Discussion:
Suppose computer age ended ...
sol gongola sdgongola@yahoo.com [PGP-Basics]
2014-08-17 15:33:02 UTC
Permalink
The reason we need to encrypt/decrypt information the way we do is
because of the use of computers and the internet where there is an
ability to intercept almost anything going from one machine to
another. We NEED to encrypt because we have something to hide that, if
revealed, can negatively affect our lives, our businesses, etc. We
WANT to encrypt because we fell threatened by the possibility that
someone else may know what we are up to or because we just want some
more privacy than what others have.

Without computers and the internet, communication reverts to snail mail implementations, messengers, telegraph or voice.. I don't know anyone who would bother encrypting a letter or postcard.

Your story is an interesting twist on a theme similar to "Contact" by Carl Sagan where computers enabled decoding of information from an alien source. Except you have no computers

As for the use of an abacus, the timing would depend on the encryption method. In some cases it may be possible split the decoding into parts assigned to several individuals. If your plot allows for it, the decoding can be distributed to international teams of abacus operators to reduce the amount of time to interpret a message. You can also develop a mechanical solution afterwards similar to the use of the ENIGMA and other machines during World War II.
FederalHill federalhillrent@yahoo.com [PGP-Basics]
2014-08-17 18:30:09 UTC
Permalink
Late coming into this.


________________________________
From: "sol gongola ***@yahoo.com [PGP-Basics]" <PGP-***@yahoogroups.com>
To: "PGP-***@yahoogroups.com" <PGP-***@yahoogroups.com>
Sent: Sunday, August 17, 2014 8:33 AM
Subject: Re: Suppose computer age ended ...







The reason we need to encrypt/decrypt information the way we do is
because of the use of computers and the internet where there is an
ability to intercept almost anything going from one machine to
another. We NEED to encrypt because we have something to hide that, if
revealed, can negatively affect our lives, our businesses, etc. We
WANT to encrypt because we fell threatened by the possibility that
someone else may know what we are up to or because we just want some
more privacy than what others have.

Without computers and the internet, communication reverts to snail mail implementations, messengers, telegraph or voice.. I don't know anyone who would bother encrypting a letter or postcard.

Your story is an interesting twist on a theme similar to "Contact" by Carl Sagan where computers enabled decoding of information from an alien source. Except you have no computers

As for the use of an abacus, the timing would depend on the encryption method. In some cases it may be possible split the decoding into parts assigned to several individuals. If your plot allows for it, the decoding can be distributed to international teams of abacus operators to reduce the amount of time to interpret a message. You can also develop a mechanical solution afterwards similar to the use of the ENIGMA and other machines during World War II.
Jon Roland jroland@linux-migration.net [PGP-Basics]
2014-08-17 16:46:15 UTC
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Assume PGP/RSA, and that the key pair and encryption has to be done
by only one individual, and the decryption by another individual in
the distant future. Would it take days, weeks, months, years, or
what? Order of magnitude estimate is all that is needed.<br>
<br>
On 08/17/2014 10:33 AM, sol gongola <a class="moz-txt-link-abbreviated" href="mailto:***@yahoo.com">***@yahoo.com</a> [PGP-Basics]
wrote:
<blockquote
cite="mid:***@web140801.mail.bf1.yahoo.com"
type="cite">As for the use of an abacus, the timing would depend
on the encryption&nbsp;<span style="font-size: 14pt;">method.</span></blockquote>
<br>
<br>
<pre class="moz-signature" cols="72">-- Jon


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'Robert J. Hansen' rjh@sixdemonbag.org [PGP-Basics]
2014-08-17 21:24:23 UTC
Permalink
Assume PGP/RSA, and that the key pair and encryption has to be done by
only one individual, and the decryption by another individual in the
distant future. Would it take days, weeks, months, years, or what? Order
of magnitude estimate is all that is needed.
"More than a human lifetime."

There are some really neat computational speedups that can improve the
speed of multiplication, but they generally involve really deep
mathemagic that would be totally beyond anyone who didn't have a Ph.D.
in mathematics. That means we're stuck with the good old fashioned
O(n**2) multiplication algorithm.

