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The Evolution of Vector factoring and Vector Cryptography.
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Austin Obyrne
May 19, 2013, 7:25:28 AM5/19/13
to
Readers might well ask what’s behind this claim by me to have invented vector-based i.e. spatial displacement cryptography so I would like to give a resume of how it evolved over twenty years and more.
It started in a UK university where I was a mature student (in my fifties) studying "Pure and Applied Mathematics" in the late 80’s.
Career achievements before that meant I did not require this degree to add to my cv for employment-enhancing reasons – I had already attained Chartered Engineer Status and a Fellowship of my Institute as well as a very good track record so I wasn’t in need of it for that reason.
In between the subjects of my various courses at the university I became interested in a new topic in mathematics that I was to call “Factorising” of a vector – a vector to be taken here as being a physical vector that is used in physics and engineering to represent physical quantities like velocity and acceleration.
What I wanted was a method of finding all of the pairs of vectors that would always multiply out in the vector or cross product to give the same result i.e. some vector to be factorised being represented as a cross product vector.
To explain, the factors are used as the multiplicand and multiplier respectively of the crossproduct multiplication process that always works out to be the same vector result that is of course the vector being factorised.
A lecturer who is the author of several books in Number Theory and Group Theory and who has had 35 years of lecturing in both UK universities and in the USA was aware of my work at the time and on one occasion gave me some small help. I do not solicit any kudos of association with an academic person(without his permission)that this might imply from this small help – he did not continue any further involvement. I mention his small involvement as tacit proof that the invention of factoring of vectors by me as his student was not some unreal pie-in-the-sky stuff.
Can I digress for a moment here also to say in general, how very transparent any claim is to a well-informed mathematician on the back of submitted proofs and how easily with few deft statements he/she can demolish an unsound claim.
The mathematics of vector factoring makes heavy use of long-established methods in the vector geometry of planes and my use of standard theorems in that topic of mathematics and how this it is projected on to the new topic of vector factoring has been demonstrated unsparingly all the way along the line. I am confident of my proofs which have been seen by a few other mathematicians, the inference being made here is that my invention of vector factoring is well proven and sound.
Vector factoring was an end in itself to me at this time and I had no interest in cryptography. I gave my paper on the subject to another mathematician to read who it transpired was in fact a cryptographer as well being a university lecture in mathematics and after reading it he introduced me to cryptography, albeit he saw no application in my work himself as a straight off result of reading my paper.
The application of factoring to cryptography came to me via my discernment of the vector equation of a straight line and a factoring application to this which I have since those early days developed into the cipher I am promoting to readers here today.
This application to cryptography has taken about fifteen years of very hard exploratory work involving thousands of test examples before the final realisation of the cipher as a working program in the Ada-95 programming language.
In all, the cryptography being called variously ”Vector Cryptography”, “Spatial Cryptography”, “Displacement Cryptography”, “Skew Line Cryptography”, has taken over 20 years of very hard work and has been thoroughly tested by me before recommending it to the readership.
Mathematician / cryptographer readers should have no difficulty in supporting it in any way.
- adacrypt
It started in a UK university where I was a mature student (in my fifties) studying "Pure and Applied Mathematics" in the late 80’s.
Career achievements before that meant I did not require this degree to add to my cv for employment-enhancing reasons – I had already attained Chartered Engineer Status and a Fellowship of my Institute as well as a very good track record so I wasn’t in need of it for that reason.
In between the subjects of my various courses at the university I became interested in a new topic in mathematics that I was to call “Factorising” of a vector – a vector to be taken here as being a physical vector that is used in physics and engineering to represent physical quantities like velocity and acceleration.
What I wanted was a method of finding all of the pairs of vectors that would always multiply out in the vector or cross product to give the same result i.e. some vector to be factorised being represented as a cross product vector.
To explain, the factors are used as the multiplicand and multiplier respectively of the crossproduct multiplication process that always works out to be the same vector result that is of course the vector being factorised.
A lecturer who is the author of several books in Number Theory and Group Theory and who has had 35 years of lecturing in both UK universities and in the USA was aware of my work at the time and on one occasion gave me some small help. I do not solicit any kudos of association with an academic person(without his permission)that this might imply from this small help – he did not continue any further involvement. I mention his small involvement as tacit proof that the invention of factoring of vectors by me as his student was not some unreal pie-in-the-sky stuff.
Can I digress for a moment here also to say in general, how very transparent any claim is to a well-informed mathematician on the back of submitted proofs and how easily with few deft statements he/she can demolish an unsound claim.
The mathematics of vector factoring makes heavy use of long-established methods in the vector geometry of planes and my use of standard theorems in that topic of mathematics and how this it is projected on to the new topic of vector factoring has been demonstrated unsparingly all the way along the line. I am confident of my proofs which have been seen by a few other mathematicians, the inference being made here is that my invention of vector factoring is well proven and sound.
Vector factoring was an end in itself to me at this time and I had no interest in cryptography. I gave my paper on the subject to another mathematician to read who it transpired was in fact a cryptographer as well being a university lecture in mathematics and after reading it he introduced me to cryptography, albeit he saw no application in my work himself as a straight off result of reading my paper.
