wkaras@yahoo.com wrote:
> Are there gateway routers

same thing . though perhaps a gateway needn't use a routing table and
perhaps a router must.

> available that can be provisioned to
> use a simple mathematical conversion between external
> and private static addresses. An example might be private
> address equals 10.0.A.B:500C where A, B, C are digits
> in the external port number 50ABC.

that port looks funny, I don't think they get that big

>The gateway would
> use ARP to route packets

ARP doesn't route packets. A network protocol e.g. IP routes packets.

> on the private lan. It would
> not need to act as a DHCP server (or gateway).

MAC addresses are usually stored by the manufacturer. How would you
ensure in your mathematics that 2 MACs don't get the same IP. It
doesn't look sensible. MAC addresses aer given to you, and private
addresses don't have much flexibility. limited ranges, and are best
contiguous/incrementing by 1 or in contiguous groups, so as to be easy
to remember and for subnetting purposes.
You could look up an addrses and make sure it's nto already taken, but
that's silly 'cos
ARP is fairly quick, and it uses an ARP Cache/table. And just looks up
the address.

So either way you're searching through a table. Yours is worse 'cos you
have to search through the whole table.