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The One-Way Function.
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adacrypt
Feb 12, 2012, 9:16:07 AM2/12/12
to
Two points in space can be defined by the position vector that
connects the two points.
In everyday standard usage one of the points is taken to be fixed at
(0,0,0) and every other point in the whole of space can be expressed
as being relative to this point.
But users are not bound to always uses (0,0,0) as the standard
reference and they can agree between themselves to use another private
reference point at say (x,y,z ) to define points in space whenever
they need to. The position vector is then totally different to what
it would be relative to (0,0,0). Only the users know just how
different because they alone are privy to (x,y,z) which could be any
point in the infinity of space.
With knowledge of (x,y,z) any person who knows this can navigate to
(0,0,0) and find the correct position vector relative to (0,0,0) when
that is needed but (x,y,z) could be any one of an infinite number of
confusingly different values in the whole of space when users decide
to keep it secret.
There is no mathematical means whatever by which (x,y,z) can be
deduced only the users know and they alone can provide the information
(but of course they are not telling).
When the users are Alice and Bob in a secure communications scheme
this ploy is called a change-of-origin. I liken it to a transfer of
data from a human memory to a computer memory that they alone can
implement and supply the correct values of (x,y,z) that enable
decryption to proceed with a correct result.
They calculate ciphertext according to (0,0,0) but publish it as being
relative to (x,y.z) and go back to (0,0,0) again at decryption time.
I am calling this a definitive one-way mathematical function in
cryptography – one-way simply because that is what it is i.e. non-
invertible by any mathematical means albeit a proper mathematical
function per se at the same time.
This powerful ploy guarantees my cipher against the attack described
as attack 1) that is foremost in basic design priority, called known
ciphertext attack.
I have no evidence that there is such a thing in academia as a “one-
way” function in mathematical parlance. (Never mind the Cryptography
Handbooks – they are not quotable outside of cryptography).
Anybody? I would appreciate any information but please quote the
source.
- adacrypt
connects the two points.
In everyday standard usage one of the points is taken to be fixed at
(0,0,0) and every other point in the whole of space can be expressed
as being relative to this point.
But users are not bound to always uses (0,0,0) as the standard
reference and they can agree between themselves to use another private
reference point at say (x,y,z ) to define points in space whenever
they need to. The position vector is then totally different to what
it would be relative to (0,0,0). Only the users know just how
different because they alone are privy to (x,y,z) which could be any
point in the infinity of space.
With knowledge of (x,y,z) any person who knows this can navigate to
(0,0,0) and find the correct position vector relative to (0,0,0) when
that is needed but (x,y,z) could be any one of an infinite number of
confusingly different values in the whole of space when users decide
to keep it secret.
There is no mathematical means whatever by which (x,y,z) can be
deduced only the users know and they alone can provide the information
(but of course they are not telling).
When the users are Alice and Bob in a secure communications scheme
this ploy is called a change-of-origin. I liken it to a transfer of
data from a human memory to a computer memory that they alone can
implement and supply the correct values of (x,y,z) that enable
decryption to proceed with a correct result.
They calculate ciphertext according to (0,0,0) but publish it as being
relative to (x,y.z) and go back to (0,0,0) again at decryption time.
I am calling this a definitive one-way mathematical function in
cryptography – one-way simply because that is what it is i.e. non-
invertible by any mathematical means albeit a proper mathematical
function per se at the same time.
This powerful ploy guarantees my cipher against the attack described
as attack 1) that is foremost in basic design priority, called known
ciphertext attack.
I have no evidence that there is such a thing in academia as a “one-
way” function in mathematical parlance. (Never mind the Cryptography
Handbooks – they are not quotable outside of cryptography).
Anybody? I would appreciate any information but please quote the
source.
- adacrypt
unruh
Feb 12, 2012, 12:57:37 PM2/12/12
to
On 2012-02-12, adacrypt <austin...@hotmail.com> wrote:
> Two points in space can be defined by the position vector that
> connects the two points.
>
> In everyday standard usage one of the points is taken to be fixed at
> (0,0,0) and every other point in the whole of space can be expressed
> as being relative to this point.
>
> But users are not bound to always uses (0,0,0) as the standard
> reference and they can agree between themselves to use another private
> reference point at say (x,y,z ) to define points in space whenever
> they need to. The position vector is then totally different to what
> it would be relative to (0,0,0). Only the users know just how
> different because they alone are privy to (x,y,z) which could be any
> point in the infinity of space.
In one dimension this is the Caesar cypher. It is easily broken.
> Two points in space can be defined by the position vector that
> connects the two points.
>
> In everyday standard usage one of the points is taken to be fixed at
> (0,0,0) and every other point in the whole of space can be expressed
> as being relative to this point.
