Perfect Secrecy and the Unbreakable Cipher - Comments

[bapowell]

bapowell submitted a new PF Insights post

Perfect Secrecy and the Unbreakable Cipher

Continue reading the Original PF Insights Post.

 

[Greg Bernhardt]

Superb Insight!

 

[jim mcnamara]

Excellent!

Shannon's entropy model is used in a lot of disparate fields.

Ecology: Species diversity can be defined precisely as you described H, Shannon's entropy. If we limit an example to tree species: Boreal and montane systems have low diversity of tree species, cloud forest systems have very high diversity of tree species - such that you often have less than one individual of a given species per hectare. Abusing your nice model, it appears cloud forest species diversity would equate to a sample of glyphs from a language with thousands of "letters". If you mix in all of the species: trees, shrubs, epiphytes, invertebrates, vertebrates, Eukaryotes on down to single-celled Prokaryotes, etc., you easily have a language with an absurd number of "letters". No wonder we don't fully understand tropical systems.

Your explanation is far better than the one I used for years to help students to understand Shannon's entropy. Darn it all...

 

[Drakkith]

I can't say I understand all the math that well, but it was interesting read!

 

[Baluncore]

A good appraisal.
But after such a confident appraisal of “unbreakable” cryptographic systems I feel the need to point out that it is all too easy to be fixated and blinded by the theoretical security of your favourite cryptographic algorithm. The clear understanding your algorithm prevents you seeing the alternative openings that may be exploited by an enemy. The belief that you have a secure algorithm is also a liability because it distracts you from the greater weakness of the surrounding security structure.
Game theory rules the day, paranoia the night.

 

[bapowell]

A good appraisal.
But after such a confident appraisal of “unbreakable” cryptographic systems I feel the need to point out that it is all too easy to be fixated and blinded by the theoretical security of your favourite cryptographic algorithm. The clear understanding your algorithm prevents you seeing the alternative openings that may be exploited by an enemy. The belief that you have a secure algorithm is also a liability because it distracts you from the greater weakness of the surrounding security structure.
Game theory rules the day, paranoia the night.

That's generally true, except when you have a provably secure encryption scheme. There is only one such scheme---the Vernam system. If the key is truly random, the Vernam cipher is theoretically unbreakable, as I hoped to demonstrate in this article.

 

[jbriggs444]

That's generally true, except when you have a provably secure encryption scheme. There is only one such scheme---the Vernam system. If the key is truly random, the Vernam cipher is theoretically unbreakable, as I hoped to demonstrate in this article.

The Vernam cipher has perfect secrecy -- disclosure of the ciphertext alone does not give the attacker any information about the message. However, secrecy is not the only goal in security. For instance, one might want immunity from message forgery.

The classic example is an attacker who knows the plaintext and can modify "Attack at dawn" to "Attack at dusk" without knowledge of the key.