by Nick Baker
‘And what exactly is that?’ demanded Aurelia.
‘The answer lies in this book,’ he said, holding the manuscript aloft once more. ‘It also explains why Michael is here tonight,’ he added, extending a squat finger in the direction of the man who was sitting quietly at his side.
Styx squirmed uneasily under the group’s attention, bowing his head and fixing his gaze firmly on the limestone floor.
‘Michael, why don’t you tell us something about yourself, or would you prefer that I do so on your behalf?’ said Frankl.
Styx refused to look up but nodded imperceptibly.
‘Very well. Please forgive Michael’s reticence. You forget what an imposing audience you are. In any case, it’s probably better that I do the introductions; I’m not sure Michael would do himself justice.’
The young man looked up uncomfortably, not relishing the attention. He had remained anonymous since his arrival and clearly preferred it that way. His eyes shifted furtively from one face to another. He wrung his hands ceaselessly, unable to keep still under the intense scrutiny directed his way, but when his gaze landed on Frankl, there was no mistaking the expression that immediately turned from misery to loathing.
‘Michael has kindly agreed to talk to us on the subject of cryptography—’
‘How exciting,’ interjected Aurelia sarcastically. ‘A lecture by this geek while we slowly suffocate. I do commend you, Josef.’
Frankl shot her a withering look. ‘Aurelia, please show some decorum. Michael is one of the youngest people ever to have worked for Internal Security. He graduated with a first-class honours degree in mathematics from Oxford at the age of fifteen and obtained a doctorate barely two years later, which, correct me if I’m wrong, Michael, was on the subject of ciphers. His work has led to many unprecedented revelations from texts that were previously considered indecipherable. Not surprisingly, he was recruited by that detestable man, Nicolas Fox.’
‘Very impressive, but what exactly is an employee of, er, Internal Security doing in our midst? It’s bad enough that you bring us to this place,’ said Strange, registering his distaste with a brief survey of the cavern walls. ‘Not only that, but you also introduce us to someone who’s working for one of our, er, greatest adversaries.’
‘I’ve said it before, Abel, you worry too much,’ said Frankl with a dismissive flick of a hand. ‘Rest assured, I have no intention of jeopardising my plans. Michael came here of his own free will. He is no threat to us. Isn’t that so, Michael?’ he added with a grotesque smile, challenging the young man to say otherwise.
Styx got up and finally began to speak of his own accord. ‘I’m here b-because of h-him,’ he said, pointing a finger accusingly at Frankl. Styx hopped uneasily from one foot to another and appeared to be shivering, whether in fear or as a result of the cold, it was not clear. He addressed the cavern floor, unable to meet the eyes that were fixed on him, and spoke hesitantly with a tremor that he could not mask. ‘It’s t-true that I came here of my own v-volition and I will not betray you to my organisation. He approached me some days ago to d-decipher a document,’ he said, uttering the words through clenched teeth while looking disdainfully at Frankl. ‘I was left with no alternative but to come.’
‘Thank you for your kind words,’ said Frankl sarcastically. ‘Michael’s here to explain about a short piece of code Piotrowski used in his manuscript and how we can go about deciphering it. It is, after all, what I believe to be the key to the Brotherhood’s secret.’
‘What do you know of this secret?’ said Lex, showing a little more interest than Aurelia, who was nonchalantly inspecting her fingernails next to him.
‘Thank you, Lex. I was just about to come on to that,’ replied Frankl. ‘I always knew that Pearly coveted this manuscript but it was only when working through his prodigious notes that I began to realise why. Much has been said in the past about lapis philosophorum—’
‘The living stone!’ called out Strange in astonishment.
‘Quite so, Abel, thank you,’ continued Frankl undeterred. ‘The living stone has existed, whether in truth or as a myth, for far longer than is generally accepted.
