Re: modulo

Bill Cunningham wrote:
Lists? Do you mean newsgroups? If so, there is sci.crypt. I haven't
ever subscribed, but it sounds like one possible place to look.

Yes newsgroups. My ISP's newserver doesn't seem to subscribe to a
sci.crypt.

That's odd that they don't carry it. The sci.* hierarchy is a
mainstream hierarchy just like comp.* is, so I don't know why they'd
carry one and not the other.

Does any of these modulos or whatever integer help against
hacking with binary logic?

I don't really understand that question, partly because the base
you use for your number system doesn't affect what you can accomplish.
Anything that can be done in binary could be done in base 10, etc.,
etc., etc. Do you perhaps mean "hardware" when you say "binary
logic"? And when you say "hacking" do you mean "attacking" or
maybe "trying to intercept the encrypted message"?

I would think even 256 or 512 bit encryption
could eventually be cracked and isn't that what encryption is trying to
defeat?

Look up the work of Claude Shannon. His work shows a very interesting
result, which is that if you have a message of some length and a
cryptography key of some length, and if you use the key to encrypt
the message and then transmit it, then as long as your key length
is shorter than your message, the cryptography IS theoretically
breakable, no matter what clever algorithm you use. (And the same
thing applies if you use your key more than once: you are then
theoretically vulnerable to the message being intercepted as well.)

To put it another way, the only way a 512-bit encryption algorithm
can be unbreakable is if the 512-bit key is used to transmit a
message whose length is in the range 1 through 512 bits, and if
the key is never used again.

XOR NOT NAND and these circuits would open anything.

There are two types of encryption: encryption that can be broken and
encryption that cannot. Almost everything falls in the category of
breakable. The Vernam one-time pad isn't breakable, so even using
dedicated hardware to attack it will never succeed. But with
encryption that in principle can be broken, it's all a matter of
feasibility. Hardware methods cannot in principle break anything
that software can't also break. They are basically equivalent except
one is faster by a constant factor.

So basically, crypto algorithms and associated key lengths fall
into one of five categories:

(1) It's feasible to break them in both hardware and software.
(2) It's theoretically possible to break them in either hardware
or software, but with software it's not really feasible and
with hardware it is.
(3) Neither hardware nor software attacks are feasible right
now, but they might be in the foreseeable future, say
50 or 100 years from now.
(4) The key length is so large that, while still theoretically
possible, it's not feasible and never will be feasible to
mount a successful attack in either hardware or software,
because the Sun will burn out before you succeed.
(5) Impossible to successfully attack in theory.

Most encryption algorithms fall into category #2 or #3. It's
not impossible to move them into category #4, though. To give an
easy analogy not directly related to cryptography, when Sun
Microsystems was choosing the size of the address space for its
new(-ish) ZFS filesystem, they chose 128 bit addresses. They
of course had to ask themselves the question, "Is this enough?",
and the answer they came up with is that in any known circuit,
if you flip a bit, it takes a certain amount of energy, and some
of that is converted into heat. And if you flip 2^128 bits, you
will create so much heat you will boil all the oceans on Earth.
So, 2^128 is probably enough, barring any plans to build a SAN
network that spans multiple planets. Cryptography can be
similar, if you are willing to use large enough key sizes.
In practice, crypto takes CPU power, so people might be happy
with putting themselves in category #3 rather than #4.

Of course, all of this depends on current cryptography systems
being as resistant to attack as they seem to be. To my
knowledge, there is no cryptosystem other Vernam one-time pad
which has been mathematically proven to be impractical to
attack. (There are surely proofs about exactly how resistant
to attack a Caesar cipher is, but since the resistances is low,
the proof of the level of resistance is not that helpful.)
You can choose a really, really long key length, but it will
not help you much if the algorithm has a flaw and someone
finds it.

- Logan
.

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