Let's take a simple question: "how long would it take to multiply
together two 1200-digit numbers by hand?" I can multiply together two
single-digit numbers in about three seconds: that's how long it takes me
to remember that 7 * 6 = 42, write down the value, and make the
appropriate carry. Since the algorithm is O(n**2), that means as a
rough estimate it would take 1.45 million seconds. Working eight-hour
days, that's the better part of a year.

But wait, it gets worse. What are the odds that during a single year
you don't make *one single error* in your multiplications? Pretty much
zero. So after you do this year-long computation, you have to do
*another* year-long computation just to check the results of the first.
When the two don't match up (and they won't) you won't know whether the
first is wrong, the second is wrong, or they're both wrong. So now you
have to do a *third* year of computation, and pray that this one matches
either the first or the second year's results. If it doesn't, well,
guess what: you're out another year's computation.

So, between three and ten years just to multiply together two 1200-digit
numbers together by hand using the same algorithm we all learned in
elementary school. Now multiply that amount of time by how many
multiplications go into a single RSA computation, and... etc.

So, yeah. Longer than a human life.


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Jon Roland jroland@linux-migration.net [PGP-Basics]
2014-08-17 21:35:05 UTC
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That long for merely a 128-bit key pair? I was hoping for at least
1024-bit, but might have to reduce that to make it human-computable.<br>
<br>
On 08/17/2014 04:24 PM, 'Robert J. Hansen' <a class="moz-txt-link-abbreviated" href="mailto:***@sixdemonbag.org">***@sixdemonbag.org</a>
[PGP-Basics] wrote:
<blockquote cite="mid:***@sixdemonbag.org" type="cite">"More
than a human lifetime."<br>
</blockquote>
<br>
<br>
<pre class="moz-signature" cols="72">-- Jon

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'Robert J. Hansen' rjh@sixdemonbag.org [PGP-Basics]
2014-08-17 21:57:40 UTC
Permalink
Post by Jon Roland ***@linux-migration.net [PGP-Basics]
That long for merely a 128-bit key pair? I was hoping for at least
1024-bit, but might have to reduce that to make it human-computable.
That's for a 4K keypair (1200 decimal digits). A 1K keypair isn't a
whole lot better: several months for each multiplication, with the same
trouble of errors and having to repeat the multiplication many, many,
many times in order to do the repeated exponentiations of public-key
crypto...


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'Robert J. Hansen' rjh@sixdemonbag.org [PGP-Basics]
2014-08-17 21:42:08 UTC
Permalink
Post by 'Robert J. Hansen' ***@sixdemonbag.org [PGP-Basics]
Let's take a simple question: "how long would it take to multiply
together two 1200-digit numbers by hand?" I can multiply together two
single-digit numbers in about three seconds: that's how long it takes me
to remember that 7 * 6 = 42, write down the value, and make the
appropriate carry. Since the algorithm is O(n**2), that means as a
rough estimate it would take 1.45 million seconds. Working eight-hour
days, that's the better part of a year.
Uff da meg. That should be about 4.35 million seconds. Eight-hour
days, that's three years and change.

It's still bad. In fact, it's worse.


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Jon Roland jroland@linux-migration.net [PGP-Basics]
2014-08-17 21:51:26 UTC
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How many flops to generate a 128-bit key pair and then use the key
to encrypt a 10KB message? What is a good estimate of the time for a
human to do one flop?<br>
<br>
Another alternative would be a one-time pad, generated from data
from some future celestial event, that is destroyed after use, but
with transmission to future recipients of the formula for generating
it, using the observed data, which cannot be known by the future
recipients until after they measure the event, which might consist
of the celestial coordinates of the n closest objects to a nova that
appears on day k of greater than magnitude y. For large enough n,
the values could be unguessable by brute force.<br>
<br>
On 08/17/2014 04:24 PM, 'Robert J. Hansen' <a class="moz-txt-link-abbreviated" href="mailto:***@sixdemonbag.org">***@sixdemonbag.org</a>
[PGP-Basics] wrote:
<blockquote cite="mid:***@sixdemonbag.org" type="cite">"More
than a human lifetime."<br>
</blockquote>
<br>
<br>
<pre class="moz-signature" cols="72">-- Jon

----------------------------------------------------------
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