{VERSION 5 0 "SUN SPARC SOLARIS" "5.0" } {USTYLETAB {CSTYLE "Hyperlink" -1 17 "" 0 1 0 128 128 1 2 0 1 0 0 0 0 0 0 1 }{CSTYLE "" -1 256 "" 1 14 0 0 0 0 0 0 0 0 0 0 0 0 0 1 }{CSTYLE "" -1 257 "" 0 1 0 0 0 0 0 1 0 0 0 0 0 0 0 0 }{CSTYLE "" -1 258 "" 0 1 0 0 0 0 0 1 0 0 0 0 0 0 0 0 }{CSTYLE "" -1 259 "" 0 1 0 0 0 0 0 1 0 0 0 0 0 0 0 0 }{CSTYLE "" -1 260 "" 0 1 0 0 0 0 0 1 0 0 0 0 0 0 0 0 } {CSTYLE "" -1 261 "" 0 1 0 0 0 0 0 1 0 0 0 0 0 0 0 0 }{CSTYLE "" -1 262 "" 0 1 0 0 0 0 0 1 0 0 0 0 0 0 0 0 }{CSTYLE "" -1 263 "" 0 1 0 0 0 0 1 0 0 0 0 0 0 0 0 0 }{PSTYLE "Normal" -1 0 1 {CSTYLE "" -1 -1 "" 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 1 }0 0 0 -1 -1 -1 0 0 0 0 0 0 -1 0 } {PSTYLE "" 0 256 1 {CSTYLE "" -1 -1 "" 0 1 0 0 0 0 0 1 0 0 0 0 0 0 0 1 }3 0 0 -1 -1 -1 0 0 0 0 0 0 -1 0 }{PSTYLE "" 0 257 1 {CSTYLE "" -1 -1 "" 0 1 0 0 0 0 0 1 0 0 0 0 0 0 0 1 }3 0 0 -1 -1 -1 0 0 0 0 0 0 -1 0 }{PSTYLE "" 0 258 1 {CSTYLE "" -1 -1 "" 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 1 }3 0 0 -1 -1 -1 0 0 0 0 0 0 -1 0 }{PSTYLE "" 0 259 1 {CSTYLE "" -1 -1 "" 0 1 0 0 0 0 0 1 0 0 0 0 0 0 0 1 }3 0 0 -1 -1 -1 0 0 0 0 0 0 -1 0 }{PSTYLE "" 0 260 1 {CSTYLE "" -1 -1 "" 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 }3 0 0 -1 -1 -1 0 0 0 0 0 0 -1 0 }} {SECT 0 {PARA 256 "" 0 "" {TEXT 256 11 "ACCESS 2007" }}{PARA 257 "" 0 "" {TEXT -1 23 "Group Project - Week 1 " }}{PARA 259 "" 0 "" {TEXT -1 39 " Due Thursday, June 21, before midnight" }}{PARA 258 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT 258 7 "Part I " }{TEXT -1 111 " \+ Set up an RSA public-key cryptography system for the 8 ACCESS grou ps. Follow the steps below carefully!!!" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 256 "(1) Each team should choose two \+ primes p,q between 10^30 and 10^31, so that the modulus N=pq is greate r than 10^60 - and thus will have at least 61 digits. This means that when you send people messages you can use up to 60 digits in each num ber packet , " }{TEXT 257 6 "before" }{TEXT -1 533 " encoding with the ir public key. This forces each packet number to be safely in the res idue range for the recipient's modulus before you encrypt it, so that \+ when the recipient decrypts it, they will recover your original messag e. (After you encode a packet it will quite likely have 61 or 62 digit s, but it will still be in the recipient's residue range because of ho w the encryption algorithm works.) Real RSA systems use much larger \+ primes, but I have chosen these lengths so that each digit packet fits onto a single text line." }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 " " 0 "" {TEXT -1 142 "(2) After picking your primes find a suitable enc ryption power e. Use e and the auxillary modulus to compute your secr et decryption power d. " }{TEXT 262 1 " " }{TEXT -1 234 "Make sure e a nd d are multiplicative inverses mod N2, check that you can successful ly encrypt and decrypt messages using your public and private informat ion, and verify that N really is bigger than 10^60, before proceding t o step (3) " }{TEXT 261 2 "- " }{TEXT -1 687 "This double-checking sho uld prevent errors which have occurred in some unfortunate ACCESS grou ps, and which have led to strings of emails with different attempts at a public key, all from the same group....and then other ACCESS groups become innocent victims. Now would also be a good time for you to sav e and email all of your public and private key data to all three group members, so that you can recover if you accidentally forget to save w ork later on. (Convert a number which is a blue Maple output picture i nto text by copying it as \"Maple text\". You want to do this, since \+ you won't be able to turn a picture of numbers back into text numbers \+ later on unless you do it by hand.)" }}{PARA 0 "" 0 "" {TEXT -1 0 "" } }{PARA 0 "" 0 "" {TEXT -1 31 "(3) Send a plain text email to " }{TEXT 263 26 "access-2007@lists.utah.edu" }{TEXT -1 278 ", identifying your group by number, with your three names, with contact email address(es ) for the group, and with your public key information. Again, make