The application of factoring to cryptography came to me via my discernment of the vector equation of a straight line and a factoring application to this which I have since those early days developed into the cipher I am promoting to readers here today.
This application to cryptography has taken about fifteen years of very hard exploratory work involving thousands of test examples before the final realisation of the cipher as a working program in the Ada-95 programming language.
In all, the cryptography being called variously ”Vector Cryptography”, “Spatial Cryptography”, “Displacement Cryptography”, “Skew Line Cryptography”, has taken over 20 years of very hard work and has been thoroughly tested by me before recommending it to the readership.
Mathematician / cryptographer readers should have no difficulty in supporting it in any way.
- adacrypt
Austin Obyrne
May 19, 2013, 1:48:30 PM5/19/13
to
On Sunday, May 19, 2013 12:25:28 PM UTC+1, Austin Obyrne wrote:
> Readers might well ask what’s behind this claim by me to have invented vector-based i.e. spatial displacement cryptography so I would like to give a resume of how it evolved over twenty years and more. It started in a UK university where I was a mature student (in my fifties) studying "Pure and Applied Mathematics" in the late 80’s. Career achievements before that meant I did not require this degree to add to my cv for employment-enhancing reasons – I had already attained Chartered Engineer Status and a Fellowship of my Institute as well as a very good track record so I wasn’t in need of it for that reason. In between the subjects of my various courses at the university I became interested in a new topic in mathematics that I was to call “Factorising” of a vector – a vector to be taken here as being a physical vector that is used in physics and engineering to represent physical quantities like velocity and acceleration. What I wanted was a method of finding all of the pairs of vectors that would always multiply out in the vector or cross product to give the same result i.e. some vector to be factorised being represented as a cross product vector. To explain, the factors are used as the multiplicand and multiplier respectively of the crossproduct multiplication process that always works out to be the same vector result that is of course the vector being factorised. A lecturer who is the author of several books in Number Theory and Group Theory and who has had 35 years of lecturing in both UK universities and in the USA was aware of my work at the time and on one occasion gave me some small help. I do not solicit any kudos of association with an academic person(without his permission)that this might imply from this small help – he did not continue any further involvement. I mention his small involvement as tacit proof that the invention of factoring of vectors by me as his student was not some unreal pie-in-the-sky stuff. Can I digress for a moment here also to say in general, how very transparent any claim is to a well-informed mathematician on the back of submitted proofs and how easily with few deft statements he/she can demolish an unsound claim. The mathematics of vector factoring makes heavy use of long-established methods in the vector geometry of planes and my use of standard theorems in that topic of mathematics and how this it is projected on to the new topic of vector factoring has been demonstrated unsparingly all the way along the line. I am confident of my proofs which have been seen by a few other mathematicians, the inference being made here is that my invention of vector factoring is well proven and sound. Vector factoring was an end in itself to me at this time and I had no interest in cryptography. I gave my paper on the subject to another mathematician to read who it transpired was in fact a cryptographer as well being a university lecture in mathematics and after reading it he introduced me to cryptography, albeit he saw no application in my work himself as a straight off result of reading my paper. The application of factoring to cryptography came to me via my discernment of the vector equation of a straight line and a factoring application to this which I have since those early days developed into the cipher I am promoting to readers here today. This application to cryptography has taken about fifteen years of very hard exploratory work involving thousands of test examples before the final realisation of the cipher as a working program in the Ada-95 programming language. In all, the cryptography being called variously ”Vector Cryptography”, “Spatial Cryptography”, “Displacement Cryptography”, “Skew Line Cryptography”, has taken over 20 years of very hard work and has been thoroughly tested by me before recommending it to the readership. Mathematician / cryptographer readers should have no difficulty in supporting it in any way. - adacrypt
Supplement to the Foregoing.
