Chapter 1

Damn. It still wouldn’t work out. This must have been the third time I had worked it through from the start and I was beginning to realize that there was a good chance I would not be able to get it.

The chair let out a plaintive creak as I leaned over the table, pulling the chair up onto two legs. I mouthed my thoughts quietly to myself as I once again began at the top.

I had x0 and x1 available as inputs and knew that h(x0) != h(x1). Well, I didn’t know they were unequal but I could justifiably assume that they were unequal since both x0 and x1 were arbitrary and h represented a collision-free hash function. More specifically, h was a MAC with a fixed key. The chances of two arbitrarily chosen inputs hashing to the same output value were very slim indeed. Damn it! The point on my pencil broke. Again. I was using a 0.5mm mechanical pencil as usual. And as usual I was going through the lead pretty quickly, breaking the point every few minutes.

I threw the pencil down in disgust and pushed the chair back. I got up and headed over to the window. I had to collect my thoughts and try a new approach. The old approach was getting nowhere and I was getting impatient. Justifiably so too, since it was already 2:30 in the morning, leaving only six more hours until my deadline. Not that I had an interest in resolving this mess quickly. Rather, because she had an interest in seeing this whole mess sorted out. My only involvement was that I was the one who created the mess. I suppose that meant that I had a certain responsibility to correct the situation. Yet even that wasn’t quite it. I just felt compelled to help her… I had tried to convince myself, unsuccessfully, that it had nothing to do with her looks.

As I stood staring out the window, with the rain-soaked street glistening in the glow of the street-light below, a feeling of despair came over me. I’d been at it since late afternoon, taking only a short break to grab dinner at the fast-food place just around the corner. I had brought the food back to my small apartment and eaten it at the kitchen table. While wolfing down the greasy burger in large mouthfuls, I had stared at the formulas scrawled on the papers strewn across the cluttered table before me. My kitchen table is barely large enough to accommodate two people, so it does not require many papers to entirely cover the surface. The papers were filled with dead ends. Every scenario I had tried had failed. Every avenue I had pursued had come up empty. I was unable to develop a chronology of events that would explain the few clues I had.

I wiped perspiration off my brow. The week before had been one of the hottest on record for Chicago and this week wasn’t much better. The rain from earlier that night had done nothing to bring down the temperature; it had only made the air moist and muggy. I was grateful that my apartment, while lacking in nearly every other respect, does have adequate air-conditioning.

The sphere of light extending outward from the street-light was cloudy with moisture. The light was not strong enough to penetrate the hot haze, leaving the rest of the street dark and murky. It matched my mood.

I sighed heavily, unclasped my hands from behind my back, and folded them across my chest instead. I had to face the possibility that I would not be able to find the problem, nevermind the solution. I was still struggling to determine what had happened the afternoon of July 11th.