[Ntp] A simpler way to secure PTP

[Daniel Franke <[e-mail]>]

As an alternative to Martin's and Heiko's drafts, I'd like to propose a
simpler approach to securing PTP. It is compatible with all PTP features,
supports the same threat model as NTS-secured NTP, introduces zero jitter,
and can be implemented entirely on the client side without the knowledge or
cooperation of the rest of the PTP infrastructure.

The trick is: run NTS-secured NTP and regular, unauthenticated PTP
side-by-side. Do not use the NTP responses to set the clock; instead, use
them only to establish maximum error bounds on the current time, and then
clamp all PTP messages to within those bounds.

The client's on-wire interaction with the NTP server is the same as it is
in normal NTS-secured NTP, but the way it processes the server's responses
is different. The client maintains an estimate `theta` of the offset
between a local, unadjusted monotonic clock `t_raw` (implemented e.g. by
CLOCK_MONOTONIC_RAW on linux) and the server's realtime clock, along with a
continuously-changing error term `lamdba`.

Upon receiving an authentic response from an NTP server, let:

  t_1 = origin timestamp captured from t_raw.
  t_2 = packet receive timestamp
  t_3 = packet transmit timestamp
  t_4 = destination timestamp captured from t_raw.
  theta = ((t_2 - t_1) + (t_3 - t_4))/2
  DTAI = TAI - UTC offset

giving a current estimated TAI time of

  t_raw + theta + DTAI

For computing error bounds, let

  hrtt = (t_4 - t_1)/2
  rdel = packet root delay
  r_1 = local clock precision
  r_2 = packet clock precision
  PHI = some appropriate upper bound on our local clock's drift rate

and then our error term is plus-or-minus

  hrtt + rdel/2 + r_1 + r_2 + PHI*(t_raw - t_1)

Only the single best clock sample, from a given NTP server, i.e. the one
that gives the tightest error bounds, need be retained. Other things being
equal, newer samples will be preferable to older ones because the
PHI*(t_raw - t_1) term will be smaller, but sometimes this may be negated
by other terms such as hrtt being larger.

A client may gain resiliency by using multiple NTS-secured NTP servers. In
this case for N servers it lets f=floor((N-1)/2), then discards the f
lowest lower bounds and the f highest upper bounds, and then treats
anything inside any of the remaining bounds as plausible.

Any PTP message whose time (after applying the usual link-delay correction)
is plausible according to these bounds is processed as usual. Any PTP
message whose time is not plausible is first clamped to the nearest bound
and then processed as usual.

And that's all there is to it!