Chapter 16: Introduction MAT 105 Fall 2008 Chapter 16: Introduction

What is an identification number? An identification number is a sequence of letters and/or numbers that identifies an object, person, place, or concept The number should unambiguously identify something: no two things should have the same ID number

Where have you encountered ID numbers? Think about the different ways you encounter ID numbers in your daily life… License plate Driver’s license number Student ID number Social Security number Phone numbers Credit card numbers ISBN (International Standard Book Number) UPC (Universal Product Code) Many, many more…

Are ID numbers random? What happens if you go to Amazon.com and try to order something with a random credit card number? What should happen?

Security Features How does the computer know that the number you typed in isn’t valid? Should the computer have to look through all the millions of credit card numbers to make sure that the one you made up isn’t on the list?

Checking Validity Most ID numbers have a quick way to check to make sure that the number is valid This is not just for security, but to detect errors If the ID number is entered incorrectly, it is important that the error is caught; you don’t want your account to get charged for someone else’s order

Kinds of Errors Substitution: 123476 instead of 123456 This error is the most common, occurring almost 80% of the time Transposition: 123546 instead of 123456 This error accounts for around 10% of all errors Jump transposition: 125436 instead of 123456 This error is much rarer, accounting for only about 1% of all errors

How Are Errors Detected? Most errors are detected using check digits Check digits are extra digits attached to the ID number that are only used for checking that the ID number is valid Many different check digit systems are used, and we will study several of them Some check digit systems are secret so that they cannot be used to generate fake (but valid) ID numbers