su re your encryption power e and modulus N are text numbers and NOT a pi cture image, so that the recipients can use them." }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 500 "(4) Nick, Meagan and Je n will try to be troubleshooters. Send Nick ALL your public and priva te information: group number, email contact info, names, p,q,N2,e,d. \+ When I (Nick) get this data I'll triple-check to see it's all O.K. (an d let you know if it is or isn't), and then I will create a master lis t of everyone's public keys which I can link to our home page. I hope \+ to complete this task Friday morning, but certainly by the afternoon. \+ Send Nick's email to his Umail account, njk4@utah.edu. " }}{PARA 0 " " 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 602 "(5a) Create a fa vorite secret message and signature, and convert your letters to numbe rs using the table on page 9 of Davis' notes. Let us agree that your \+ plain text message will end with a sentence ender (period, exclamation mark or question mark) and a space, so that after conversion it ends \+ in 7010, 6310, or 8610. Let us agree that no plain text message is lo nger than 88 letter-punctuation characters long, so that after table c onversion the corresponding list of numbers is at most 176 digits lon g. If you have a longer message send part of it as plain text and onl y encrypt the best parts." }}{PAGEBK }{PARA 0 "" 0 "" {TEXT -1 355 "(5 b) We are using the secure signature feature, so decrypt your signatur e using your own (secret) decryption power. This will create a long s equence of digits (a number less than your groups' modulus but probabl y with 61 or 62 digits). Append this sequence onto the digits from th e converted plaintext message, to create a single long string of numbe rs." }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 722 "( 5c) NOW, break the single long string (your converted message followed by the digits of your decrypted converted signature), into packets. \+ Make each packet at most 60 digits long. (You will probably find that \+ your signature gibberish fills all of your last packet and a few space s in the preceding one.) Being at most 60 digits long, your packets a re all less than everybody elses moduli \"N\", and so in their residue range. Thus, after your recipients decrypt each packet you sent and glue the decryptions back together, they should recover your single l ong string. They will know where your message ends and their signature begins by finding one of the message enders, 7010, 6310, 8610, follow ed by nonsense numbers." }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 780 "(5d) Send your message packets to two groups: if yo u are group x then send messages to groups (x+1) and (x-1), mod 8. Fo r example, group 3 sends messages to groups 2 and 4; group 8, also kno wn as group 0, sends messages to groups 7 and 1. Please use the same plain text message and signature for both recipient groups - so you w ill be working with the same long string from (5b), for both recipien t groups. (Of course, after you encrypt using the their different keys , you will be sending two different ciphertexts.) Since your original message had at most 88 letters (=176 digits) and since your decrypted signature is less than 10^62 (<63 digits), you should have at most 17 6+63=239<240 digits before encrypting, so at most 4 packets of length \+ up to 60 digits will suffice." }}{PARA 0 "" 0 "" {TEXT -1 1 " " }} {PARA 0 "" 0 "" {TEXT -1 414 "(6) Use your private key and reverse th e encryption process to decode the messages you receive from your two \+ neighbor groups. Using the fact that their converted plain text messa ge ends in 7010, 6310, or 8610, separate off their decrypted signature and use their encryption key (and Davis' table) to recover what their signature was. (This part of the project always gives fits to a coupl e of the ACCESS groups.)" }}{PAGEBK }{PARA 0 "" 0 "" {TEXT -1 0 "" } {TEXT 259 8 "Part II " }{TEXT -1 29 " Create a project report. " }} {PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 1234 " Th