Get out your decoder ring
Perfect security IS possible. That is to say, there is a foolproof way to keep a secret.
Say, for instance, that Jane and Debby know one another and are in a room together. Jane has a secret. The path to perfect security of that secret is for Debby and Jane not to speak and to have Debby kill Jane before she divulges it. There is now no longer any risk of the secret being divulged.
Kinda harsh, eh? Well, a less harsh way to do it is that Jane just never tells anyone about it (sure, if you want to get all non-homocidal about things). For even more security, she forgets the secret herself.
Perfect openness is actually harder. If Jane wanted Debby to know she could just speak the words, tell her. That assumes that Debby can hear and that they speak the same language. A billboard? Methinks you are assuming both sight AND literacy here.
Time for that decoder ring now (set it to G9).
Now put Jane and Debby in separate rooms and assume that Jane WANTS to tell Debby the secret but that she doesn't want anyone else to know.
From lowest security and up:
Jane YELLS the secret to Debby. Anyone within earshot hears it.
Jane SPEAKS the secret to Debby. The range of people within earshot is lower, however Debby may not hear it.
Jane WHISPERS the secret to Debby. Chances are that Debby will not hear. There is a risk that someone nearby did, however.
Now, if Jane were to write the secret down and get it to Debby, that may limit the spread of information. Let's say she wrote it down and handed it to someone to hand to Debby. There is a chance that the person did not read it, so security is better that way. But unless Debby destroys the note, the secret can still be read.
If Jane and Debby had a language only they knew, then there is more of a chance for security. But languages can be translated, if you use them enough then context and simple repitition can ferret out the meaning.
Decoder ring. Now this is probably before the era of many of you. A toy that used to be given away in breakfast cereal or if you sent in boxtops or whatever was the SECRET DECODER RING. The concept was simple. Each letter in the English language was assigned a corresponding number or letter. The standard alphabet was displayed on one side of a ring and on an adjacent one, there was the decode.
The simplest ones had A,B,C,D....on the inside and 1,2,3,4 on the outside. If alligned to A1 then CAT would be 3,1,20. Setting the ring meant you set a certain letter against a certain number (hence my G9 comment earlier).
If Jane and Debby had decoder rings and knew what the other person set theirs to, they could have a secret message.
But there are ways to crack this too. In the English language there are patterns on letters, certain ones show up more frequently. Certain patterns repeat - a lot. A persistent person could crack it pretty fast.
So, what to do? Change the code for each letter. Use that code for each communication. But...if your code falls into the wrong hands then it is useless.
So change the code for each communication. Destroy it and the note each time.
Basically it is all just a pain in the rear.
Keeping a secret is hard, even when everyone wants to.
There is no such thing as a perfect secret once it has been shared. Does that mean it isn't worth trying?
This has been your bizarre post of the month.
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