‘So I began my analysis. A common technique in breaking ciphers is to study the distribution of letters. The most common symbol is likely to correspond to a common letter in plain language - E perhaps, or S, or T. But this fragment is too short to enable such a count. I experimented with scytales of various dimensions, to no avail. And I tried all the possible cyclic permutations, with no luck either. With all the permutations exhausted, I racked my brains for a new way forward.’

Joan murmured, ‘And in the end, after much heroic struggle, you found a way, did you?’

Bacon blithely ignored her sarcasm. ‘A simple variant on cyclic substitution is to use a key.’

‘A key?’ Saladin asked.

‘Caesar, for instance, could have used his own name.’ He wrote it out: CAESAR. ‘We must eliminate repetitions.’ He crossed out the second A. ‘Now we use this five-letter key as the foundation of our cipher.’ He wrote out a twenty-three Latin letter alphabet with a code beneath it:

‘You see? A substitution with the shift depending on the key word, and with those letters removed. So the word CAESAR now encodes as—’ He wrote it out:

ECRQCP

‘It’s a poor sort of code,’ Saladin observed. ‘The last few letters are transcribed without change.’

‘You’re a practical man, I can see that,’ Bacon said. ‘That’s true. But there are easy variants. The simplest is to put the key word at the end of the alphabet, not the beginning, and to proceed backwards.’ He scribbled quickly,

‘Now all the letters save one have a different symbol.’

‘This is all very well,’ Joan said, ‘but we don’t have a key, do we?’

‘Oh, but we do,’ Bacon said. ‘You gave it to me - or rather, to Thomas.’

‘I did? What key?’

‘It was in the letter you received. From your cousin in Spain. The phrase she was particularly interested in, that appeared to be left incomplete on the scrap of parchment you held.’

‘Incendium Dei,’ Saladin said, wide-eyed.

Joan stared at Bacon. ‘Can it really be as simple as that?’

Bacon grinned. He now had a full hold on their attention, Saladin thought, and he knew it. ‘Shall we try it?’ He wiped the table clean of chalk with his sleeve, and began to scribble again. The three of them bent over to see. ‘We begin with the key,’ Bacon said. He wrote,

INCENDIVM DEI

‘The U replaced by V as you see. Next we eliminate duplicates.’

INCEDVM

‘There is our key. So we construct our code. I tried out a forward substitution, but succeeded with a backward . . .’ He scribbled rapidly.

‘Now we reconstruct our message. That first B becomes a P, the M becomes R . . .’

BMQVK XESEF EBZKM BMHSM BGNSD DYEED OSMEM HPTVZ HESZS ZHVH

PRGSL CVEVO VPALR PRMER PNYET TBVVT IERVR MHDSA MVEAE AMSM

Saladin stared at the new string, unreasonably disappointed. ‘It’s still nonsense.’