Math 348 (Cryptography)

Prof. Weibel

Spring 2008
Homework Assignments
All assignments are due on Tuesdays.
Go to the current assignment
DueSection/Problems Section/Problems
1/29/08 (Tues)Encrypt: your name in Caesar (k=13);
'Rutgers' with k=1st letter of your last name		 1.1#7,14; 1.2#12,19;
1.3#3; 1.4#1,7,9,14,19
2/5/08 (Tues)Cryptoquotes: XVQB WJOIVQJ ULV YL SLB BIAJ IS ZSBJPJQB ZS MLEZBZOQ
YLIQ SLB FJIS MLEZBZOQ RLS'R BIAJ IS ZSBJPJQB ZS ULV. - MJPZOEJQ
ETSUJ LWPEK KUBRS UGGUF JNBVU CBGCK GVNKL KUWEO EWILK JNBVU
CBSUXL -LKOSNGV EIEOL 		2.3 #1, 2;
2.4 #2, 3 (affine);
3.1 #1, 4
2/12/08 (Tues)Jumbles ZEROF, FLOWEL, TYMIA, HYNWIN
SSA PSE TJX SME CRE STO THI GEI (padded)		 3.2 #7,9; 3.3 #4,7,11;
3.4 #1,2,9,10; 3.5 #1,3
2/19/08 (Tues)Use the Kasiski attack on the "Vigenère message" handout to find the keylength, key and decrypt. 4.1 #2,7,8,9; 4.3 #1,4,10
VIGENERE TEXT (505 characters)
qfxlb mwbuy rwdmg sydua ianks bevgw hyhma uefsr vsbnm qrkyn aeffe nlmay
roxeo gqlhs slhow xrwiz svsal ycinj iorxv dsfew fwivi knfjb ipbfu nyxbj
muwje wtyvm pcvli cyada lylku hxlrt kcphv fwowi qoqmx lrxel qielq pivak
yarss lxyvi qdyir sasbv erlkj liigd ewexr vmbiv rlxyw mqwmu povfv lsrgg
vdsla keher qbebr wbfsi vtbjq nilrs tkyee lulwm flexe cnldy mpfgd mxvrw
jnlif mrdig gkjuy kulmy vitju yopnl yhwgv wdwiw nftyr kyaib jvrkx girnf
tmstu gcivi fkjoh mrvjb iaugb yryzt ulwea vqlmx ueunm gwmdc svfsd xwiaa
elwwg mtcih ygwcg eavjl mkbfe gixeq jihel kegis slxcw qnlul meyai neytz
jcrqn lxwsq cmjux mbfqf wovdb
2/26/08 (Tues)Friedman attack on last week's "Vigenère message" 4.4 #5,10; 4.5 #1,2
3/4/03Find key for Z/26 Hill Cipher B=3, e(DAA BBA CDB)=(DUD DAB IFK), and key for Z/17 Hill cipher with B=3: e(100 3AB 13F)=(162 006 FG5). (G=16=-1) 8.1 #1,2; 8.2 #1; decrypt Hill cipher TZZZ AZIZ SSTS using probable word 'BEARS', B=2
3/9Find (x+1)-1 and (x2+1)-1 in F4, F8 and in F256 = F2[x]/P,
where P= x8 + x4 + x3 + x + 1.		 7.3 #5; 7.5 #3,4;   19.4 #5,7;   26.1 #2,3;
26.4 #1,2,3;   26.5 #3,4
3/25Midterm Exam (Open book, open note exam)
4/8Given RSA modulus N=667 and e=3, decrypt (101, 717, 376);
Find the Diffe-Hellman key, with prim.root 2 mod p=59, given X=20 and Y=3. 		10.2 #2,4,8;   12.5 #2,4,5,10   13.6 #2,3
4/15 Find all square roots of 2 modulo p for p=17, 31, 103, 1999, 4001 10.4 #1,2,3 (header=98 for #3);
12.6 #4,10   13.8 #3,4;   15.5 #1,5,7,14
4/22 A. Using 22.5, find a square root of 6 mod 1997, and of 2 mod 4001
B. For N=250,997 an oracle says x=126,250 is a square root of 9 mod N. Factor N, and find all solutions to x^2=4 mod N.
C. For RSA with modulus N and public key e=5, find the decryption key d. 		13.2 #3,4;    
13.3 #3,5,6
22.5 #4
4/29Use the Solovay-Strassen test to show that 1729 isn't prime 16.1 #1,4   16.6 #2,5
24.1 #1,3     27.1 #2,6,10
5/2 1. Use a method in this course to factor n=232+1 = 4,294,967,297     (Euler did this in 1732 at the age of 25.)
2. For the elliptic curve y2=x3-1 modulo 5, G=(3,1) and P=(0,2), find e so that Ge=P.
5/12Term paper due by noon
5/14Final Exam (4-7 PM) in ARC 207

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Charles Weibel / weibel@math.rutgers.edu / April 15, 2008