Write each as a numeral. 1) six hundred twenty-four thousand, five hundred four 2) six hundred ninety-nine thousand, ninety-eight 3) four hundred thousand, five hundred thirty-seven 4) three hundred thirty thousand, four hundred eighteen 5) three thousand, one hundred ninety-six 6) two thousand, eight hundred 7) five thousand, one hundred ninety 8) eight thousand, fourteen 9) ninety thousand, n...

Chaum’s Dining Cryptographers protocol crystallises the essentials of security just as other famous diners once captured deadlock and livelock: it is a benchmark for security models and their associated verification methods. Here we give a correctness proof of the Cryptographers in a new style, one in which stepwise refinement plays a prominent role. Furthermore, our proof applies to arbitraril...