> Readers might well ask what’s behind this claim by me to have invented vector-based i.e. spatial displacement cryptography so I would like to give a resume of how it evolved over twenty years and more. It started in a UK university where I was a mature student (in my fifties) studying "Pure and Applied Mathematics" in the late 80’s. Career achievements before that meant I did not require this degree to add to my cv for employment-enhancing reasons – I had already attained Chartered Engineer Status and a Fellowship of my Institute as well as a very good track record so I wasn’t in need of it for that reason. In between the subjects of my various courses at the university I became interested in a new topic in mathematics that I was to call “Factorising” of a vector – a vector to be taken here as being a physical vector that is used in physics and engineering to represent physical quantities like velocity and acceleration. What I wanted was a method of finding all of the pairs of vectors that would always multiply out in the vector or cross product to give the same result i.e. some vector to be factorised being represented as a cross product vector. To explain, the factors are used as the multiplicand and multiplier respectively of the crossproduct multiplication process that always works out to be the same vector result that is of course the vector being factorised. A lecturer who is the author of several books in Number Theory and Group Theory and who has had 35 years of lecturing in both UK universities and in the USA was aware of my work at the time and on one occasion gave me some small help. I do not solicit any kudos of association with an academic person(without his permission)that this might imply from this small help – he did not continue any further involvement. I mention his small involvement as tacit proof that the invention of factoring of vectors by me as his student was not some unreal pie-in-the-sky stuff. Can I digress for a moment here also to say in general, how very transparent any claim is to a well-informed mathematician on the back of submitted proofs and how easily with few deft statements he/she can demolish an unsound claim. The mathematics of vector factoring makes heavy use of long-established methods in the vector geometry of planes and my use of standard theorems in that topic of mathematics and how this it is projected on to the new topic of vector factoring has been demonstrated unsparingly all the way along the line. I am confident of my proofs which have been seen by a few other mathematicians, the inference being made here is that my invention of vector factoring is well proven and sound. Vector factoring was an end in itself to me at this time and I had no interest in cryptography. I gave my paper on the subject to another mathematician to read who it transpired was in fact a cryptographer as well being a university lecture in mathematics and after reading it he introduced me to cryptography, albeit he saw no application in my work himself as a straight off result of reading my paper. The application of factoring to cryptography came to me via my discernment of the vector equation of a straight line and a factoring application to this which I have since those early days developed into the cipher I am promoting to readers here today. This application to cryptography has taken about fifteen years of very hard exploratory work involving thousands of test examples before the final realisation of the cipher as a working program in the Ada-95 programming language. In all, the cryptography being called variously ”Vector Cryptography”, “Spatial Cryptography”, “Displacement Cryptography”, “Skew Line Cryptography”, has taken over 20 years of very hard work and has been thoroughly tested by me before recommending it to the readership. Mathematician / cryptographer readers should have no difficulty in supporting it in any way. - adacrypt
A vector to be factored (factorised if you prefer) is proposed initially as being the defining normal vector of a plane that passes through the origin at (0,0,0)i.e. it contains the point (0,0,0)
This defining normal vector is designated N say.
The factors of N (the vector being factorized) then occur as the position vectors (V) of consecutive number points ‘n’ and ‘n-1’ on special factor lines that lie within the plane such that:
Vn x V(n-1) = N - true for all ‘n’ although only integer values of n are used in the cryptography that emanates from this topic of ‘factoring of a vector’.
Many readers will see straight away that there is very profound classroom discussion possible coming from this use of plane geometry to begin with even before any discussion of the cryptography that later follows even starts.
As applied to cryptography, only integer values of ‘n’ are used and furthermore, only non-zero integer coefficients of the i, j, k unit vectors of N are used by deliberate design.
Outside of cryptography, factoring of a vector is a "solution waiting for problems" and may yet becomie very useful to design people in many other disciplines also.
- adacrypt
Austin Obyrne
May 20, 2013, 3:37:49 AM5/20/13
to
On Sunday, May 19, 2013 6:48:30 PM UTC+1, Austin Obyrne wrote:
> On Sunday, May 19, 2013 12:25:28 PM UTC+1, Austin Obyrne wrote: > Readers might well ask what’s behind this claim by me to have invented vector-based i.e. spatial displacement cryptography so I would like to give a resume of how it evolved over twenty years and more. It started in a UK university where I was a mature student (in my fifties) studying "Pure and Applied Mathematics" in the late 80’s. Career achievements before that meant I did not require this degree to add to my cv for employment-enhancing reasons – I had already attained Chartered Engineer Status and a Fellowship of my Institute as well as a very good track record so I wasn’t in need of it for that reason. In between the subjects of my various courses at the university I became interested in a new topic in mathematics that I was to call “Factorising” of a vector – a vector to be taken here as being a physical vector that is used in physics and engineering to represent physical quantities like velocity and acceleration. What I wanted was a method of finding all of the pairs of vectors that would always multiply out in the vector or cross product to give the same result i.e. some vector to be factorised being represented as a cross product vector. To explain, the factors are used as the multiplicand and multiplier respectively of the crossproduct multiplication process that always works out to be the same vector result that is of course the vector being factorised. A lecturer who is the author of several books in Number Theory and Group Theory and who has had 35 years of lecturing in both UK universities and in the USA was aware of my work at the time and on one occasion gave me some small help. I do not solicit any kudos of association with an academic person(without his permission)that this might imply from this small help – he did not continue any further involvement. I mention his small involvement as tacit proof that the invention of factoring of vectors by me as his student was not some unreal pie-in-the-sky stuff. Can I digress for a moment here also to say in general, how very transparent any claim is to a well-informed mathematician on the back of submitted proofs and how easily with few deft statements he/she can demolish an unsound claim. The mathematics of vector factoring makes heavy use of long-established methods in the vector geometry of planes and my use of standard theorems in that topic of mathematics and how this it is projected on to the new topic of vector factoring has been demonstrated unsparingly all the way along the line. I am confident of my proofs which have been seen by a few other mathematicians, the inference being made