e first section of your project report should be a 3-5 page discussion of public key cryptography. Explain what it is and why its advent was such a revolutionary development. Explain the RSA algorithm and why \+ it works for public transactions. We have given you various reference s for this part of your report, but we encourage you to also do more i ndependent research. Questions I would enjoy you finding answers to a re: When you engage in secure internet transactions (i.e. at any URL \+ starting with https://....) how much of this interaction is typically \+ made using public key cryptography? Is the RSA algorithm universally \+ used for public key cryptography or are other algorithms also being ap plied? When RSA is being used, what is the typical modulus size? How is \"security certificate\" authentication related to the RSA secure \+ signature feature, if at all? Is it now possible to not only send doc uments, but also to make secure phone calls over the internet, using \+ \"pretty good privacy\"? What strategies do groups like the National \+ Security Agency adopt in their quest to track potential enemies, in or der to get around the fact that public key cryptography apparently all ows for secure information transmission? " }}{PARA 0 "" 0 "" {TEXT -1 667 " In the second section of your report describe the process you went through to set up the ACCESS RSA system. Exhibit your publi c and private key information, your original plain text message and s ignature, and the various transformations of your message and signatur e as you prepared them for transmission to your two target groups. Ex hibit the encoded messages you received, explain how you decoded them, and exhibit the final results. Make sure all numerical representation s of your messages are numbers and not pictures, so that we will have \+ an easy time checking your work (which we will do!). Present this dat a in a careful, organized way. Explain well." }}{PARA 0 "" 0 "" {TEXT -1 877 " Although different subjects and professors may have different standards for how papers should be formatted, there are cer tain common elements. Reports should begin with a cover page or titl e area, containing the title, the authors, and the date. This should \+ be followed with an introduction which summarizes the report's conten ts. The body of the project report may be split into sections, and a conclusion section may be appropriate. Make sure to cite all referen ces. With MSWord the easiest way to do this is by inserting footnotes, and I prefer that they be endnotes. For internet references include \+ a link to the web page, the site title, author and download date. The \+ RSA paper by Rivest-Shamir-Adelman is an excellent example of how to w rite a paper in mathematics. When I googled \"writing a science resea rch paper\", one of the top hits I liked was the site" }}{PARA 260 "" 0 "" {URLLINK 17 "http://abacus.bates.edu/~ganderso/biology/resources/ writing/HTWgeneral.html" 4 "http://abacus.bates.edu/~ganderso/biology/ resources/writing/HTWgeneral.html" "" }{TEXT -1 0 "" }}{PARA 0 "" 0 " " {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT 260 19 " Paper submission: " } {TEXT -1 805 " Please submit your paper to me (Nick, njk4@utah.edu) \+ and Jen (guajardo@math.utah.edu), as an attachment in an email. Your d ocument should either be in Microsoft Word or Word Perfect format. T his project is due by Thursday June 21, before midnight. Help each ot her - you're all on the same ACCESS team! If you think a group sent y ou a defective message, contact them and explain what isn't working, a s a prelude to both sides trying to troubleshoot the problem. If you c an't unstick each other, see if Meagan, Jen or I can help. I will also plan to be available from 2-4 on Wednesday afternoon next week, in th e large Marriott computer room, in case any groups are stumped. Pleas e send me an email if you wish to take advantage of this meeting time, since if no one asks I won't show up. Have fun!!" }}}{MARK "28 0" 877 }{VIEWOPTS 1 1 0 1 1 1803 1 1 1 1 }{PAGENUMBERS 0 1 2 33 1 1 }