🚀 go-pugleaf

In article <1992Oct14.184555.26717@sqwest.wimsey.bc.ca> Mark Henderson
writes:

>In article <ARI.HUTTUNEN.92Oct13203817@cardhu.cs.hut.fi> Ari.Huttunen@hut.fi
> (Ari Huttunen) writes:
>>In article <wa6JsB7w165w@works.uucp> ferret@works.uucp (Dave Ferret) writes:
>>
>>! Just a sidenote to 'Hackers' words...
>>
>>!   There are also encryption algorithms that when used to encrypt the 
>>! plaintext over and over and over, will yield the un-encrypted text. (Ie: 
>>! Its a circular encryption -- Sorry, I don't know the correct term here)
>>
>>Any encryption scheme that has a fixed block length *must* do this. Think
>>of a series of encryptions:
>>	x_1 -> x_2 -> x_3 -> ... -> x_k -> ... -> x_n -> ...
>>If 'n' is greater than the possible number of messages that can be encoded
>>in the fixed length block, there must be some blocks in the chain that
>>are the same (pigeonhole principle). Let x_k and x_n be the same blocks.
>>Then by encrypting x_k (n-k)-times yields x_k.
>>
>>(n-k) might be quite large, though. ;-)>
>
>However there is nothing in your argument to say that (k,n) are not
>dependent on the original block being encrypted.>
>
>for "circular", we want something more like:>
>
>there exists n such that
>
> n
>E (x) = x   for all blocks x  >>
>
>where E is the encryption function in question.

Few encryption systems have this property in general.  As I recall, the
system known as Bifid (see H. F. Gaines' Cryptanalysis for a brief
summary) has this property.  For a given keysquare and period, n is not
known, but is fixed for that particular set.

For other systems, this property seldom holds in general or for
specific keys.  The simplest way to show this is to do Simple Substitution
ciphers.  One can re-arrange the standard two alphabet key as
chains of substitutions.  For instance, consider (for brevity) the following
simple substitution key 

ABCDEFGHIJK...   for plaintext and
REPUBLICAND...   for ciphertext.

This has B->E->B (and hence, is B<->E), but G->I->A->R->morestuff->G.  This
sort of irregular value for n is commonplace in ciphers.

Simple substitution, in fact, does represent the general case.  Some number
of cipher and plaintext pairs will be each other's inverse, some will have
a third party inbetween, some a fourth, etc., thus taking on a wide variety
of values of n.  If one could make predictions about this, it might form
the basis of an attack.  However, except for degenerate forms of keys for
a given system (example:  REPUBLICAN... and YZREPUBLICAN... as the 
alphabets in simple substitution), I don't know of cases other than Bifid
where it might be useful and none offhand where the value of n is even uniform.

-- 
   Larry W. Loen        |  My Opinions are decidedly my own, so please
                        |  do not attribute them to my employer