here is that my invention of vector factoring is well proven and sound. Vector factoring was an end in itself to me at this time and I had no interest in cryptography. I gave my paper on the subject to another mathematician to read who it transpired was in fact a cryptographer as well being a university lecture in mathematics and after reading it he introduced me to cryptography, albeit he saw no application in my work himself as a straight off result of reading my paper. The application of factoring to cryptography came to me via my discernment of the vector equation of a straight line and a factoring application to this which I have since those early days developed into the cipher I am promoting to readers here today. This application to cryptography has taken about fifteen years of very hard exploratory work involving thousands of test examples before the final realisation of the cipher as a working program in the Ada-95 programming language. In all, the cryptography being called variously ”Vector Cryptography”, “Spatial Cryptography”, “Displacement Cryptography”, “Skew Line Cryptography”, has taken over 20 years of very hard work and has been thoroughly tested by me before recommending it to the readership. Mathematician / cryptographer readers should have no difficulty in supporting it in any way. - adacrypt Supplement to the Foregoing. A vector to be factored (factorised if you prefer) is proposed initially as being the defining normal vector of a plane that passes through the origin at (0,0,0)i.e. it contains the point (0,0,0) This defining normal vector is designated N say. The factors of N (the vector being factorized) then occur as the position vectors (V) of consecutive number points ‘n’ and ‘n-1’ on special factor lines that lie within the plane such that: Vn x V(n-1) = N - true for all ‘n’ although only integer values of n are used in the cryptography that emanates from this topic of ‘factoring of a vector’. Many readers will see straight away that there is very profound classroom discussion possible coming from this use of plane geometry to begin with even before any discussion of the cryptography that later follows even starts. As applied to cryptography, only integer values of ‘n’ are used and furthermore, only non-zero integer coefficients of the i, j, k unit vectors of N are used by deliberate design. Outside of cryptography, factoring of a vector is a "solution waiting for problems" and may yet becomie very useful to design people in many other disciplines also. - adacrypt
Supplement – 2
> On Sunday, May 19, 2013 12:25:28 PM UTC+1, Austin Obyrne wrote: > Readers might well ask what’s behind this claim by me to have invented vector-based i.e. spatial displacement cryptography so I would like to give a resume of how it evolved over twenty years and more. It started in a UK university where I was a mature student (in my fifties) studying "Pure and Applied Mathematics" in the late 80’s. Career achievements before that meant I did not require this degree to add to my cv for employment-enhancing reasons – I had already attained Chartered Engineer Status and a Fellowship of my Institute as well as a very good track record so I wasn’t in need of it for that reason. In between the subjects of my various courses at the university I became interested in a new topic in mathematics that I was to call “Factorising” of a vector – a vector to be taken here as being a physical vector that is used in physics and engineering to represent physical quantities like velocity and acceleration. What I wanted was a method of finding all of the pairs of vectors that would always multiply out in the vector or cross product to give the same result i.e. some vector to be factorised being represented as a cross product vector. To explain, the factors are used as the multiplicand and multiplier respectively of the crossproduct multiplication process that always works out to be the same vector result that is of course the vector being factorised. A lecturer who is the author of several books in Number Theory and Group Theory and who has had 35 years of lecturing in both UK universities and in the USA was aware of my work at the time and on one occasion gave me some small help. I do not solicit any kudos of association with an academic person(without his permission)that this might imply from this small help – he did not continue any further involvement. I mention his small involvement as tacit proof that the invention of factoring of vectors by me as his student was not some unreal pie-in-the-sky stuff. Can I digress for a moment here also to say in general, how very transparent any claim is to a well-informed mathematician on the back of submitted proofs and how easily with few deft statements he/she can demolish an unsound claim. The mathematics of vector factoring makes heavy use of long-established methods in the vector geometry of planes and my use of standard theorems in that topic of mathematics and how this it is projected on to the new topic of vector factoring has been demonstrated unsparingly all the way along the line. I am confident of my proofs which have been seen by a few other mathematicians, the inference being made here is that my invention of vector factoring is well proven and sound. Vector factoring was an end in itself to me at this time and I had no interest in cryptography. I gave my paper on the subject to another mathematician to read who it transpired was in fact a cryptographer as well being a university lecture in mathematics and after reading it he introduced me to cryptography, albeit he saw no application in my work himself as a straight off result of reading my paper. The application of factoring to cryptography came to me via my discernment of the vector equation of a straight line and a factoring application to this which I have since those early days developed into the cipher I am promoting to readers here today. This application to cryptography has taken about fifteen years of very hard exploratory work involving thousands of test examples before the final realisation of the cipher as a working program in the Ada-95 programming language. In all, the cryptography being called variously ”Vector Cryptography”, “Spatial Cryptography”, “Displacement Cryptography”, “Skew Line Cryptography”, has taken over 20 years of very hard work and has been thoroughly tested by me before recommending it to the readership. Mathematician / cryptographer readers should have no difficulty in supporting it in any way. - adacrypt Supplement to the Foregoing. A vector to be factored (factorised if you prefer) is proposed initially as being the defining normal vector of a plane that passes through the origin at (0,0,0)i.e. it contains the point (0,0,0) This defining normal vector is designated N say. The factors of N (the vector being factorized) then occur as the position vectors (V) of consecutive number points ‘n’ and ‘n-1’ on special factor lines that lie within the plane such that: Vn x V(n-1) = N - true for all ‘n’ although only integer values of n are used in the cryptography that emanates from this topic of ‘factoring of a vector’. Many readers will see straight away that there is very profound classroom discussion possible coming from this use of plane geometry to begin with even before any discussion of the cryptography that later follows even starts. As applied to cryptography, only integer values of ‘n’ are used and furthermore, only non-zero integer coefficients of the i, j, k unit vectors of N are used by deliberate design. Outside of cryptography, factoring of a vector is a "solution waiting for problems" and may yet becomie very useful to design people in many other disciplines also. - adacrypt
Even seasoned mathematicians and professional exponents in other disciplines will find this cryptography very difficult to understand.
