# 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

Curve” cryptography.

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

the lily”.

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

scalar methods.

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

Bob.

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

arithmetic.

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

of efficiency.

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

you do.

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.

- adacrypt

.

- Prev by Date:
**Re: Skew Curve Cryptography – The Winds of Inevitable Change.** - Next by Date:
**Primes in arithmetic progressions** - Previous by thread:
**Cryptanalysis of this New Cryptography** - Next by thread:
**Primes in arithmetic progressions** - Index(es):