For an hour he pondered the question. The answer did not leap at him as it did to Archimedes in his bath, it crept up slowly. If he just knew the length of the keyword it would be a start. Common letter sequences, such as THE, AND and TION, would have been repeated in the text, and would sometimes have coincided with repeats of the letters of the keyword, thus leading to repetitions in the en crypted text. If he measured the distances in letters between each repeated sequence, he should be able to calculate the length of the keyword. In his ‘message’ BZP were letters seven to nine, and twenty-five to twenty-seven. So the start of the second sequence fell eighteen letters after the start of the first. His keyword, THOMAS, had six letters. Eighteen was divisible by six. The letters of the keyword had been repeated exactly three times before meeting the same plain-text sequence of letters again. It was a matter of simple arithmetic. Then an awkward thought occurred. Eighteen was also divisible by one, two, three, nine and itself. Not so simple, after all. Time for another stroll. He locked his door and set off.
Outside Pembroke, Thomas turned left towards the ancient castle. Head down and lost in thought, he barely noticed the beggars and whores who infested this part of the town. Jumbles of letters and numbers tumbled about in his mind, as if trying to make some sort of sense but never quite managing it. He walked round the castle and back towards St Ebbe’s. Could he find the length of the keyword from repeating sequences of letters, and, if so, how could he use it? He felt the vague stirring of an idea.
He did not see the boys until it was too late. Three of them came hurtling towards him, and, before he could move aside, knocked him off his feet into a drain. At least they had the grace to stop and help him up, dusting him down and enquiring if he was hurt. Although he knew that his shoulder was bruised, he assured them that he was only shaken, and advised them to take more care in future. They promised to do so and offered to help him home. Not wishing to be helped, he declined the offer and walked alone back to Pembroke, conscious that he looked and smelt exactly as if he had fallen into a drain.
For once, Silas was not on sentry duty, so he did not have to undergo an inquisition. At the door to his room, he reached into his pocket for the key. It was not there. He tried the other pocket. Not there either. ‘Damnation,’ he said out loud, ‘it’s in that shit-filled drain. And it’ll have to stay there.’
He returned to find Silas back at his post. Having offered a feeble lie for his condition and for the loss of the key, he was grudgingly given a replacement. ‘I keep three keys for each lock, sir. One for the gentleman, one for me and one spare. Now you’ve lost yours, I’ve got no spare until I can get another made, and only the good Lord knows when that will be. The forges are all busy sharpening swords and shoeing horses.’
Inside his room at last, Thomas stripped off his foul clothes, washed himself down with water from the jug and tried to examine his shoulder. It hurt, but he could see no signs of a wound. Tomorrow he would be fine.
At dawn, the vague idea stirred again. In a longer text, there would be more than one letter sequence repeated. If he took the letter measurements between all repeated sequences of the same letters, he should find a common factor, suggesting the length of the keyword. To test this theory, he started by counting the number of different repeated sequences in the text, ignoring those of less than three letters. He found ten of them, including three repetitions of IFS. He could not be entirely sure that he had not missed any, but ten should be enough for a test. He drew a line under the repeated sequences and counted the letters separating each repetition of each sequence.
URF UBD HE XQB TF KGA OEMD RRFUO TLC WMG LRB WHT R XHGORKZ IO KPW769 WA MQFV BVMF HPL ZFTD RVV57 4SEWMFREJ VGL SVKMGE 852 GTSC WZTD QE TIJG IVL GJT RA KDOE IK EOJAAQLV GGJR MQU IOIGSI GRQF HBFZG JGY ALG EE OLWEEA GJR YIFS1 82AEL2 64SGE SC AAD ZVY JP KP WXR JB JTN XBZ77 5XNW WJBS LA LWAK371 EAIH TPA AD RVV BAP TWPVV AGDN WWJ URR VUT IW EW HTI QCT WY QDT37 1IE852 769UMHT RKC CONT WSGV WMG IEN DJEE KW IHV ZW PNU EAIH371 ZV GJR YIFSS NQ DA BV NGGCVL LD SVMC IRLKW DN KMJ BS WINDU IITAE KW42177 5OX LCIVK IJM LXMV IFS PCI UT FFZ SEPI MZTNJQGCOW3 71E ZDWZTD QE SZGJ GYB LD 574SKIFS RVIV N GFL OX LC QFV WV AZPLCJJX NX IF TNU BG IHZA OP RJWGC
The results he wrote on a table, with the sequences in the left column, the letter distances he found for each in the second column, and the numbers three to ten across the top row, working on the assumption that the keyword would be more than two and less than eleven letters long.
Only the number five divided into all ten separations. The keyword must have five letters.
So delighted was he at the first hint of progress that Thomas almost forgot to hide his papers before hurrying to tell Abraham. He prised up the floorboard, put the papers in the space below it and replaced the pisspot on top. Then he picked up the pot and filled it up. Oddly, it reminded him of the king’s musketeers pissing down the barrels of their muskets to cool them down. That should keep prying eyes at bay. He locked his door and went to give Abraham the good news.
Expecting to be summoned straight in, he knocked loudly on Abraham’s door. When there was no response, he knocked again. Still no response. He tried the door, which was locked. Odd. Perhaps Silas would know where he was. He found Silas at his post. ‘Silas, Master Fletcher’s door is locked and he appears to be out. Do you know where he is?’
‘No, sir. Master Fletcher never goes out unaccompanied, and I haven’t seen him today. Perhaps he’s asleep.’
‘Have you a spare key to his rooms?’
‘I have, sir,’ replied Silas suspiciously, ‘but I’d prefer not to lose it. If you don’t mind, I’ll come with you and unlock the door myself.’ He took a large bunch of keys from a drawer and followed Thomas to the room. They knocked again, but there was still no response. Silas found the right key and unlocked the door. Thomas entered first, and gasped. The room had been ransacked. Every one of Abraham’s books had been torn from its spine and thrown on the floor. His chair and table were in pieces, and his few clothes and other possessions were strewn about everywhere. Thomas went cold. What in the name of God had happened here?
He called out. ‘Abraham? Where are you?’ There was no reply. They went cautiously in, and tried the door to the small chamber where Abraham slept. It was unlocked. Thomas entered. On his blood-soaked bed lay the naked body of the old man. His face and chest bore the signs of torture, his eyes had been gouged out and his throat cut. Thomas’s stomach heaved. He put his hand to his mouth and closed his eyes. Silas looked past him into the chamber, and vomited. For several minutes, neither man could speak. Both stood with hands on knees, trying to breathe. Thomas was the first to recover. ‘What manner of human filth could have done this? And why?’
Silas, too, was recovering. ‘I’ll fetch the coroner, sir. You’d best stay here.’
‘Be quick, Silas. The coroner must see this at once.’
When Silas had gone, Thomas sat on the floor by the door. His old friend, a gentle man who had never harmed a soul and had helped many, foully murdered in this monstrous, sickening, obscene way. His tears flowed and he howled in anguish. God in heaven, how could any man commit such an act? What could drive a man to inflict such suffering on another? Why take the eyes of a man who could not see?
For an hour, Thomas barely moved. The strength had gone from his legs and his mind was numb. He sat staring at the room and thought of nothing but Abraham’s premonition. Somehow the old man had known. God forbid that he had known it would be like this.