6 Gb/s
(unidirectional, assuming 32 bytes per query, not taking into account
query submission pauses)

* The target and the attacker can't be more than 1.5m (5ft) apart

* The target must be able to compute a scalar multiplication in 30
cycles on a 3GHz core (about the L3 cache latency on Skylake)

Importantly, many of these bottlenecks are under control of the target,
not the attacker, so there is no need to speculate about potential
attacker capabilities.