An Important Realisation of Elliptic Curve Cryptography.
- From: adacrypt <austin.obyrne@xxxxxxxxxxx>
- Date: Tue, 7 Feb 2012 03:06:12 -0800 (PST)
Let me zoom in as quickly as possible so that readers can synchronise
their thoughts with what I am saying.
I have been labouring the point all along that the perceived weakness
in all current cryptography is the sheer natural transparency of our
beautiful number system that makes it so unsuitable for cryptography.
I have made the point also that the solution to this is to stop using
numbers directly in their Arabic form as code points on an arbitrary
straight line and instead to go over to using analogues of the same
numbers that enables alternative methods in cryptography.
The alternative that I propounding is by means of several ciphers in
‘displacement’ theory as cryptography that uses vector methodology.
I have already produced one or two methods that use vectors that
enable this to succeed and there are many more from the same source
but is it necessary to go any further is a good question.
This brings me up to what I want to say next.
The vector method that I first used is a straight ‘directed’ number
line, the sort that is defined by a vector equation.
A variation of this came next as something that I am calling “Skew
The penny has dropped with me now however – the second method i.e.
skew curve is only a variation of the first and indeed is not quite as
good technically. What is important to realise is that there is no
point in going any further looking for other new vector methods – I
already have the best there is and looking for more is simply “gilding
This is displacement cryptography by generic name and is the way
forward for all future cryptography in my view.
What is immensely important in my view now is to realise also that
“Elliptic Curve Cryptography” is also nothing else but displacement
cryptography that is being done by the much more difficult means of
This is retrogressive hard work because that is what Rowan Hamilton
invented vector methods for i.e. to obviate the horrendous task of
doing spatial mechanics by scalar geometric means – read ‘ditto’ now
for today’s cryptography instead of mechanics, the difficulty is just
the same and can fortunately be solved by the same means.
Displacement cryptography by scalar means is what the elliptic curve
cipher is attempting to do and I say stop doing it because it seems to
be retrogressive. I believe the authors of elliptic curve crypto are
instinctively doing what I am also doing i.e. realising that
displacement cryptography is the way to overcome the natural weakness
of numbers a la the universal number line and instead they realise
that widely displaced numbers are what is needed instead – by analogy
to a fisherman - numbers that are cast out disparately into three-
dimensional by Alice but in a controlled way for reeling in later by
This is not a criticism nor any attempt at denigrating other peoples’
work but I honestly think that we are all at cross purposes here and
that there is an all round benefit to be had from pooling our
resources by going over to displacement cryptography completely, once
and for all but using the well established methods in vector
Elliptic curve is a scalar method of doing the same thing as my vector
cryptography but by analogy again it is like trying to construct a
grand piano using a blunt stone as the woodwork cutting tool, in terms
I believe I am right here in making these bullish statements because
the implications to future cryptography are enormous – the way forward
is in displacement cryptography that uses vector methods and that
should embrace elliptic curve crypto also.
The current elliptic curve cipher is only one scalar alternative to
vector methods that may be derived in the future – there will be lots
more to come in other geometric models but again they will be so
difficult that they will be no better than this first one and they are
so laborious that they are to be compared to cycling backwards while
playing Mantovani. Don’t do it I is what I am saying now and instead
start pooling our resources in a general, fresh new-leaf approach to
displacement cryptography as an alternative to the status quo.
Vector methods are as much to cryptography today as they were to
mechanics nearly three centuries ago – I think this fact is escaping
the notice of the elliptic curve protagonists - the writing is on the
wall, realise it now and go for it – we will all benefit from it if
I am not seeking to rattle the bars of anybody’s cage here – this is
an altruistic attempt at a well-meaning contribution to cryptography.
I haven’t studied elliptic curve crypto deeply except to get a quick
idea of how it works – there is no need for me to go deeply into it to
make the observation that it is merely a scalar way of doing what is
much more easily done by using the already well-known vector
methodology in mathematics that I am propounding.
Elliptic curve cryptography as far as I can see is a variation of what
I am calling displacement cryptography – what I am advocating is to
stop duplicating well established vector methods with more difficult
scalar methods and join forces in staking out methods now for the all
round general good in the future without further ado.