MAT 105 Spring 2008

 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

 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…

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

 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?

 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

 Substitution: instead of  This error is the most common, occurring almost 80% of the time  Transposition: instead of  This error accounts for around 10% of all errors  Jump transposition: instead of  This error is much rarer, accounting for only about 1% of all errors

 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