Re: Mathematics and Cryptography

On Apr 1, 4:10 pm, Unruh <unruh-s...@xxxxxxxxxxxxxx> wrote:
num...@xxxxxxxxx writes:
On Apr 1, 8:08 am, David Eather <eat...@xxxxxxxxxx> wrote:
num...@xxxxxxxxx wrote:
On Apr 1, 3:23 am, num...@xxxxxxxxx wrote:
On Apr 1, 2:31 am, Unruh <unruh-s...@xxxxxxxxxxxxxx> wrote:

num...@xxxxxxxxx writes:
On Mar 31, 10:41 pm, num...@xxxxxxxxx wrote:
Hello, I'm a cryptography developer who is working on some new
approaches involving neural networks and coupled pendula. I'm
investigating the application on nonlinear high-dimensional
trajectories, mathematical chaos and coupled systems to adaptive time-
dependent encryption and decryption. I'm wondering if anybody knows
of any related papers regarding these fields of mathematics applied to
computer security?
Found
http://citeseer.ist.psu.edu/cache/papers/cs/32292/http:zSzzSzwww.ccs....
which cites a couple of papers discussing the application to
communication. Basically, the idea is to view communicating machines
as each having one or more black boxes which are chaotic or otherwise
dynamical systems that exchange coupling information alongside the
information to be exchanged. The principle is that the state of each
black box, being mathematically chaotic, will have trajectories that
are difficult, if not impossible, to approximate and these states
result in a large number of floating-point numbers for algorithmic
utilization at each instant. The initial states would have to be
exchanged between the machines. This approach is more exciting to me
than number theoretical approaches. Hoping to find more papers
regarding this idea. Thanks.
One of the key features of most chaotic systems, is that although they in
detail are unpredictable, they are really very predicatable in a course
sense. Furthermore, your idea would require accurate time synchronization
between the systems.
Note that any good crypto system IS a chaotic system. It is a simply
dynamical system, such that even single bit changes in the input produce
huge changes in the output. Your "black boxes" are exactly the
cryptographic algorithms. However they are designed to be really really
chaotic, whereas most physical systems are far from that.
The "initial state exchanged" is called the key in a cryptosystem.- Hide quoted text -
- Show quoted text -
That is a good point about the time granularity. There might need to
be extra packets or even continuous packets sent between machines for
this to work. I'm just looking over some physics-based dynamical
systems and thinking that if two machines could have the same system
on them, then the bits from the floating-point numbers, say modulo
after a scaling, could be of use to other cryptographic algorithms.
I'm also thinking synchronizing information, possibly based on
transmitted content, could be useful in channel-based adjustment to
these black boxes over time. I see your point about time granularity
but would argue that looking at bit ranges as opposed to the entire
floating-point number might be of use. With your point, the
significant bits would be too predictable and the least might have
noise on them. Just theory for now, but the math is interesting.- Hide quoted text -

- Show quoted text -

I suppose an argument against this theoretical approach would be that
pseudo-random number generators could be used instead of modelled
physical systems, reseeded from packet properties such as checksums.
I'm not sure which would have better results.

I'd use a different argument against the new approach. You should know
and understand the goals of cryptography first, know and understand how
those goals are obtained and how and why they might sometimes fail.
Then you yourself would be in a position to know if a proposed new idea
is something interesting or just a waste of everyones time.- Hide quoted text -

- Show quoted text -
I should have clarified better. The interesting thing about one-time-
pass and initial key exchange approach is that it makes eavesdrop
based attacks difficult unless this initial key is obtained. Thus,

True for any cryptography.

the design goal is to make deciphering the plaintext as difficult or
computationally expensive as possible. The goal of the theory I'm

The other design goal should be to make use of the system as easy as
possible.

Good point. I'm writing a side project now in c#.


offering for discussion is to make a complex system based on initial
key exchange that cannot be readily deciphered from eavesdropping
between machines. That is, I'm imagining (trying at least) systems
that would require every packet sent between machines to be recorded
to decipher the current packets being sent. As for whether packet-

And if a packet got lost along the way, the two machines would forever
after be unable to communicate.

True, there would have to be some buffering for UDP.


based, adaptive channel-based approaches (evolving cryptographic
systems based toward reasoning in last sentence), I don't know if the

No idea what these sentences are supposed to mean.

Basically trying to say algorithms that adjust parameters based on the
content or properties of the content (packets) being sent. I made up
the term "channel-based" though other terms might already exist. For
example, the parameters an algorithm could use for a packet may be an
original key and a checksum, timestamp, hash and/or other content from
the decrypted previous packet(s) received from the recipient (thus the
need for a UDP reliability layer). I've coded a proof of concept on
synchronizing parameters via packet checksums over two-way UDP-- the
theory is to accumulate information on both machines during packet
exchange that increasingly strengthens security.


theory is stronger than present theory so I only know the ideas are
interesting to me, and hope they're not a waste of everyones time.
The goal is to make the computation of decrypting a channel between
two machines a continuous process.

You might want to have other desiderata as well. LIke robustness, and ease
of use.- Hide quoted text -

- Show quoted text -

.

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