Exercises
Some exercises will require theory that will not be lectured. You should read the required theory on your own. If no references are given, you will find the material in Stinson.
Some of the exercises will be in the Department of Mathematical Sciences' student computer lab.
| Week | Date | Exercises | Notes |
|---|---|---|---|
| 35 | 28/8 | Stinson 1.5, 1.7, 1.10, 1.12, 1.16, 1.21 a+c, 1.23 | |
| 36 | 4/9 | Stinson 1.21 b+d, 2.2, 2.5, 3.2, 4.11 | |
| 37 | 11/9 | Stinson 6.4 a+b, 6.7 a+b. And a+b from this exercise. | |
| 38 | 18/9 | Stinson 6.4 c+d, 5.20, 5.21, 5.22. And c+d from this exercise. | In the computer lab. |
| 39 | 25/9 | Stinson 6.2, 6.3, 6.5, 6.6. For those who know finite extension fields: 6.10, 6.11. A small challenge. | In the computer lab. |
| 40 | 2/10 | Consider the elliptic curve y² = x³+x+2 over the field with 10000000019 elements. (a) Write a program to compute point multiples on the curve. (b) Write a program to determine the number of points on the curve. Hint: There's a subgroup of order 358573. (c ) Write a program to compute discrete logarithms in this group. (d) Join up in threes. Two should run the Diffie-Hellman protocol to agree on a secret, while the third should listen to the protocol, compute an appropriate discrete logarithm and find the secret. | In the computer lab. |
| 41 | 9/10 | Stinson 6.13, 6.14, 6.15, 6.16 | 822 |
| 42 | 16/10 | Stinson 5.10, 5.11, 5.13 and 5.15. Problem 5 from the 2001 exam. | 822 |
| 43 | 23/10 | Stinson 5.25, 5.26, 5.27, 5.29, 5.30. Also factor the numbers n1, n2 and n3 given below. | In the computer lab. |
| 44 | 30/10 | Stinson 4.1, 4.2, 4.6, 4.9, 4.5. | 822 |
| 45 | 6/11 | Stinson 7.2, 7.3, 7.8, 7.11, 7.12 | 822 |
| 46 | 13/11 | Exam 2008, all problems. | 822 |
Numbers for Exercise 23/10
\(n_1\) = 81590706502223701858602532049765353535397062060277693361902 93437599143685666641047326361669702898053771309136168691147 55117066317438807808079408965629254484386171079191048501979 12259433389944739480874970521803746601939025202497814791637 13830435437235859404973640772742677945228739231079395800655 06236258465576939488869252147091359387430169871079135403772 08875455108340486707774931860798118219929263886901187298318 09232479554755573295239277146488484161760353503598397995487 86554198156193493296891453662149996140033582376792137720040 54004868062088714509891145087884413427338480272116075355745 56884520260169632298192009759016363935876247032601957514434 28148097822588572204072652320970558890077968071963162995234 95744078785567383329228227704623184674036770239499461519760 15016847280296514064428560588142986395485662359270321254002 66009365784363992564086078096470620341243905751167876507718 48321598974604414342506219162203398533373440935099100867457 72826225953610773819770365770570304456271006428864741800941 86256007464247053294074096351483585712763490707522022879662 88846282219204459957820010099289689023659196389605882528090 84837133662032170922750039304747922913060266698925954453123 35401164935241430533401570688164446522252042721691098461936 13982300490499418313050552220473678057441993503085581093689 12836718713873052289104659789508624838653705267421177054309 42889757583265937779835220903957686825569299491579036657841 25409245541178099403747714198099425003026757642430220062791 03740259874331155292200263125859929190431670399390647223930 85970396838701102740737691498092982343909089885843003274651 52997953876229689439403319342700471759128733049396514647793 76294155550924136954788207324780229697557269978007905146419 55887421155771224523760564122635241322405309880000742809302 53515261232858459188115100316672098745973521177847993806129 39792696260255663825378574557523112279412673857319712305046 55082509367125061541951119262020612156214596133487427475366 77129435283901715644991042237157707434200601968847559589406 7759766321451237469,
\(n_2\) = 11394162268456541618600279164803770561305904129170502714221 26074044875403485751695692809172531708809856046914325584513 18957353198395717991092566467048353635691686067765221040313 88743467928309273575361480941586517580707102563900334817293 19214381908097649335095144346627725412032898740915703081215 026872669753019,
\(n_3\) = 11298202139570110182321889918200758661982937649807399563715 76482253074406006055628707470153258407487444934333416109308 42421319766656486039017266898432633838488265246521310887331 62402414246703696305273951967137522110366283478958519446495 16928367161113211704416062453740033393127241474387103005748 43278802156884867979577460059002277576496434776786186185999 72712331436519711080063572522606304107331149746461107394106 27176717088136901394560965166167425763606022664944014843620 15655339799362209068731803839606425306650994480862032961519 09851134027860678129005754264647123514519601448432811704305 6446565121717