Sunday 8 August 2010

Codebreaker is broken

Thoughts today turn to the fickle fragility of faith – how easy it is to burst the bubble of belief. It is Sunday, after all!

Regular readers will remember how I have been playing with the cryptanalytical challenges posed in the back of Stephen Pincock and Mark Frary’s book “Codebreaker – the history of secret communication”. I had been sailing along, happily revealing the messages in Challenges I – IV until I hit an obstruction at Challenge V.

The subject of Challenge V is Public-Key Encryption and, some two weeks ago, I followed the authors’ advice and referred back to Chapter 5 for help, before tackling the challenge. This was a big mistake – this was where all the corrosive doubt set in – here faith faltered and belief burst. For the example which seeks to illustrate the workings of PKE on pp 134 – 135 contains an error.

The error looks harmless enough – it simply gives the product of 11 and 17 as 181 (when, in truth, 11*17 = 187). It may even be that the mistake crept into the process during transcription of a hand-written 187 into a type-written 181 – the character “7” can look like “1” in some fists. (Indeed this is precisely the reason I use the affectation of putting a line through my scripted sevens, in the continental style).

Unfortunately, this potentially innocuous error propagates through the entire example, which is then totally incorrect – the mathematical transformation through the encryption “function” is not undone by the inverse function, such that we do not have a viable encryption scheme.

All might have been fine if this were just an error in the body of the book – but I had learned from previous Challenges that the examples in the text often couple directly to the configuration of the challenges (as, for example, where the Polybius Square in the text was used verbatim in Challenge IV) – so I began to suspect that the error in the example might contaminate and undermine Challenge V. As soon as I began to suspect, the cascade to doubt, faithlessness and disbelief followed.

My suspicions were compounded when I looked at the “Solutions” page

This solution resource is interesting because it ONLY gives the solution – not the “working” that explains how to get to the solution (which I have included in my posts about Challenges I – IV, Blogs passim).

In looking at the “solution” to Challenge V, you will see that there is not a unique mapping between cyphertext characters and plaintext characters (of course it is possible and desirable to make ciphers which are not “character based” in that sense – but my suspicion and belief is that the present Challenge is to be interpreted in that "character-based" manner – certainly that is the authors’ strong implication).

Looking at the first three cyphertext characters, each has a multi-valued mapping into plaintext (according to the "solution")...

Cyphertext Plaintext
N T, T, S, E
C A, O
W E, E, N, I, E

Sorry – but I don’t buy it!

Of course, there are lots of other “issues” in the solution of this Challenge that I haven’t alluded to here (particularly in relating alpha characters to the numerical codes that represent them), but I won’t bore you with those.

At this point, I wrote to both authors (using that familiar contemporary “code-breaking” method of finding peoples’ email address when they prefer to remain anonymous), thanking them for the book and pointing – politely and constructively - to their error in the description of PKE. I did not mention my crumbling belief or identify myself with this blog. To date, I have had no reply. Evidently Stephen and Mark are too busy penning their next bestseller/contribution to the remainder bin (delete as appropriate). Pity.

I’m not going on with the remaining challenges at the moment – in fact, I’m setting one myself...

If anybody has “solved” Challenge V (I am NOT saying it is wrong or intractable – I’m just saying that I have currently lost faith in it) PLEASE contact me. (What do you mean - "you haven't got my email address"?) I would be happy with just a clue which re-instates my faith and I would even pick up the challenge again!

All this nonsense and frustration has, at least, had one good outcome – I was tempted to buy another “code-related” book -

Perhaps I'll share my impressions of B. Jack Copeland et al's book when I've had a chance to open it. Until then, here's an end to all this Cryptic distraction - let's get back "on message" with some radio-related content!

...-.- de m0xpd


  1. Hi, do you by any chance still have the solutions page? It's been a while and it's not available anymore at that link and I can't find it anywhere now. I thought maybe if I can look at it I can get an idea for the last two challenges. Thanks.

    1. Sorry A. - I searched and couldn't find it in my files.