She explained, ‘There are mistakes in every cipher – just like when we write a document we get things wrong and misspell words. If there aren’t too many mistakes and the error rate isn’t too high, so that it’s within accepted parameters, it’s allowed.’ She had designed the last exercise on the understanding that RECOVERY was an ordinary cipher, with the normal low error rate. If on the other hand there was a serious problem with RECOVERY, the rate of errors would be much higher than normal, and so our calculations would not support her theory.

‘So you now think that the rate of errors in RECOVERY is higher than normal?’ I said.

She shook her head. ‘I don’t think it’s very likely, which is why right now my most important task is to prove my method for finding the key, in the hope that I can then quickly discover where the problem lies and come up with a new approach which takes account of it.’

‘And if you prove that there is nothing wrong with the method you have developed for finding the key?’

‘Then I would suspect that there is a fundamental problem with RECOVERY, and hence there is an unusually high error rate.’

Chen said, ‘So either way, you don’t believe the results of the exercise; you only believe in yourself.’

‘I have faith in my theory,’ she replied, ‘but I am worried about the deductive process – that’s why I want to check it again and come up with a new plan.’

‘And when will your new plan be ready?’ asked Chen.

She smiled bitterly. ‘That’s very difficult to say. If it’s quick, it might be really quick, but if it’s slow, I might never come up with anything.’

Comrade Chen shook his head. ‘That’s pretty cold comfort!’

‘Those are the conditions under which every cipher ever created was decrypted!’ she said.

Chen looked at me and shook his head. I said, ‘She’s right.’ I wasn’t about to side with him.