‘My best advice is that you put it away for today. Go for a walk. Hill’s magic might return with the dawn.’
Taking heed, Thomas spent the afternoon by the river, and the evening with his friend Montaigne. He fell asleep thinking of Polly and Lucy, and of Jane Romilly, who had stormed out of his room in a fierce temper.
The next three days were spent on the intercepted message. The marks on the paper had become his enemies. He tried a variety of double and triple alphabetic substitutions, he tried assuming that all the numbers were meaningless, that they hid keywords, that the message was in Latin, that it had been written backwards, and he even guessed at a few possible keywords to create alphabetic shifts, such as PARLIAMENT, OXFORD and PROTESTANT. The guesswork was futile without at least some facts, and he knew it. He gave it up when Montaigne tapped gently on his shoulder, and whispered in his ear, ‘Thomas Hill, have I taught you nothing? Rational thought is greatly superior to intuition. Think, don’t guess.’
On the fourth morning, he went again to see Abraham, and again reported his lack of progress. Abraham tried to be encouraging. ‘Thomas, you have made progress,’ he said. ‘You know a good many things that this cipher is not.’
‘Indeed. But if I have to eliminate all the things it is not before discovering what it is, I shall be even older than you when I finally do so.’
Abraham laughed, and then voiced the thought that both had so far left unspoken. ‘Could we be facing Vigenère, Thomas?’
‘It’s possible, of course, although the numbers must also be serving some purpose. Have you heard of a square used with numerical codes?’
‘I haven’t, but that doesn’t mean they don’t exist. If the numbers are codes, the cipher will work just as well if they are ignored.’
‘Abraham, a Vigenère cipher has never been broken, with or without word codes.’
‘I know. Trust a Frenchman to come up with such a diabolical thing. Tedious to encrypt, tedious to decrypt, and proof against even you, Thomas, unless you can divine the keyword.’
‘I can try, Abraham, but you know it’ll take a miracle.’
Abraham was thoughtful. ‘Perhaps not. Look again at the numbers. Could they be telling us which rows on the square to use? If so, the cipher would still be secure against anyone un familiar with Monsieur Vigenère.’ He picked up a thin strip of wood with a straight edge and passed it to Thomas. ‘If it’s Vigenère, you’ll need this.’
Thomas took the strip of wood. ‘Thank you. I’ll assume it’s Vigenère and try the numbers again. Prayers thrice daily, Abraham, please. I shall need them.’
That evening, Tobias Rush visited again. All in black, silver-topped cane in hand, he called to tell Thomas that his letter had been safely delivered to Margaret. ‘Was there a reply?’ asked Thomas hopefully.
‘Unfortunately, no. The courier had to reach Southampton by dusk and could not afford to wait,’ said Rush with a shrug. ‘No doubt your sister will find a way of writing back, however. Do let me know when she does.’ He paused. ‘And how did you enjoy the masque?’
‘Masque? Oh, the masque. Remarkable. A remarkable entertainment.’
‘Indeed. Their majesties have unerring eyes for beauty. And speaking of beauty, how did you find Lady Romilly? Well, I trust?’
‘Quite well. An unusual lady.’
‘You refer to her eyes, I imagine?’
‘In part, yes. They are striking. But not just her eyes. She’s a lady of spirit.’ As I am only too well aware, thought Thomas.
Rush smiled his thin smile, and changed the subject. ‘How goes your work, Master Hill?’ he asked, looking casually around the room. His working papers were underneath others on the table. Just as well, thought Thomas, although I must be more careful in future. Abraham had insisted on absolute secrecy, even from Master Rush. He dissembled. ‘Routine matters only. Not much has changed since I last worked with codes. I would prefer something more interesting.’
‘Oh? Have the enemy not offered you anything at all appro priate to your skills?’
‘Not as yet, sir.’
‘Be sure to let me know if they do. The king has impressed upon me my duty to assist you in any way that I can. I would not wish either of us to disappoint him. Now, I shall bid you good day.’ And he was gone.
Odd how he’s here one minute and gone the next, thought Thomas, and how he changes the course of a discussion. A hard book to read and a hard bird to cage.
Work on the numbers began before dawn. If this was a Vigenère square, the king’s enemies would assume that its secrets were safe and would see no need to change their plans. The square itself had remained unbroken for over seventy years. Using the strip of wood as a guide, Thomas began by writing out the square.
If the message had been encrypted using the square, each letter would have twenty-six possible encryptions. The letters in the top row represented the letters used in the message, and the letters of the keyword were contained in the first column. So if the keyword began with the letter T, the letter O would have been encrypted as H.
Then he wrote out the forty-five digits at the top of the message. For some time, he sat and stared at them. Apart from the dupli cations, he saw no patterns. If the numbers were indicating the rows of the square to be used for decrypting, any number above twenty-six must be either a null or have some other function. Proceeding on this basis, he divided the digits into arbitrary one- and two-digit numbers and tried decrypting the first line according to the rows indicated by his selection. When the word DOG appeared, he thought he was on to something. But when the following words turned out as KTLO, BQICMS and XPD, he knew that the dog’s appearance was no more than chance.
All morning Thomas sat at his table, the encrypted page, sharpened quills, inkpot and a pile of blank papers before him. The pile diminished as the floor became covered in used and discarded ones. Just as well Abraham had laid his hands on a good supply. By the time his stomach started complaining, how ever, he had achieved very little. Nothing, in fact, except the growing certainty that these numbers did not hold the key to the rows. He had tried adding and subtracting, transposing the digits of the higher numbers, multiplying and dividing — all to no effect. Apart from dog, not a single plain word had appeared from the text. It was a bad start. He did not need the unwelcome compli cation of codewords, tricks or traps. What he did need was a clue to guide him to the keyword. And he needed fresh air.
Emerging into the daylight, Thomas was greeted by a beautiful late-summer day — dry and windless. The Pembroke courtyard was still a military dump, young officers and their women still lounged about doing very little, and the stench of human waste was still sickening, but the sky was cloudless and the sun warm. Thank God one was permanent and the other, God willing, merely temporary. Perhaps very temporary if he could break the encryption.
Thinking that he had been so preoccupied with the message that he had again lost touch with what was happening beyond his room, he wandered down to the meadow. As always, it was a mass of soldiers and their weaponry, and, unless he was mistaken, there was even more hustle and bustle than before. No one made any objection as he walked among the lines of artillery pieces and the knots of men gathered around them, for the first time paying the armoury more than passing attention. He stopped to examine a huge cannon loaded on to a long flat cart with wheels of different sizes. Two shafts protruded from the back, into which a horse would be harnessed. Wondering how far a ball would travel when fired from such a monster, he stooped to peer down the barrel. There was a tap on his shoulder and he turned to see a grinning artilleryman. In a thick shirt, leather trousers to the knee, woollen stockings and wooden clogs, the poor man must have been slowly cooking.
‘Take care, sir,’ he said cheerfully. ‘If you fall in, I’ll have to fire you out.’ He spoke with a strong accent — German perhaps, or Dutch.