Along with the subsection on the Chinese Remainder Theorem, you may find this pa

Question

Along with the subsection on the Chinese Remainder Theorem, you may find this page from Cut-the-Knot to be helpful: http://www.cut-the-knot.org/blue/chinese.shtml.

If you are interested in Cryptography, then you might want to visit the RSA Data Security: http://www.rsa.com.  This is the company that owns the patents on RSA.

In particular, you may wish to visit the RSA Labs page: http://www.rsa.com/node.aspx?id=1297.

Finally, here is a page with some interesting Cryptography applets, which include descriptions of the encryption systems involved:http://www.math.psu.edu/dlittle/java/cryptography/index.html.

Once you have completed your reading and explorations, provide your impressions of applications of congruence. Make sure you include a discussion of some of the following points. (It is not necessary to research every question; pick a topic that interests you)

1. Describe the purpose of check digits.

2. Explain how is the check digit determined for an ISBN. Is this a fool-proof system? Why or why not?

3. Explain how the check digit is determined for a UPC. Explain how UP numbers are translated into barcodes and read by a scanner. Can you identify the UP number associated to any of the barcodes in example 8?

[Barcode Magic might be helpful for this exploration].

4. Discuss the Chinese Remainder Theorem. What is this theorem saying in plain English? Find out what you can about the history and significance of the CRT. [Remember to properly cite your sources].*

5. How does the RSA Algorithm work? Explain how you would use RSA to encrypt or decode a message.

6. How and when was RSA developed?  Are there other well-known encryption algorithms? What can you say about these?*

Be sure to provide some examples.

*Some of these items will require a bit of research on your part. Do not use Wikipedia or other encyclopedic sources. Be sure to properly cite any sources that you do use and use quotation marks when appropriate.

Explanation / Answer

1.A check digit is the twelfth and final number in a USPS bulk mail barcode string and is used by the USPS to detect barcode errors. The first eleven digits depict three groupings: the delivery zone (your 5-digit ZIP code), the region within the zone (+4) and the exact location for the mail drop (+2 , the delivery point (DP), or the last two digits of a mailbox or flat). The check digit is calculated by adding up the eleven digits, then subtracting the last digit of that result from 10. To illustrate this, the total, when adding up the 11 digits associated with the company I work for, is 34. Since 4 is the last digit in that number, I subtract it from 10 and get our check digit, 6. You can also use an online ZIP+4 lookup that returns the check digit at the end of the barcode string. Try http://bit.ly/ZIPplus4 Type in your address and push Search, then scroll all the way to the bottom of the page for easy-to-read Return Results. 2.The Luhn checksum is not some super secret security feature, it was a simple system designed to identify errors when exchanging credit card numbers in common use. At best, it can play a minor role in basic security checks to weed out those who just try random numbers. The system is designed to catch common errors. If one digit of the 15 digits is entered incorrectly the checksum will fail. For example if the correct number is 4217 6601 2345 6784 (here 4 is the checksum) then if the number is given as 4217 6681 2345 6784, where the

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