‘In the early days, alchemists sought to transmute base metals into gold, a concept that originated twelve hundred years ago with the Islamic alchemist, Jabir ibn Hayyan. He believed that every substance was comprised of four basic qualities—fire, earth, water and air—and that every known metal was a combination of these four principles. He conjectured that the transmutation of one metal into another could be achieved by the rearrangement of these fundamental elements—’
‘Which, as we know,’ interrupted Strange excitedly, ‘is how modern-day alchemists undertake internal rearrangements.’
‘Thank you again, Abel,’ said Frankl, casting a glare in his direction. ‘Perhaps you’d do me the courtesy of allowing me to finish?’
Strange nodded and dropped his head. His face coloured at the rebuke, but his embarrassment was not easily discerned in the crepuscular light.
‘Now, where was I?’ said Frankl, more to himself than his audience. ‘Ah, yes, with our friend, Jabir.
‘He considered that the rearrangement of these four qualities required an additional substance, which he named “al-iksir”, which is, of course, the Arabic word for the English “elixir”. Jabir’s elixir was purportedly a dark red powder, which he called Carmot, made from a mythical stone. This, my friends, was alchemy’s first encounter with the living stone.’
‘Do tell,’ said Aurelia unenthusiastically.
Frankl gave a slight shake of his head but continued unwaveringly. ‘This stone was the much sought-after substance that allowed the transmutation of base metals into gold. With time, the stone became associated with dangerous metaphysical alchemy and was thought to be the key to the fundamental secrets of the universe; not only transforming base metal into gold, but also the resurrection of life!’
A gasp went up inside the natural stone auditorium, and while Frankl scanned the audience for the source of the sound, they all stared back at him, waiting for him to continue.
‘Are you, er, all right, Josef?’ enquired Strange suddenly. ‘You’re breathing has become rather, er, rapid and the candles have dulled to a glimmer.’ Strange frowned before a look of enlightenment appeared on his face. ‘Ah, yes. I suspect these are signs of oxygen depletion,’ he concluded, gazing uncertainly at the others.
‘I’m fine, Abel,’ Frankl retorted, shaking his head dismissively. ‘Now, Please, let me continue,’ he added, briefly composing himself before he went on with his narrative.
‘I learnt from Pearly’s research that the Esoteric Brotherhood inherently believed the living stone to be allied to an elixir of life,’ he said, displaying a fierce passion that burned in his eyes. ‘Whether they had truly discovered this secret for themselves, Pearly never found out, but it led him to make certain preparations in the event of his death.’
‘What do you mean by “certain preparations”, Josef?’ demanded Aurelia.
‘I’m not at liberty to reveal this to you at the moment, Aurelia, I’m afraid. I have Price’s copy of Piotrowski’s manuscript, but we must also recover the only other copy before I can fully answer your question.’
‘But—’
‘I have said all I can, Aurelia,’ Frankl cut in. ‘For the time being, you’ll have to make do with what Michael knows of the Piotrowski manuscript.’
‘I suppose there’s little point in arguing,’ said Aurelia, throwing Frankl a look that threatened to shake the bedrock in which they were incarcerated.
‘Now, Michael, perhaps you’d be kind enough to explain what you know of the code,’ said Frankl.
Styx stood up and squinted into the gloom. With his audience invisible, he raised his hunched shoulders and began to speak with more confidence than he had previously displayed. ‘As you’ve already heard, there are two manuscripts written in Piotrowski’s hand. I’ve managed to analyse these copies based on the recently
stolen manuscript and Black’s notes, and it is evident that there are subtle differences between the two. The manuscript held in Amsterdam contains a short passage of text that, at first glance, appears unintelligible, but it’s pretty obvious to anyone worth their salt that it’s encrypted. It’s been examined by the country’s foremost cryptologists, but despite intense scrutiny, it’s never been successfully deciphered. With just one copy, that doesn’t surprise me.’
‘Do you have any idea what’s hidden in the code?’ said Aurelia, suddenly showing some interest.