>
> But users are not bound to always uses (0,0,0) as the standard
> reference and they can agree between themselves to use another private
> reference point at say (x,y,z ) to define points in space whenever
> they need to. The position vector is then totally different to what
> it would be relative to (0,0,0). Only the users know just how
> different because they alone are privy to (x,y,z) which could be any
> point in the infinity of space.
Similarly in three, assuming that xyz are the same for the whole
message. It is breakable because the message contains masses of
redundancy, and possibly known plaintext. Ie, If I know the coordinates
of three points in your xyz translated system and in the 000 system
(known plaintext) I also know what xyz are and thus can decrypt the
entire message.
If you change xyz for each and every point, and those changes are
completely random, then this is a one time pad, with all the problems of
such (the necessity of conveying to your partner in a totally secure
manner, the whole range of xyz values. If you have such a secure way of
conveying them why not use that means of conveying the message?) If the
xyz are created by some algorithm, this is just a stream cypher. with
the usual means of attack on the generating function for the stream of
xyz.
>
> With knowledge of (x,y,z) any person who knows this can navigate to
> (0,0,0) and find the correct position vector relative to (0,0,0) when
> that is needed but (x,y,z) could be any one of an infinite number of
> confusingly different values in the whole of space when users decide
> to keep it secret.
>
> There is no mathematical means whatever by which (x,y,z) can be
> deduced only the users know and they alone can provide the information
> (but of course they are not telling).
displacement and you know what its value should be (with respec to 000)known plaintext)
youknow what xyz is.
>
> When the users are Alice and Bob in a secure communications scheme
> this ploy is called a change-of-origin. I liken it to a transfer of
> data from a human memory to a computer memory that they alone can
> implement and supply the correct values of (x,y,z) that enable
> decryption to proceed with a correct result.
>
> They calculate ciphertext according to (0,0,0) but publish it as being
> relative to (x,y.z) and go back to (0,0,0) again at decryption time.
>
> I am calling this a definitive one-way mathematical function in
> invertible by any mathematical means albeit a proper mathematical
> function per se at the same time.
Nope. A one way function is one where, even if you know what xyz is, you
> function per se at the same time.
cannot figure out what the values are for 000.
Ie, in crypto, a one way function is one where, even if you can
perfectly encrypt a message ( in your case you know what xyz is and can
make the change of origin) you cannot decrypt it.
Clearly not true of your scheme.
>
> This powerful ploy guarantees my cipher against the attack described
> as attack 1) that is foremost in basic design priority, called known
> ciphertext attack.
>
> way? function in mathematical parlance. (Never mind the Cryptography
> Handbooks ? they are not quotable outside of cryptography).
FireXware
Feb 12, 2012, 1:00:12 PM2/12/12
to
On 02/12/2012 07:16 AM, adacrypt wrote:
> Two points in space can be defined by the position vector that
> connects the two points.
>
> In everyday standard usage one of the points is taken to be fixed at
> (0,0,0) and every other point in the whole of space can be expressed
> as being relative to this point.
>
> But users are not bound to always uses (0,0,0) as the standard
> reference and they can agree between themselves to use another private
> reference point at say (x,y,z ) to define points in space whenever
> they need to. The position vector is then totally different to what
> it would be relative to (0,0,0). Only the users know just how
> different because they alone are privy to (x,y,z) which could be any
> point in the infinity of space.
>
> With knowledge of (x,y,z) any person who knows this can navigate to
> (0,0,0) and find the correct position vector relative to (0,0,0) when
> that is needed but (x,y,z) could be any one of an infinite number of
> confusingly different values in the whole of space when users decide
> to keep it secret.
Nothing usable is infinite; It's not practical.
> Two points in space can be defined by the position vector that
> connects the two points.
>
> In everyday standard usage one of the points is taken to be fixed at
> (0,0,0) and every other point in the whole of space can be expressed
> as being relative to this point.
>
> But users are not bound to always uses (0,0,0) as the standard
> reference and they can agree between themselves to use another private
> reference point at say (x,y,z ) to define points in space whenever
> they need to. The position vector is then totally different to what
> it would be relative to (0,0,0). Only the users know just how
> different because they alone are privy to (x,y,z) which could be any
> point in the infinity of space.
>
> With knowledge of (x,y,z) any person who knows this can navigate to
> (0,0,0) and find the correct position vector relative to (0,0,0) when
> that is needed but (x,y,z) could be any one of an infinite number of
> confusingly different values in the whole of space when users decide
> to keep it secret.
>
> There is no mathematical means whatever by which (x,y,z) can be
> deduced only the users know and they alone can provide the information
> (but of course they are not telling).
>
> When the users are Alice and Bob in a secure communications scheme
> this ploy is called a change-of-origin. I liken it to a transfer of
> data from a human memory to a computer memory that they alone can
> implement and supply the correct values of (x,y,z) that enable
> decryption to proceed with a correct result.
