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; you may learn about other ideas by reading and responding to posts made by your peers.) 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. Please do not just copy and paste from an online source!

Explanation / Answer

The concept of congruence is not restricted to the study of geometry. it plays an important role in everyday living. We may be able to buy a refill for our pen when the ink runs dry. We use congruence to replace a worn out part of the car, looking for the 'same part number'. In construction, they have to use the blocks of a 'standard size'. When using screws, we look for the kind of screw that we need and also screwdriver that fits. In each of these examples, the idea of sameness of shape and sizes applies.

Related Questions

Navigate

• Browse (All)
• Browse A
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.