Section 3.1: Identification Numbers

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# Section 3.1: Identification Numbers - PowerPoint PPT Presentation

Math for Liberal Studies. Section 3.1: Identification Numbers. What is an identification number?. An identification number is a sequence of letters and/or numbers that identifies an object, person, place, or concept

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Math for Liberal Studies

### Section 3.1: Identification Numbers

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…
• 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 type in something random when it asks you for a credit card number?
• What should happen?
Security Features
• How does the computer know that the number you typed in isn’t valid?
• There are some quick ways it might be able to tell
• You typed in some letters or symbols instead of all numbers
• You didn’t type in 16 digits
Format
• ID numbers typically have a common format
• Standard PA license plates have a format of three letters followed by four digits
• Social security numbers are 9 digits long
• Phone numbers are 10 digits long (with area code)
Security Features
• What if you type in a number with the correct format?
• Should the computer have to look through all the millions of credit card numbers to make sure that what you typed in isn’t on the list?
• There are billions of credit cards in the world, even with fast computers this would take too long
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 an 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
• What kinds of errors can occur when reporting an ID number like this?
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?
• We can immediately see that any of those ID numbers are incorrect, but that’s because we know the real ID number
• Put yourself in the position of the company representative on the other end of the phone
• That person doesn’t know what the real ID number is, they only know what you tell them
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
Validity vs. Correctness
• When an ID number is communicated, errors can occur, and we can sometimes detect those errors by determining that the erroneous number is invalid
• However, sometimes even ID numbers with errors turn out to be valid. In these cases there is no way to know that the ID number is incorrect
A Sample ID Number System
• Suppose we run a company that sells phone cards, and each card comes with an account number
• The format of the account number is a 6-digit number
• Validity is determined using this rule: if the sum of the digits of the account number is 20, then the number is valid. If not, then the number is invalid
Checking Validity
• Someone calls in to phone card service and wants to place a call using account number 516224
• We can use our system to determine whether or not this is a valid ID number
• 5+1+6+2+2+4 = 20, so this number is valid
Checking Correctness
• However, just because the number is valid does not mean that it is correct
• It is possible that there was an error that our system didn’t detect
Detecting Errors
• Suppose you want to use your account, which has ID number 153182
• However, when you go to type in your number, you accidentally type in 156182
• We can see that an error has occurred because we can see both numbers, but the company only knows the number you typed
Detecting Errors
• Is the error detected?
• We try our system: 1+5+6+1+8+2 = 23
• Since the sum isn’t 20, we know the ID number 156182 is invalid
• We have detected the error
Undetected Errors
• This time, suppose you type in your ID number (153182) as 153812
• Again, we can see that an error has occurred, but the question is whether the ID number system can detect the error
• In this case, 1+5+3+8+1+2 = 20, which means that the new ID number is valid
• The error is not detected!