Silvio Micali taught me cryptography. To explain one-way functions, he gave the following example of encryption. Alice and Bob procure the same edition of the white pages book for a particular town, say Cambridge. For each letter Alice wants to encrypt, she finds a person in the book whose last name starts with this letter and uses his/her phone number as the encryption of that letter.
To decrypt the message Bob has to read through the whole book to find all the numbers. The decryption will take a lot more time than the encryption. If the book increases in size the time it takes Alice to do the encryption almost doesn’t increase, but the decryption process becomes more and more draining.
This example is very good for teaching one-way functions to non-mathematicians. Unfortunately, the technology changes and the example that Micali taught me fifteen years ago isn’t so cute anymore. Indeed you can do a reverse look-up online of every phone number in the white pages.
I still use this example, with an assumption that there is no reverse look-up. I recently taught it to my AMSA students. And one of my 8th graders said, “If I were Bob, I would just call all the phone numbers and ask their last names.”
In the fifteen years since I’ve been using this example, this idea never occurred to me. I am very shy so it would never enter my mind to call a stranger and ask for their last name. My student made me realize that my own personality affected my mathematical inventiveness.
Since modern technology is murdering my 15-year-old example, I would like to ask my readers to suggest other simple examples of one-way functions or ways to resurrect the white pages example.Share: