TL;DR → The main problem is coming up with a way to reorder an array non-randomly but without introducing bulky code. Like the effect of shuffling a deck of cards in a deterministic cheating way.
Full background:
I would like to generate reference numbers for letters sent via postal mail. An sqlite db is used to track the sequence numbers (but not the reference numbers). This is the bash code I have so far:
typeset -a symbolset=(a b c d e f g h j k m n p q r s t u v w x y z 2 3 4 5 6 7 8 9)
ln_symbolset=${#symbolset[@]}; # 41 is the answer, not 42
itemseq=$(sqlite3 ltr_tracking.db "select max(counter) from $tbl;")
printf '%s\n' "next letter reference number is: $(date +%Y)-${symbolset[$((itemseq / ln_symbolset))]}${symbolset[$((itemseq % ln_symbolset))]}"
An array is defined with alphanumeric symbols, taking care to eliminate symbols that humans struggle to distinguish (e.g. 1l0o). Then integer div and mod operations produce a two character number which is then prefixed with the year. So e.g. 2024-aa. Just two chars gives more numbers than would ever be generated in one calandar year.
This code mostly satisfies the need. But there’s a problem: a recipient who receives two letters can easily realise how many letters were sent in the time span of the two letters they receive. Most numbers will start with “a” “b” or “c”.
I do not need or want a cryptographic level of security which then leads to ungodly 16 byte numbers. Simplicity¹ is far more important than confidentiality. Just a small tweak to stifle the most trivial analysis would be useful.
One temptation is to simply manually mix up the order of chars in the symbolset array, hard-coded. But then that makes the code less readible. So I probably need to create a 2nd array “symbolseq” which arbitrarily unorders the symbolset array. I say arbitrary and not random because the sequence must be deterministic and static from one execution to the next.
An associative array is one idea:
typeset -A symbolset_lookup_table=(
[a]=k
[b]=3
[c]=s
…
I’m just slightly put off by the fact that it’s not readily evident that the RHS values are all used from the same set as the LHS keys exactly once.
I should probably encode the year as well. This would give a two char year:
printf '%s ' "$(((2024/41) % 41))" "$((2024 % 41))" "→ ${symbolset[$(((2024 / 41) % 41))]}" "${symbolset[$((2024 % 41))]}"
output:
8 15 → j s
(edit)
All the calculations must be easily reversible so a ref number can be converted back into a sequence number for DB queries.
¹ simplicity in both the code and in the numbers generated.
I probably need a perfect hash function. This code seems to do the job:
output
answer → js-wy answer → js-w2 answer → js-w4 answer → js-w6 answer → js-w8 answer → js-wa answer → js-wd answer → js-wg answer → js-wk answer → js-wp answer → js-ws answer → js-wv answer → js-w3 answer → js-w9 answer → js-we answer → js-wm answer → js-wt answer → js-w5 answer → js-wf answer → js-wr answer → jt-wy answer → jt-w2 answer → jt-w4 answer → jt-w6 answer → jt-w8 answer → jt-wa answer → jt-wd answer → jt-wg answer → jt-wk answer → jt-wp answer → jt-ws answer → jt-wv answer → jt-w3 answer → jt-w9 answer → jt-we answer → jt-wm answer → jt-wt answer → jt-w5 answer → jt-wf answer → jt-wr answer → ju-wy answer → ju-w2 answer → ju-w4 answer → ju-w6 answer → ju-w8 answer → ju-wa answer → ju-wd answer → ju-wg answer → ju-wk answer → ju-wp answer → ju-ws answer → ju-wv answer → ju-w3 answer → ju-w9 answer → ju-we answer → ju-wm answer → ju-wt answer → ju-w5 answer → ju-wf answer → ju-wrThis is close to ideal, but I just thought of another problem: what if a year-seq pair were to derive an encoded number like “fy-ou” or “us-uk” or “sh-it”? A bias that nearly ensures a digit is used would help avoid generating offending words. But I guess I’m getting well into over-engineering territory.
This is the decode function if anyone is interested:
decoded_reference()