>
> They calculate ciphertext according to (0,0,0) but publish it as being
> relative to (x,y.z) and go back to (0,0,0) again at decryption time.
>
> I am calling this a definitive one-way mathematical function in
> cryptography – one-way simply because that is what it is i.e. non-
> invertible by any mathematical means albeit a proper mathematical
> function per se at the same time.
>
> This powerful ploy guarantees my cipher against the attack described
> as attack 1) that is foremost in basic design priority, called known
> ciphertext attack.
>
small vectors will encrypt to values close to the key, making brute
force much easier.
In fact, if you have a known-plaintext (a,b,c) and it's ciphertext
(x,y,z), you can get the key by subtracting the ciphertext from the
plaintext: (a,b,c) - (x,y,z) = key.
Why? Because (0,0,0) + key + (x,y,z) = (a,b,c), so key = (a,b,c) - (x,y,z).
> I have no evidence that there is such a thing in academia as a “one-
> way” function in mathematical parlance. (Never mind the Cryptography
> Handbooks – they are not quotable outside of cryptography).
>
Mark Murray
Feb 12, 2012, 1:56:11 PM2/12/12
to
On 12/02/2012 14:16, adacrypt wrote:
> Anybody? I would appreciate any information but please quote the
> source.
Try studying the work of Claude Shannon.
> Anybody? I would appreciate any information but please quote the
> source.
The very accessible essays of Bruce Schneier are also worth reading;
these are in his "Crypto-Gram" column on his website.
M
--
Mark "No Nickname" Murray
Notable nebbish, extreme generalist.
adacrypt
Feb 12, 2012, 1:46:37 PM2/12/12
to
On Feb 12, 5:57 pm, unruh <un...@invalid.ca> wrote:
> > - adacrypt- Hide quoted text -
>
> - Show quoted text -
Do you want to try a sample of plaintext with the accompanying
ciphertext - let me know - adacrypt
>
> - Show quoted text -
Do you want to try a sample of plaintext with the accompanying
ciphertext - let me know - adacrypt
adacrypt
Feb 12, 2012, 2:11:24 PM2/12/12
to
On Feb 12, 5:57 pm, unruh <un...@invalid.ca> wrote:
> > - adacrypt- Hide quoted text -
>
> - Show quoted text -
Please ignore that challenge of sending you a sample of plaintext and
>
> - Show quoted text -
ciphertext - that was a bit rude and ungrateful.
I'm taking it that the semantics of my claim are wrong but that does
mean the cipher is weak.
Each ciphertext item is a resultant vector that has an infinite number
of possible ways of resolution. Bob and Alice alone know which one in
each case.
The ciphertext is forever changing so any statistical effort by Eve is
futile
- adacrypt
Mark Murray
Feb 12, 2012, 2:28:19 PM2/12/12
to
On 12/02/2012 19:11, adacrypt wrote:
> Each ciphertext item is a resultant vector that has an infinite number
> of possible ways of resolution. Bob and Alice alone know which one in
> each case.
>
> The ciphertext is forever changing so any statistical effort by Eve is
> futile
Only if you ignore the methods that have already been demonstrated to
> Each ciphertext item is a resultant vector that has an infinite number
> of possible ways of resolution. Bob and Alice alone know which one in
> each case.
>
> The ciphertext is forever changing so any statistical effort by Eve is
> futile
you.
Remember those? The ones that you called "unfair" or "illegal"?
Best you understand what "cribs" are. They are routinely used in
real-life cryptographic attacks, and your cipher has no defences
against them.
adacrypt
Feb 12, 2012, 2:36:18 PM2/12/12
to
On Feb 12, 5:57 pm, unruh <un...@invalid.ca> wrote:
> > - adacrypt- Hide quoted text -
>
> - Show quoted text -
>
> - Show quoted text -
<If you change xyz for each and every point, and those changes are
<completely random, then this is a one time pad, with all the problems
of
<such (the necessity of conveying to your partner in a totally secure
<manner, the whole range of xyz values. If you have such a secure way
of
<conveying them why not use that means of conveying the message?) If
the
<xyz are created by some algorithm, this is just a stream cypher.
with
<the usual means of attack on the generating function for the stream
of
<xyz.
Mutual Database tecnology obviates this with a once only secure
<completely random, then this is a one time pad, with all the problems
of
<such (the necessity of conveying to your partner in a totally secure
<manner, the whole range of xyz values. If you have such a secure way
of
<conveying them why not use that means of conveying the message?) If
the
<xyz are created by some algorithm, this is just a stream cypher.
with
<the usual means of attack on the generating function for the stream
of
<xyz.
delivery at the outset of creating a secure loop.