It requires a lot of one-to-one chalk ‘n talk.
Understanding the algorithm alone is a major task but keeping au fait with the source code of the programmed cipher is something also that I have to do often myself by rewriting it again and again just to keep in touch.
For all that, this is not a ‘complexity-theoretic’ cryptography and a cipher once it is understood and put to bed as source code is not at all difficult to operate and can be done by non-specialist persons who only need minimal training.
The good side of it all is that this cryptography is clearly unbreakable no matter how much computer power is available to do it.
It is just simply impossible for anybody to write a brute force program that can read the minds of the entities because that alone and nothing less is virtually what is required to break the ciphertext.
No amount of computer power will ever be a threat to the security of this cryptology in the future.
http://www.adacryptpages.com/
http://www.adacrypt.com/
- adacrypt
Austin Obyrne
May 20, 2013, 7:29:09 AM5/20/13
to
On Monday, May 20, 2013 8:37:49 AM UTC+1, Austin Obyrne wrote:
> On Sunday, May 19, 2013 6:48:30 PM UTC+1, Austin Obyrne wrote: > On Sunday, May 19, 2013 12:25:28 PM UTC+1, Austin Obyrne wrote: > Readers might well ask what’s behind this claim by me to have invented vector-based i.e. spatial displacement cryptography so I would like to give a resume of how it evolved over twenty years and more. It started in a UK university where I was a mature student (in my fifties) studying "Pure and Applied Mathematics" in the late 80’s. Career achievements before that meant I did not require this degree to add to my cv for employment-enhancing reasons – I had already attained Chartered Engineer Status and a Fellowship of my Institute as well as a very good track record so I wasn’t in need of it for that reason. In between the subjects of my various courses at the university I became interested in a new topic in mathematics that I was to call “Factorising” of a vector – a vector to be taken here as being a physical vector that is used in physics and engineering to represent physical quantities like velocity and acceleration. What I wanted was a method of finding all of the pairs of vectors that would always multiply out in the vector or cross product to give the same result i.e. some vector to be factorised being represented as a cross product vector. To explain, the factors are used as the multiplicand and multiplier respectively of the crossproduct multiplication process that always works out to be the same vector result that is of course the vector being factorised. A lecturer who is the author of several books in Number Theory and Group Theory and who has had 35 years of lecturing in both UK universities and in the USA was aware of my work at the time and on one occasion gave me some small help. I do not solicit any kudos of association with an academic person(without his permission)that this might imply from this small help – he did not continue any further involvement. I mention his small involvement as tacit proof that the invention of factoring of vectors by me as his student was not some unreal pie-in-the-sky stuff. Can I digress for a moment here also to say in general, how very transparent any claim is to a well-informed mathematician on the back of submitted proofs and how easily with few deft statements he/she can demolish an unsound claim. The mathematics of vector factoring makes heavy use of long-established methods in the vector geometry of planes and my use of standard theorems in that topic of mathematics and how this it is projected on to the new topic of vector factoring has been demonstrated unsparingly all the way along the line. I am confident of my proofs which have been seen by a few other mathematicians, the inference being made here is that my invention of vector factoring is well proven and sound. Vector factoring was an end in itself to me at this time and I had no interest in cryptography. I gave my paper on the subject to another mathematician to read who it transpired was in fact a cryptographer as well being a university lecture in mathematics and after reading it he introduced me to cryptography, albeit he saw no application in my work himself as a straight off result of reading my paper. The application of factoring to cryptography came to me via my discernment of the vector equation of a straight line and a factoring application to this which I have since those early days developed into the cipher I am promoting to readers here today. This application to cryptography has taken about fifteen years of very hard exploratory work involving thousands of test examples before the final realisation of the cipher as a working program in the Ada-95 programming language. In all, the cryptography being called variously ”Vector Cryptography”, “Spatial Cryptography”, “Displacement Cryptography”, “Skew Line Cryptography”, has taken over 20 years of very hard work and has been thoroughly tested by me before recommending it to the readership. Mathematician / cryptographer readers should have no difficulty in supporting it in any way. - adacrypt Supplement to the Foregoing. A vector to be factored (factorised if you prefer) is proposed initially as being the defining normal vector of a plane that passes through the origin at (0,0,0)i.e. it contains the point (0,0,0) This defining normal vector is designated N say. The factors of N (the vector being factorized) then occur as the position vectors (V) of consecutive number points ‘n’ and ‘n-1’ on special factor lines that lie within the plane such that: Vn x V(n-1) = N - true for all ‘n’ although only integer values of n are used in the cryptography that emanates from this topic of ‘factoring of a vector’. Many readers will see straight away that there is very profound classroom discussion possible coming from this use of plane geometry to begin with even before any discussion of the cryptography that later follows even starts. As applied to cryptography, only integer values of ‘n’ are used and furthermore, only non-zero integer coefficients of the i, j, k unit vectors of N are used by deliberate design. Outside of cryptography, factoring of a vector is a "solution waiting for problems" and may yet becomie very useful to design people in many other disciplines also. - adacrypt Supplement – 2 Even seasoned mathematicians and professional exponents in other disciplines will find this cryptography very difficult to understand. It requires a lot of one-to-one chalk ‘n talk. Understanding the algorithm alone is a major task but keeping au fait with the source code of the programmed cipher is something also that I have to do often myself by rewriting it again and again just to keep in touch. For all that, this is not a ‘complexity-theoretic’ cryptography and a cipher once it is understood and put to bed as source code is not at all difficult to operate and can be done by non-specialist persons who only need minimal training. The good side of it all is that this cryptography is clearly unbreakable no matter how much computer power is available to do it. It is just simply impossible for anybody to write a brute force program that can read the minds of the entities because that alone and nothing less is virtually what is required to break the ciphertext. No amount of computer power will ever be a threat to the security of this cryptology in the future. http://www.adacryptpages.com/ http://www.adacrypt.com/ - adacrypt
