There is a significance I think in my finding some of the most
incredible relations in number theory as 2007 closes, as I hope at
this point in time that 2008 will open a new and much better chapter
on a saga that has tested my ability to answer denial with discovery,
as I've been forced to find ways to get around the mathematical
community's refusal to acknowledge my research.

Necessity has been the mother of discovery, and at this time I have to
admit that I just sit and stare at the fundamental factoring relations
almost in disbelief. So yes, it more and more feels worth it, as who
knows? Would I have ever really put everything into the factoring
problem if I didn't really, really, really need it?

But that is how history goes and I guess why it can be so strange.
Now I know I had the ability to make these discoveries because I've
made them, but if mathematicians had been an honest and dedicated crew
that didn't turn to insults and questioning people's sanity, would I
ever have reached my potential?

The equations given in my previous post "Fundamental factoring
relations" can also be used to solve quadratic residues modulo p.

Given a quadratic residue q modulo p where p is an odd prime and not
3, where you wish to find k, where

k^2 = q mod p.

you start with

T = 2q mod p

where you'd want the smallest T, as next you have to factor it to
solve for z, as

z^2 = y^2 + T

so with f_1 and f_2 where f_1*f_2 = T,

z = (f_1 + f_2)/2, where f_1*f_2 = T.

And finally you get k from

k = 3^{-1}(2z) mod p.

Limitations set in because p has to be coprime to y and z, also if
abs(T) is very small, k will probably be a negative number. My guess
is that in general to have a k such that 0 greater than or roughly equal to p^2.

Example: Let q=2, p=17 so T = 2(2) mod 17 = 4 mod 17.

Given

z^2 = y^2 + nT

where T is the target composite to be factored, n is some nonzero
integer, and z and y are rational you can solve for z modulo any odd
prime p coprime to 3, y, z and nT, with the following crucial
congruences:

z = 2^{-1}(3k) mod p

and

k^2 = 2^{-1}(nT) mod p

And those are the fundamental factoring relations.

Those of you who are honest will, once you check and verify that they
always work, as they do, that RSA encryption is over. But if you wish
to lie to the world and deny that fact then I hope you are brave
enough to handle the consequences that I now assure you will be there.

James Harris

I try to understand the key differences between cryptographic hash
functions versus non-cryptographic hash functions. My understanding is
that the cryptographic hash functions are hash functions that are used
in the field of cryptography, and it should be more efficient and more
secure than non-cryptographic hash functions? They both are hash
functions that produce the fixed size output with the fixed size
input.

http://en.wikipedia.org/wiki/Cryptographic_hash_function

http://en.wikipedia.org/wiki/List_of_hash_functions

Please advise. Thanks!

Scenario: two nodes (A and B), each possessing a unique RSA keypair,
use their public keys as self-certifying identifiers.

In order to self-certify, a challenge/response is issued. E.g., node
A certifies node B by encrypting some random data with B's public key,
challenging B to return the random data decrypted to make B prove that
it does indeed possess B's private key, i.e., that it isn't just
masquerading with B's public key.

However, it would be nice for node A not to have to keep server-side
state (the original random data), so it instead encrypts the data plus
a timestamp with it's own (A's) public key, and then signs this result
and sends it to B [1]. It now expects B to decrypt the data as before
as the response, but to also return the original signed/encrypted
challenge so that A can make sure the two match. node A will accept
any such response as an authentication token for B, given that the
timestamp is not older than some acceptable time window T.

Is there anything wrong with this scheme? Any plausible attacks that
an adversary or node pretending to be B could mount? Is there an
issue with the challenge data length (constraints on how small/large
this should be) that affects the security of a node's private key?

Does an IDE-to-IDE or SATA-to-SATA encryption device exist that use a
dedicated direct (non keyloggable) device for password/PIN input?

I mean an input device like this: http://www.rocstor.com/Products/rocsafepx.html
for a encryption system like this: http://www.enovatech.net/products/mx_info.htm
(still not in a commercial product?)

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C A L L F O R P A P E R S
===============================

The 2008 International Conference on Security
and Management
SAM'08

Date and Location: July 14-17, 2008, Las Vegas, USA

You are invited to submit a full paper for consideration.
All accepted papers will be published in the conference proceedings/
book.

SCOPE: Topics of interest include, but are not limited to, the
following:

O Security protocols
O Key management techniques
O Security algorithms
O Security in e-Commerce and m-Commerce
O Surveillance technologies
O Mobile network security
O Hacking techniques...

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The Tech-Investigator shows how technology compliments
investigations. Four new posts are up dealing with GPS, Biometrics,
Security and Computers at http://tech-investigator.blogspot.com/ .

If there is anything you all would like to see please do not hesitate
to let me know.

-gs