Introduction to Cryptography with Coding Theory, 3rd Edition

A.11 Examples for Chapter 18

Example 39

Here is a game you can play. It is essentially the simplified version of poker over the telephone from Section 18.2. There are five cards: ten, jack, queen, king, ace. They are shuffled and disguised by raising their numbers to a random exponent mod the prime 24691313099. You are supposed to guess which one is the ace. To start, pick a random exponent. We use the semicolon after khide so that we cannot cheat and see what value of $k$ is being used.

In[1]:= k = khide;

Now, shuffle the disguised cards (their numbers are raised to the $k\text{th power mod }p$ and then randomly permuted):

In[2]:= shuffle

Out[2]= {14001090567, 16098641856, 23340023892, 20919427041, 7768690848}

These are the five cards (yours will differ ...