This preview shows pages 1–5. Sign up to view the full content.
This preview has intentionally blurred sections. Sign up to view the full version.
View Full DocumentThis preview has intentionally blurred sections. Sign up to view the full version.
View Full Document
Unformatted text preview: MATH 4023 Name ' ' K E
Exam 3 July 23, 2010 Score: 4 1
Instructions: This is a closed book, closed notes exam. Please read all instructions carefully and
complete all problems. Be sure to show your work in order to receive full credit, an answer with no supporting work will receive no credit. 1. This problem concerns arithmetic modulo 20 (in Z20). All answers should only involve
expressions of the form "dwith a an integer satisfying 0 g a < 20.
(a) Compute g + ﬁ. 4‘ .........—. m :l“ 1': 20/ \l (b) Computeg 17. M’
6,...»— ‘é‘oﬁt: 1L. (c) Compute ? ‘1. m h.» 23’ :l W242 (d) Find all zero divisors of 220. ' ,_ E. (Ev— wf» ,xrT‘ r" T" ' {6 {as
ﬂ/¢/§/é/g/[@F(?’flﬁfd/lg) / 2. Find the 1ast2 digits of 15101. 3. This problem makes use of the following equation:
1 :1527—4101.
Using this equation (not necessary to prove it!) answer the following. (a) Compute the multiplicative inverse of 15 in Z101. r ./_‘ yr“,— . IF; A "ﬁr: ‘1 P: z s y 21} 7:9 Z— 3r s we rumw {15,55
(b) Compute 15101 mod 101. , ‘! ,._ v 3" ﬂ!
> . w . WNW ‘ ﬂora/va
6,61) C mm) C l :3 i 3/
‘ i ,Eal : r, 1— g  (
i5 :5 i 3, i fan ,)
(c) Solve the equation 15:5 : 8 mod 101.
L+ {all ) 1‘3
w—«m r» “'7”
‘ T _ P A l" M; "l: (W'Ewﬁﬂ CZ: )
SAL owbwD'WD 29’3"?" g V 2 1/ l 1’
(d) Solve the simultaneous linear congruences:
3: E 7 mod 101
, I E 3 mod 27  4;. J q ‘  . e I .a ' .kr bx. g 1/1, om ‘fguvw/ 'w a r; 1¢JMV3M g} __
ii, 1 3L “3;, hon—«2 :‘c
K ’L 3 : 2 e .1. ‘
my? .517“); §< : 5i"; m1 (:9 :4 4w + 5'61 1”“ xi“
‘31 9c: 3% MCW Xe; "ﬁledl 02 4. Assume that for an RSA cryptosystem n = 143 and the enciphering exponent is e = 103,
wheren : 143 = 11 X 13. (3) Compute the deciphering exponent d.
chm) : (150431;) 3" 16x )2 :7 12/22)
2 a“ _
“1035 r— e a r 20 Cit/fie M;aé~€ﬁm «a: . _ P / Vb, .4 e”;
f i p .
“‘9 775.2. 3 7% “"H—J‘U 2"” ' rd m @C,D(j03;ize)5’ y
{Ir/km a”; ’4 .3; '
(b) Assume that the following letter to number translation table is used:
J:1,Q:2,R:3,L=4,D=5,A=6,S=7,Y=81T:9,O:0 Encrypt the message ” SO”. 3'5; WW9 3%? '3‘?“ ’55 (“we/w) . . 7075 . , ‘ A 1
(S e Era) (“"53 W3) fro 5 Z 35 {‘ guy? #5.?" I: :2 ?/ y! $4,371} gift)“: ‘2’: 2;} ("z/.45 _ aw _.,: '  : {35.3} (c) Assume that a message has been grouped into blocks of two letters, enciphered and
send out as 10 03. Decipher the message. 0?) 3L"; I c; Wong? “#1 a) , ﬂ”; m.) E
kpé) {097% <+re> 730L693 1.45 (99 ‘ﬁﬁrwﬂkeeﬁﬁ 5. Let C be a binary code with generator matn'x (3) Find the Partity check matrix of C. (b) Find all of the codewords of C
.309; (33;, em, sea, on; W: “9/ “f  , qgjif‘tHUCJO
a. ﬁ " n. .  r n {‘3' Cezucw‘z‘réw ﬁQGUEJOO/i amm ;) Druid, / (c) How many redundant digits are there in a codeword? 5 (d) What is the minimum distance d of C?
‘U . , A at C c1) 2 3 I (c) How many errors can it detect? How many errors can it correct?
Lute Q ,erm~S/t >/ 737997
W i " .51"?st , I Z; is; E) (f) Use this coding to encode 101. [GHOW ...
View
Full
Document
This note was uploaded on 12/11/2011 for the course MATH 4023 taught by Professor Staff during the Spring '08 term at LSU.
 Spring '08
 Staff
 Algebra

Click to edit the document details