Supplement-3
> On Sunday, May 19, 2013 6:48:30 PM UTC+1, Austin Obyrne wrote: > On Sunday, May 19, 2013 12:25:28 PM UTC+1, Austin Obyrne wrote: > Readers might well ask what’s behind this claim by me to have invented vector-based i.e. spatial displacement cryptography so I would like to give a resume of how it evolved over twenty years and more. It started in a UK university where I was a mature student (in my fifties) studying "Pure and Applied Mathematics" in the late 80’s. Career achievements before that meant I did not require this degree to add to my cv for employment-enhancing reasons – I had already attained Chartered Engineer Status and a Fellowship of my Institute as well as a very good track record so I wasn’t in need of it for that reason. In between the subjects of my various courses at the university I became interested in a new topic in mathematics that I was to call “Factorising” of a vector – a vector to be taken here as being a physical vector that is used in physics and engineering to represent physical quantities like velocity and acceleration. What I wanted was a method of finding all of the pairs of vectors that would always multiply out in the vector or cross product to give the same result i.e. some vector to be factorised being represented as a cross product vector. To explain, the factors are used as the multiplicand and multiplier respectively of the crossproduct multiplication process that always works out to be the same vector result that is of course the vector being factorised. A lecturer who is the author of several books in Number Theory and Group Theory and who has had 35 years of lecturing in both UK universities and in the USA was aware of my work at the time and on one occasion gave me some small help. I do not solicit any kudos of association with an academic person(without his permission)that this might imply from this small help – he did not continue any further involvement. I mention his small involvement as tacit proof that the invention of factoring of vectors by me as his student was not some unreal pie-in-the-sky stuff. Can I digress for a moment here also to say in general, how very transparent any claim is to a well-informed mathematician on the back of submitted proofs and how easily with few deft statements he/she can demolish an unsound claim. The mathematics of vector factoring makes heavy use of long-established methods in the vector geometry of planes and my use of standard theorems in that topic of mathematics and how this it is projected on to the new topic of vector factoring has been demonstrated unsparingly all the way along the line. I am confident of my proofs which have been seen by a few other mathematicians, the inference being made here is that my invention of vector factoring is well proven and sound. Vector factoring was an end in itself to me at this time and I had no interest in cryptography. I gave my paper on the subject to another mathematician to read who it transpired was in fact a cryptographer as well being a university lecture in mathematics and after reading it he introduced me to cryptography, albeit he saw no application in my work himself as a straight off result of reading my paper. The application of factoring to cryptography came to me via my discernment of the vector equation of a straight line and a factoring application to this which I have since those early days developed into the cipher I am promoting to readers here today. This application to cryptography has taken about fifteen years of very hard exploratory work involving thousands of test examples before the final realisation of the cipher as a working program in the Ada-95 programming language. In all, the cryptography being called variously ”Vector Cryptography”, “Spatial Cryptography”, “Displacement Cryptography”, “Skew Line Cryptography”, has taken over 20 years of very hard work and has been thoroughly tested by me before recommending it to the readership. Mathematician / cryptographer readers should have no difficulty in supporting it in any way. - adacrypt Supplement to the Foregoing. A vector to be factored (factorised if you prefer) is proposed initially as being the defining normal vector of a plane that passes through the origin at (0,0,0)i.e. it contains the point (0,0,0) This defining normal vector is designated N say. The factors of N (the vector being factorized) then occur as the position vectors (V) of consecutive number points ‘n’ and ‘n-1’ on special factor lines that lie within the plane such that: Vn x V(n-1) = N - true for all ‘n’ although only integer values of n are used in the cryptography that emanates from this topic of ‘factoring of a vector’. Many readers will see straight away that there is very profound classroom discussion possible coming from this use of plane geometry to begin with even before any discussion of the cryptography that later follows even starts. As applied to cryptography, only integer values of ‘n’ are used and furthermore, only non-zero integer coefficients of the i, j, k unit vectors of N are used by deliberate design. Outside of cryptography, factoring of a vector is a "solution waiting for problems" and may yet becomie very useful to design people in many other disciplines also. - adacrypt Supplement – 2 Even seasoned mathematicians and professional exponents in other disciplines will find this cryptography very difficult to understand. It requires a lot of one-to-one chalk ‘n talk. Understanding the algorithm alone is a major task but keeping au fait with the source code of the programmed cipher is something also that I have to do often myself by rewriting it again and again just to keep in touch. For all that, this is not a ‘complexity-theoretic’ cryptography and a cipher once it is understood and put to bed as source code is not at all difficult to operate and can be done by non-specialist persons who only need minimal training. The good side of it all is that this cryptography is clearly unbreakable no matter how much computer power is available to do it. It is just simply impossible for anybody to write a brute force program that can read the minds of the entities because that alone and nothing less is virtually what is required to break the ciphertext. No amount of computer power will ever be a threat to the security of this cryptology in the future. http://www.adacryptpages.com/ http://www.adacrypt.com/ - adacrypt
Please see above the lines - “The defining normal vector is designated N say.”