‘Firstly, it’s a cipher and not a code. The distinction is important as I’ll explain later. As to what the cipher is hiding, well, presumably it has something to do with this ludicrous secret that was mentioned earlier,’ said Styx dismissively. ‘Before you ask, it is not for me to speculate on the text; that is for you. I’m here to decrypt the cipher and nothing more. I believe that Piotrowski wrote two copies of the manuscript with the specific purpose of hiding a secret for as long as the books were separated. Individually, the manuscripts are useless; together, we’ll have all we need to decipher the text.’
‘What do you know of this cipher, er, Michael?’ Strange asked.
‘I believe it is a polyalphabetic substitution cipher first described by Blaise De Vigenère from the court of Henry III of France in the sixteenth century.’
‘Oh, please spare us the history lesson. Just get on with it,’ said Aurelia.
The flush that spread across Styx’s cheeks was evident despite the murky light, and when he replied, there was a shakiness to his voice. ‘As … as you w-wish. It’s not … so … er … s-simple to explain to someone who’s not familiar with this sort of cipher. I’ll try to be brief … please bear with me,’ he said, trying to regain his composure.
‘Perhaps you’d be so kind as to begin with an explanation of the difference between a cipher and a code,’ said Frankl, placing a reassuring hand on Styx’s shoulder.
Styx recoiled as if he had been touched by a leper. ‘A cipher implies that one letter substitutes for another, whereas a code may be a letter or symbol substituting for a word, phrase or even an entire message. A polyalphabetic substitution cipher works on the principle that the encrypted text is linked to a keyword or phrase that’s only known to the writer and, of course, the decipherer. What makes the cipher so difficult to crack is the keyword or phrase can be any combination of letters. Not surprisingly, the longer the keyword, the harder it is to break the cipher. This particular cipher was so effective that it remained virtually unbreakable for three hundred years after it was first described. Even now, without knowing the keyword, it can be a tough cipher to crack.’
‘How can you be so sure about the, er, exact type of cipher?’ enquired Strange.
‘A good question,’ replied Styx, beginning to warm to the task. ‘I’ve carried out a provisional analysis of the enciphered text and I can conclude that it’s a substitution cipher with all the hallmarks of Vigenère.’
‘So how does this fit with Piotrowski?’ continued Strange, eager to hear more from this pale, strange young man.
‘Ah, I was just coming on to that,’ replied Styx, his uneasy, gaunt expression barely evident in the shadowy candlelight. ‘I suspect that the moment Piotrowski completed the manuscript, the two copies were separated and have been kept apart ever since. The copy that we have here, I believe, contains the keyword that will enable me to decipher whatever is hidden in the cipher.’
‘But surely if we have the copy containing the keyword, then we’re already in a position to decipher the code … cipher … whatever you want to call it. You’ve already told us Pearly made a copy of the cipher when he visited Amsterdam. What are we waiting for?’ said Aurelia, sounding exasperated that no one else had already grasped the fact.
‘A good point, but I’m afraid finding the keyword is not as simple as you might assume. I’ve already made a superficial evaluation of the manuscript, and there’s nothing in the text to point to the keyword. You’ve already heard of the differences that exist between the two copies. I believe that only by comparing them will I be able to determine the keyword.’
‘Oh, and please don’t spare the detail,’ said Aurelia, yawning theatrically.
Styx was no longer fazed by Aurelia’s predictable interruption and continued unabated. ‘The process of encryption begins with a table of alphabets in the form of a square measuring 26 by 26 for each letter of the alphabet. The alphabet is written in its customary order from A to Z in a row across the top, and a second alphabet is written out in a column perpendicular to the first, leaving a blank square containing 676 spaces.
‘On the first line, the alphabet is again written out in its usual order, but on the line below, there is a shift of one, two, three, or however many letters the author chooses. In this way, the alphabet is written out but moved to the right by the number of units corresponding to the shift selected—a technique known as a Caesar shift. It was named after Julius Caesar who used this method to communicate with his generals.
‘This process is continued on each line until the tabula recta, or Vigenère table, is complete. It’s a little too dark in here to see as clearly as I would wish, but I’ve written one out for you to inspect,’ said Styx, withdrawing a piece of paper covered in small, neat hand-writing, which he passed to Strange. ‘The example, here, shows a Caesar shift of one letter on each line.’
