If you had a set of ten standard digits from the base 10 set 0 to 9,
you could start with a few of them and extend the series using a
simple choice of rules until the series repeated as a closed loop.
There is nothing fancy here at all but the primitive is im****tant.
Consider a three digit seed of say 123. Using a choice of rule and
adding the last two digits mod 10 the series can grow digit by digit:
12358314594...123. AS I said, not a large loop and digits can produce
really short loops with that rule as 000 is finished.
If you add in a constant like 2 to the sum of the last two digits,
then using mod 10 to get the added digit you get a different series.
Starting with 000 again, you would get a different and longer loop be
it comprised of all even digits.
A larger set, say an alphabet of 26 letters, indexed from 0 to 25
could be used to generate series of letters. Using a program, let's
start with the three letter series of ABC, use a standard series of
letters, and add a constant of 3 in at each step. The result as
re****ted is: "For SEEDS <abc> & 3 & Set LC26:
abcdefghijklmnopqrstuvwxyz; Cycle to regenerate <abc> in a repeating
loop needed 1280 characters and ended with yzzabc."
Going to a larger seed of four letters, here is the result: "For SEEDS
<abcd> & 3 & Set LC26: abcdefghijklmnopqrstuvwxyz; Cycle to regenerate
<abcd> in a repeating loop needed 10979 characters and ended with
zaabcd."
Larger seeds produce much larger loops, quickly to many thousands or
millions of letters but the simple set of characters as one part of
the key can be replaced by a deranged set therefore that key rather
more involved.
Using a deranged alphabets generated by a process beyond that
essential for discussion here, the series of characters might be made
obscure. Some examples are:
1) For SEEDS <abc> & 3 & Set LC26: gdtnauqwmzjxpcolbrsvyekfhi
Cycle to regenerate <abc> in a repeating loop needed 1280 characters
and ended with ywqabc.
2) For SEEDS <abcd> & 3 & Set LC26: fqrdgejzhmkwvslanbtcxoupiy
Cycle to regenerate <abcd> in a repeating loop needed 2195 characters
and ended with ewabcd.
3) For SEEDS <words> & 3 & Set LC26: hpxvneqrmkojulsdgzycftwabi
Series made from <words> was TERMINATED at 15000 characters, an
incomplete loop.
I considered 15000 characters would be sufficient for example purposes
plus longer seeds would probably be used with a stream cipher. So,
for today:
Wrestle with these words and solve the keys.
Gplmagn smso dpxqb mdzze abk wafdq hje ljpt.
Mkpisqt oaay jjmaa qcded aut ggthq zpe dhzv.
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