And also,
Vn x V(n-1) = N
Vn becomes V1 and V(n-1) becomes V0
This is a ‘seeding’ pair of position-vectors that are used to define a ‘factor’ line within the plane of N (much more description is needed on this bit that comes later in the more complete notes). N is drawn from an infinite domain of integer vectors and ‘n’ as an integer is technically infinite also.
A point I want demonstrate here is the profusion of almost casually infinite random keysets that emerges freely straight away with many more to follow later (described more fully in the cipher documentation) in this cryptography – the vastness of three-dimensional space as a selection domain is kicking in already.
In this cryptography, these infinitely random keysets exist as memorised data in the minds of Alice and Bob but that is only a figurative analysis – in practice, they assign these to arrays of random keysets in the cipher computer program.
These keysets are truly infinite in scope and are truly random.
Additionally, the eventual ciphertext elemental items are also an infinite (in scope) set of truly random keys.
All of these keysets (and there are several more to come) are random keys that are totally indeterminable by any cryptanalysis.
As long as the entities i.e. the Alice and Bob pair of a secure communications loop keep their databases safe from ordinary criminal theft they can enjoy complete security of communications for evermore.
In the best tradition of Kerckoffs’ Principle, the security of the communications loop depends only on keeping the key(s) information safe.
There is much more to come on this cryptography but these notes are starting to become complicated now and require some proficiency in essential maths in vector methods before proceeding any further.
‘Infinite’ above means within the confines of the computer being used.
- adacrypt
bert
May 20, 2013, 2:33:41 PM5/20/13
to
On Monday, 20 May 2013 12:29:09 UTC+1, Austin Obyrne wrote:
> On Monday, May 20, 2013 8:37:49 AM UTC+1, Austin Obyrne wrote:
> > On Sunday, May 19, 2013 6:48:30 PM UTC+1, Austin Obyrne wrote:
> > > On Sunday, May 19, 2013 12:25:28 PM UTC+1, Austin Obyrne wrote:
I suppose it is too much to hope that you might draw an
> On Monday, May 20, 2013 8:37:49 AM UTC+1, Austin Obyrne wrote:
> > On Sunday, May 19, 2013 6:48:30 PM UTC+1, Austin Obyrne wrote:
> > > On Sunday, May 19, 2013 12:25:28 PM UTC+1, Austin Obyrne wrote:
appropriate conclusion from the fact that almost nobody
sees anything worth replying to in your posts, except you.
