Reply To: JUST SOME RANDOM STUFF!
Ah, esteemed friend, this humble one has two matters upon which to reflect and offer discourse. Pray, allow me to lay them before you in the manner of a wanderer sharing his observations by the light of the moon.
First, I shall speak of a curious observation regarding the modulo. It is my humble assertion that there exists a symmetry in the distribution of values, where those from 0 to 21 are met with equal likelihood, whilst those from 22 to 25 find themselves somewhat less fortunate, their occurrence a touch rarer. Let me explain: imagine, if you will, that there exists a one in one hundred chance of obtaining each of the values from 00, 01, 02, all the way to 97, 98, 99. However, once the modulo is invoked, all multiples of 26 are bound together as equals, as if by the hand of fate. Thus:
0 = 26 = 52 = 78
1 = 27 = 53 = 79
…
20 = 46 = 72 = 98
21 = 47 = 73 = 99
22 = 48 = 74
23 = 49 = 75
24 = 50 = 76
25 = 51 = 77
From this, it becomes clear: the first twenty-two values, from 0 to 21, are each bestowed a chance of 4 in 100, or 1 in 25, to be selected, whilst the last four, those from 22 to 25, are only granted a chance of 3 in 100. Though my knowledge in such matters is not so profound, I cannot say with certainty that this affects the peculiar density of words and near-words that emerge from the cipher’s depths. Nevertheless, it is a curious statistical anomaly worthy of mention. The thought has crossed this one’s mind, too, that the letters X and Z, being among those rarest, may show a tendency to remain unchanged, or perhaps transform into the likes of Q or J with greater frequency than one might expect. A mystery indeed.
Now, to the second point, which I offer in the spirit of humble inquiry. Pray, enlighten me: did you employ the aid of an automatic breaker, one that calculates the key with precision, or was the key chosen at random, as one might pick a stone from a brook? Should the former be true, then the Vigenere solver would, I surmise, divide the ciphertext — if one may call it so in such a situation as this — into columns, many columns, as one divides a finely ground powder into neat portions, and endeavour to make each of these columns conform to the distribution of letters in standard English. Once all these columns, shaped by the solver’s hand, are reunited, the resulting “plaintext” will take on the semblance of standard English, or at least, something akin to it. It is my belief that this is the root of the strange proliferation of words, and half-formed words, that emerge from the cipher’s cryptic embrace. Yet, I find myself pondering the matter further.
Could it be that the effect is more pronounced when the key is short, such that the “ciphertext” is divided into columns of but a few characters in length, and thus, each Caesar cipher run upon each column does not so much emulate the structure of standard English as it simply fills the result with the most common of letters? That is to say, should one run a Caesar cipher on a fragment of text such as “AAB,” it would not result in a refined word, but merely “eet,” the most frequent letters in English. Would then, the ‘plaintext’ outputted not simply be a series of “e”s, “t”s and “a”s
And what of the situation when the key is so long as to match the ‘ciphertext’s length? Surely, I ask, would this not result in an outcome where each column is reduced to a single letter — thus making the ‘plaintext’ a simple pattern, repeating, repeating, where all characters are “e”s? I admit, my understanding of the Vigenere solver’s workings grows murkier with each passing moment. The mind struggles to grasp how 200 characters with a 200-long key could result in such a simple pattern. Perhaps there is a fitness method, more advanced than I know, which eludes my grasp.
But alas, should you have used a randomly generated key, then this humble one is left quite perplexed, my thoughts in disarray, like a leaf caught in the winds of fate. Truly, the mysteries of the cipher stretch beyond the reach of my current understanding.
And so, dear friend, I offer these musings not as conclusions, but as the curious thoughts of one who has wandered far and pondered much. Perhaps we shall discover the answer together, in time.