Math 395 (An Introduction to Cryptography)

Prof. Weibel

Spring 2003

Homework Assignments

All assignments are due on Tuesdays.
Due dateSection/Problems Section/Problems
1/28/02your name in Caesar (k=13); 'cryptography' with k=1st letter of your last name 1.1#6,14; 1.2#13,18; 1.3#1; 1.4#1,6,9,12,19
2/4/02Cryptoquote: IDIED IVJIE DJUUJ TGEIT JHAPG SJEEJ QUJPI
JOXJT GOTSJ EEGLS JVGOR - LN EXADD JSSJTWJ		 2.3 #1,2; 2.4 #1,3 (affine); 3.1 #3,4
2/11/02Jumbles 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
2/18/02Kasiski attack on "VIGNERE" text below (incl. decrypt) 4.1 #2,7,8,9; 4.3 #1,4,10
VIGNERE TEXT (331 characters)
VVHQW VVRHM USGJG THKIH TSSEJ CHLSF CBGVW CRLRY QTFSV GAHWK CUHWA UGLQH NSLRL JSHBL TSPIS PRDXL JSVEE GHLQW KASSK UWEPW QTWVS PGOEL KCQYF NSVWL JSNIQ KGNRG YBWLW GOVIO KHKAZ KQKXZ GHYCE CMEIU JOQKW FWVEF QHKIJ RCLRL KBIEN QFRJL JSDHG RHLSF QTWLA UQRHW DMWLG USGIK KFLRY VCWVS PGPML KASSJ VOQXE GGVEY GGZML JCXXL JSVPA IVWIK VRDRY GFRJL JSLVE GGVEY GGEIA PUUIS FPBTG NWWMU CZRVT WGLRW UGUMN CZVILE
2/28/03Friedman attack on "VIGNERE" text above 4.4 #5,10; 4.5 #1,2
3/4/03Find key for Hill Cipher B=3, e(DAABBACDB)=(DUDDABIFK), and
key for the Affine Hill cipher B=2, e(GA HF BC)=(WH ZA HZ)		 8.1 #1,2; 8.2 #1; decrypt Hill cipher TZZZ AZIZ SSTS
using probable word 'BEARS', B=2
3/11/03Find (x+1)-1 and (x3+1)-1 in F2[x]/P, P= x8 + x4 + x3 + x + 1. 7.5 #4,7; 7.8 #1,2; 26.4 #2,4; 26.5 #1,3,5
3/25/031) Find DES subkeys if 64-bit key is [100...0];
2) Encrypt [000000100000100] using one round of DES with subkey [11...11]; 		3) Which inputs yield F from S-box #2?
4) Find DES' Initial Permutation
4/1/03Use ByteSub in the AES to encrypt the byte `21' And to decrypt the byte `39'
4/8/0210.2 #2*,4,7,8,    10.4 #1,2,3 (header=98 for #3)   (RSA and El Gamal) 12.5 #1,2*,   13.6 #3;   13.7 #2,8*
4/15/0212.6 #3,4,9,10;    12.7 #1,6 13.8 #4;    15.5 #1,3,5,6,7
4/22/02Build a square-root oracle for n=55, 399
solve x2=-1 modulo n=1013, 2003, 55, 399.		 13.2 #2,9; 13.3 #5,6
Factor 399 using oracle
4/29/02 See handout: describe numbers, polynomials and protocol to find secret combination 203
  (Need 2/3 and 4/6 on two committees to consent; one (x,y) is the same for both)		 16.1 #1,2; 16.2 #1,2;   24.1 #1,2; 24.2 #1,2;
Build oracle for n=899 & factor 899 using oracle

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Charles Weibel / weibel@math.rutgers.edu /April 28, 2003