--
Austin Obyrne
May 21, 2013, 5:22:31 AM5/21/13
to
On Sunday, May 19, 2013 12:25:28 PM UTC+1, Austin Obyrne wrote:
> Readers might well ask what’s behind this claim by me to have invented vector-based i.e. spatial displacement cryptography so I would like to give a resume of how it evolved over twenty years and more. It started in a UK university where I was a mature student (in my fifties) studying "Pure and Applied Mathematics" in the late 80’s. Career achievements before that meant I did not require this degree to add to my cv for employment-enhancing reasons – I had already attained Chartered Engineer Status and a Fellowship of my Institute as well as a very good track record so I wasn’t in need of it for that reason. In between the subjects of my various courses at the university I became interested in a new topic in mathematics that I was to call “Factorising” of a vector – a vector to be taken here as being a physical vector that is used in physics and engineering to represent physical quantities like velocity and acceleration. What I wanted was a method of finding all of the pairs of vectors that would always multiply out in the vector or cross product to give the same result i.e. some vector to be factorised being represented as a cross product vector. To explain, the factors are used as the multiplicand and multiplier respectively of the crossproduct multiplication process that always works out to be the same vector result that is of course the vector being factorised. A lecturer who is the author of several books in Number Theory and Group Theory and who has had 35 years of lecturing in both UK universities and in the USA was aware of my work at the time and on one occasion gave me some small help. I do not solicit any kudos of association with an academic person(without his permission)that this might imply from this small help – he did not continue any further involvement. I mention his small involvement as tacit proof that the invention of factoring of vectors by me as his student was not some unreal pie-in-the-sky stuff. Can I digress for a moment here also to say in general, how very transparent any claim is to a well-informed mathematician on the back of submitted proofs and how easily with few deft statements he/she can demolish an unsound claim. The mathematics of vector factoring makes heavy use of long-established methods in the vector geometry of planes and my use of standard theorems in that topic of mathematics and how this it is projected on to the new topic of vector factoring has been demonstrated unsparingly all the way along the line. I am confident of my proofs which have been seen by a few other mathematicians, the inference being made here is that my invention of vector factoring is well proven and sound. Vector factoring was an end in itself to me at this time and I had no interest in cryptography. I gave my paper on the subject to another mathematician to read who it transpired was in fact a cryptographer as well being a university lecture in mathematics and after reading it he introduced me to cryptography, albeit he saw no application in my work himself as a straight off result of reading my paper. The application of factoring to cryptography came to me via my discernment of the vector equation of a straight line and a factoring application to this which I have since those early days developed into the cipher I am promoting to readers here today. This application to cryptography has taken about fifteen years of very hard exploratory work involving thousands of test examples before the final realisation of the cipher as a working program in the Ada-95 programming language. In all, the cryptography being called variously ”Vector Cryptography”, “Spatial Cryptography”, “Displacement Cryptography”, “Skew Line Cryptography”, has taken over 20 years of very hard work and has been thoroughly tested by me before recommending it to the readership. Mathematician / cryptographer readers should have no difficulty in supporting it in any way. - adacrypt
Suplement - 4
Number-theoretic cryptography took off in earnest when computers came into vogue in the 1970’s.
Cryptographers thoughtlessly (why shouldn’t they? one may well ask) used the traditional data systems as the selection domain for raw data in cryptography because after all, there was no need to question its suitability. The fact that it had worked for them in billions of other cases since the year dot was probably so entrenched that it just didn’t bear questioning.
However, with hindsight, it can be seen today that this was a mistake for several reasons.
The raw data used for encryption transformations in cryptography should ideally come with a lot of *manageable disorder* as an intrinsic property (call this innate ‘starting’ entropy if you like) such that a design cryptographer has only to invent minimal new entropy to add to it by means of an encryption algorithm to produce an unbreakable cipher.
That is not the case with the popular data sources that have been used however as the selection domains by cryptographers, namely, our number system , our natural alphabets and even the ASCII code that was created specially with computers in mind.
This data is so perfectly ordered that it has zero entropy (as disorder) which means the cryptographer has a mountain to climb in providing the necessary extra entropy that will make it into even ‘strong’ cryptography with little chance of making it totally unbreakable cryptography.
Nobody seems to have noticed this and cryptographers have filled the void with studiously contrived 'compensating' (for the transparency) extra complexity. Their entire modus operandi has been spent on thinking up (complexity intensive) difficult-to-invert algorithms. These are horrendously difficult to invent and so far there has not been even one successful cipher that is totally immune to inversion by brute force (even AES isn’t completely safe). (This is disregarding the impractical OTP.)
Going down this wrong road in cryptography can be easily understood given that our number system has served mathematics perfectly for thousands of years even to the extent of a moon landing. Why should anybody stop to think that it might not be suitable for some purpose like cryptography and suddenly require changing – but that is what is required now – cryptographers must stop using these highly ordered data systems, to wit, the integer set, natural alphabets and information codes like ASCII are all taboo to cryptography in their unscrambled state.
Not mentioned so far and hugely important also is the fact that cryptanalysts have had the same access to these same data systems that were being mutually used by cryptographers all along, which is tantamount to giving them a head start in their nefarious trade of cryptanalysis. This is key information made available to adversaries that is there for the picking up, absolute and total folly is the only way to describe it.
Summarising.
The use of integers and alphanumeric data taken directly (i.e. without substitution into any other form) from the highly ordered traditional sources as the selection domain by cryptographers for encryption transformations must stop forthwith because clearly, it is unsuitable to cryptography. Being used as the selection domain for the raw data that will be used in encryption transformations is tantamount to handing ‘giveaway’ information on a plate to adversaries.
It is amazing that this has gone on so long unnoticed.
The huge list of papers, past, present and future still being read in the establishment to day makes one wonder how much longer this fruitless search (for the essential make-up compensating complexity that is required to mask the natural transparency of numbers and alphanumeric data) will go on when the only and proper solution is to stop using numbers from ordered number lines altogether.
Vector cryptography puts all of this right and guarantees unbreakable cryptography. No amount of computer power can break it.
There is no triumphalism or egoism on my part in what I say here – this is a mathematical and scientific fact – a part of the Universe.
I think most readers will see the sense of what I am saying here.
- adacrypt
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