Many thanks for your help. -adacrypt
Mark Murray
Feb 12, 2012, 3:28:43 PM2/12/12
to
On 12/02/2012 19:36, adacrypt wrote:
> Mutual Database tecnology obviates this with a once only secure
> delivery at the outset of creating a secure loop.
When (not if) your key material is compromised, you are screwed, just
> Mutual Database tecnology obviates this with a once only secure
> delivery at the outset of creating a secure loop.
like the OTP user with no more key material, except you are further
screwed because you are deluded into thinking you are still safe.
At least the OTP user knows she's out of key material, and thus
gets a hint that committing further secrets to communications
channels is dodgy.
Both of the above scenarious have horribly expensive initial key
exchanges. Only one of them is provably secure. You want references?
Shannon's theorem; look it up.
Now you stick your fingers in your ears, sing "lalalalalala" and
mutter away about "provable security" and how wonderfully rosy
things are, OK? It must be amazingly comforting not to have to
take reality into account.
Pubkeybreaker
Feb 12, 2012, 5:13:36 PM2/12/12
to
On Feb 12, 9:16 am, adacrypt <austin.oby...@hotmail.com> wrote:
> Two points in space can be defined by the position vector that
> connects the two points.
Yet another nonsensical mathematical claim from the resident village
> Two points in space can be defined by the position vector that
> connects the two points.
idiot.
Here is a vector in E^2. Please tell the rest of us what the two
points are?
(3i', 4j')
Give it up adacrypt. You are clueless.
adacrypt
Feb 12, 2012, 6:20:45 PM2/12/12
to
>
> - Show quoted text -
It can be demonstrated that the ciphertext is itself can be made a
> - Show quoted text -
random external key that may be used to resist any statistical attack
on the ciphertext as the last ditch attack..
current key lenghs of up to 50000 key elements are very easily
achievable and vastly greater are possible.
Considering a key set of only 50000 elements this has a manageable
potential of 50000 ! (50000 factorial) permutations of the same random
keyset (doubling as ciphertext all the time but there for the finding
as keys in other arrangements) - This is an unthinkably large number -
* there is not shortage in theory at least of key material - get real.
- adacrypt
Mark Murray
Feb 12, 2012, 6:33:40 PM2/12/12
to
On 12/02/2012 23:20, adacrypt wrote:
> It can be demonstrated that the ciphertext is itself can be made a
> random external key that may be used to resist any statistical attack
> on the ciphertext as the last ditch attack..
Then demonstrate it, conclusively. The time for assertions is over.
> It can be demonstrated that the ciphertext is itself can be made a
> random external key that may be used to resist any statistical attack
> on the ciphertext as the last ditch attack..
No handwaving - bloody do it!
> current key lenghs of up to 50000 key elements are very easily
> achievable and vastly greater are possible.
Exactly 791010.
> Considering a key set of only 50000 elements this has a manageable
> potential of 50000 ! (50000 factorial) permutations of the same random
> keyset (doubling as ciphertext all the time but there for the finding
> as keys in other arrangements) - This is an unthinkably large number -
> * there is not shortage in theory at least of key material - get real.
Karl-Uwe Frank
Feb 13, 2012, 8:43:39 AM2/13/12
to
Isn't your idea of such a random keyset and multiple coordinates into
the pool nothing else than a Maurer-PRNG?
In the paper "Security Weaknesses in Maurer-Like Randomized Stream
Ciphers" by Niels Ferguson, Bruce Schneier and David Wagner they mention
that Ueli Maurer had the idea of building a pool that is large enough to
make it infeasible to read the entire contents of the pool. Also
mentioned that Ueli Mauerer proposed digitizing the surface of the moon
as one means of getting enough public randomness to make the cipher work
and resistant against cryptanalysis. After reading some of your postings
from my point of view it seems to be your scheme is basically the same
idea as Ueli Mauerer's.
And have you ever tested your keyset for randomness to give such a
simple prove?
http://www.ciphersbyritter.com/RES/RANDTEST.HTM
http://www.random.org/analysis/
Cheers,
Karl-Uwe
the pool nothing else than a Maurer-PRNG?
In the paper "Security Weaknesses in Maurer-Like Randomized Stream
Ciphers" by Niels Ferguson, Bruce Schneier and David Wagner they mention
that Ueli Maurer had the idea of building a pool that is large enough to
make it infeasible to read the entire contents of the pool. Also
mentioned that Ueli Mauerer proposed digitizing the surface of the moon
as one means of getting enough public randomness to make the cipher work
and resistant against cryptanalysis. After reading some of your postings
from my point of view it seems to be your scheme is basically the same
idea as Ueli Mauerer's.
And have you ever tested your keyset for randomness to give such a
simple prove?
http://www.ciphersbyritter.com/RES/RANDTEST.HTM
http://www.random.org/analysis/
Cheers,
Karl-Uwe
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