Strange scrutinised the creased paper inquisitively, holding it inches from the concave lenses perched on the end of his nose. He studied it for a few moments, but perhaps because of his poor sight in the failing light or because he was already familiar with the cipher, he wasted no time before handing it to Aurelia. The note spent even less time with her, and without a glimpse, she passed it on to Lex, who began to read with interest.
‘Now that I assume you all understand how to construct a Vigenère table, you’ll see that it’s relatively straightforward to convert the plaintext into a cipher,’ said Styx. ‘Again, I’ve got an example for you here,’ he added, proffering a second piece of paper.
‘If you look at this example, you’ll see that I’ve used the name of the village we passed through on our way here as the plaintext, and my surname as the keyword. It is a simple example, but it should illustrate the point.’
Strange accepted the paper and began to read.
Plaintext: RIDDLESCOMBE
Keyword: STYXSTYXSTYX
ciphertext: JBVADXQZGFZB
Styx waited for them all to inspect the note before he continued. ‘Take the first letter of the plaintext and that of the keyword, and you have the letters R and S. If you scrutinise the table, the combination of these letters produces the first letter of the ciphertext, which in this case is the letter J. If this process is repeated in the same manner for each pair of letters, then the ciphertext begins to take shape.’
‘All very fascinating,’ said Aurelia, ‘but I’m rather surprised by your assertion that this cipher is hard to break. It appears to me that it’s little more than a simple substitution cipher.’
‘A perceptive point, but if you don’t have access to both the ciphertext and keyword, the cipher is extremely difficult to crack, particularly if the keyword is long. It may be possible to break the cipher without the keyword by using frequency analysis, but that can be a most laborious task taking months, if not years, to fulfil. It’s much simpler with the keyword—’
‘Assuming we find the keyword,’ interjected Frankl, ‘which might be difficult without the other book. For the sake of argument, though, how does frequency analysis work?’
‘Simple mathematics,’ replied Styx. ‘We know that letters such as e and words such as the appear regularly in the English language. This creates an inherent weakness in the cipher and allows patterns to develop in the ciphertext that can be exploited by a suitably gifted mathematician. The key to breaking the cipher is to determine the length of the keyword. Once that’s done, the ciphertext can be broken down into s
trings of letters consistent with the length of the keyword, thus allowing the ciphertext to be dealt with as separate, but relatively simple, substitution ciphers.’
‘How can the length of the keyword be determined without knowing the keyword?’ enquired Strange.
‘That’s also an interesting question,’ continued Styx confidently, finally appearing at ease while being questioned on a subject that was the only major interest in his life. ‘I’m afraid, however, that without a major dissertation on the subject of cryptology, it’s almost impossible to explain.
‘Suffice to say, it’s possible to determine the length of the keyword by undertaking a mathematical analysis of the strings of letters in the ciphertext and looking for repetition. By measuring and factoring the distance between repetitions, it’s feasible to work out various possibilities for the length of the keyword. If the whole process is repeated for different repetitions, eventually, only one number will appear in all of the lists, which is likely to represent the actual length of the keyword. Is that clear?’
No one replied, but the bemused expressions on the faces of the audience were only masked by the increasing darkness as the candlelight dwindled.
‘Once the length of the keyword is known,’ continued Styx, ‘the ciphertext can be broken down into separate strings consistent with individual parts of the keyword. Each string can be treated as a simple substitution cipher. As I mentioned earlier, this becomes a relatively straightforward exercise for the cryptologist to break.’
Frankl stood up and smiled. ‘Thank you, Michael. Your explanation has given us all an essential understanding of the problem. To put it quite simply, it could take forever to crack the cipher without the keyword, and that, of course, is where you come in, Lex.’
‘Yes. All we need now is the other book,’ Lex said casually, trying to conceal his excitement, but as he was speaking, a candle guttered and died, sending a plume of smoke spiralling into the unfathomable recess above his head.
