XPost: alt.folklore.computers
From: antispam@fricas.org
In alt.folklore.computers c186282 wrote:
> On 12/29/25 12:28, The Natural Philosopher wrote:
>> On 29/12/2025 14:31, Peter Flass wrote:
>>> On 12/29/25 03:42, Richard Kettlewell wrote:
>>>> Bobbie Sellers writes:
>>>>> On 12/28/25 22:40, rbowman wrote:
>>>>>> On Mon, 29 Dec 2025 01:17:50 -0500, c186282 wrote:
>>>>>>> For most 'office' uses you do NOT need AES-256 encryption for yer
>>>>>>> damned payroll or budget files. Nobody, not even Vlad or Xi, CARES.
>>>>>> We were dealing with NPS sites like Yellowstone and Rocky
>>>>>> Mountain. The Dept. of Interior certainly cares.
>>>>>
>>>>> Any employer who has a payroll has the Social Security numbers
>>>>> of the employees. This certainly deserves the best encryption that
>>>>> can be set up.
>>>>>
>>>>> The encryption schemes are all breakable with enough power
>>>>> brought to bear.
>>>>
>>>> At this point you should take a moment to work out how much ‘enough’
is.
>>>>
>>>> Let’s assume that:
>>>> - you have a circuit design that can do a single AES-128 key
>>>> schedule and decrypt operation in one cycle
>>>> - you can fit a million copies of this design onto one chip
>>>> - you can run the chip at 10GHz
>>>> - you can manufacture a trillion instances of the chip
>>>> (and put enough of a computer around them to do something useful)
>>>> - you can somehow power and cool this unrealistically large
>>>> supercomputer.
>>>>
>>>> This lets you test 10^6 * 10^10 * 10^12 = 10^28 keys per second. There
>>>> are 2^128 possible AES-128 keys so it will take you a little over one
>>>> thousand years to break AES-128. Your SSN will no longer be relevant by
>>>> this point.
>>>
>>> Right now, but people who work with this stuff are worried about what
>>> quantum computers can do with it.
>>>
>>>
>> Enigma codes were also 'unbreakable'
>
> Well ... kinda true.
>
> The Brits did develop early computer tech to
> help them - but the main breakthroughs came
> when NAZI operators screwed up and repeated
> the exact same message using different keys.
Actually, Enigma was broken by Polish cryptographers (M. Rejewski,
J. Różycki, H. Zygalski). British were relatively late to the game
and received information from Poland. That included internal
connections of the machine and methods to recover keys.
Polish method were mainly based on the following property: up
to IIRC 1943 German operators were supposed to start from
pre-assigned position (changing with time), choose their
own position, encrypt it using the pre-assigned position,
send it and than change to the new position to encrypt main
message. Imporant part is that operators were instructed to
repeat initial position twice. That is position was encoded
using 3 letters, they doubled this to 6 letter string and
encrypted those letters. This procedure left a lot of
redundancy in the first 6 letters of encrypted message.
Initially Germans changed machine settings rather slowly.
The settings included choice of rotor order, switchboard settings
(IIUC capable of producing arbitrary permutation, but German
did not use its full potential) and pre-assigned position.
French agents managed to steal instruction for operators
and some info about past setting (there is some discrepancy
in various report what exactly they were able to steal).
Polish cryptographers managed to use redundancy that I
mentioned above and collection of intercepted encrypted
German messages to set up system of equations for connections
of first Enigma's rotor (this rotor moved in quite regular
way). Such system of equations alone would not be enough
(Polish cryptographers did not know how to solve it in general),
but Germans made mistakes, like chosing regular patterns of
letters for starting positions. That allowed simplifying the
system of equations. After simplification it would be still
very hard to solve, but French info supplied one variable,
that is switchboard settings. With that info Polish
cryptographers were able to reconstruct connections of the
first rotor. Since Germans were permuting rotors,
each one were first on some dayse, so that actually gave
connections of all rotors. There were some extra things:
non-movable disc sometimes called "reversing disc" whose
connections were determined as part of detemining connections
of the rotors. There were disc passing signals from
switchboard to rotors: to make breaking machine more
difficult this disc should semi-randomly permute signals.
But Polish cryptographers guessed that it may be in
alphabetitic order and it was. Fist rotor were mowing in
very regular way, the other two in less regular way, so
their movement had to be determined. Later Germans
introduces more rotors (each time machine used only 3,
but those 3 could be taken from bigger pool).
After internal connections of machine were known there was
need to determine current settings, that is switchboard
connections and pre-assigned starting positions. In
a sense main trouble was due to switchboard: with 5
rotors there were 60 ways to chose 3 that were used,
17576 ways to choose intial position and factorial 26
potential setting of the switchboard. In bit terms
the whole key had 108.39 bits of which 88.38 corresponded
to the switchboard. Polish used similar system of
equations as used to break the machine to find
information about rotors. They developed machine called
"cryptological bomb" to go trough all postions and
combination of the rotors to match rotor position with
collected information. Once rotor postions were known
statistiacal method allowed finding switchboard settings
(with effect of rotors defeated switchboard just worked
as a kind of substitution cipher which is easily breakable).
What could be done to make Enigma harder to break? First,
faster changes to settings would make it harder to intercept
enough messaage. Second, initially machines started at the
same position, later Germans modified this so the operator choose
initial "position" (actually offset from preassigned position),
send it in clear and used this position to encrypt the position
used for main body to the massage. This interferd with Polish
method of setting equation system, after that change there
were less information so finding postions were harder.
I mentioned that Germans introduced extra rotors. Two
extra rotors increased number of possible rotor combinations
10 times, which means more effort to break machine, but that
was relatively mild quantitative difference. Changed
operationg procedure added much more difficulty. Completely
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