Homework 2: Crypto Basics

CSC 466/566 
Computer Security Homework 2: Crypto Basics
Homework 2: Crypto Basics
This homework is due Wednesday, February 23, 2022 at 11:59 p.m. and counts for 5% of your
course grade. Late submissions on the next day (24 hours) will be penalized by 30%. Submission
within second and third day (24-72 hours) will penalized by 60%. We will not accept any submissions after that. If you have a conflict due to travel, interviews, etc., please plan accordingly and
turn in your homework early.
Please submit one pdf file to D2L named [Your UA NETID]_HW1.pdf. Please do not submit an
image of your handwritten solutions. Make sure to comment your code with clear explanations and
be sure to cite any references used.
We encourage you to discuss the problems and your general approach with other students in the
class. However, the answers you turn in must be your own original work, and you are bound by the
Honor Code. Solutions must be submitted electronically via D2L following the instructions at the
end of this document.
To solve some of these problems, you might need to write some short programs; submit them with
your answers. We recommend Python, but you may use any common language or numerical package.
1. (20 points) Here is some ciphertext that was produced by a simple substitution cipher that we
learned about in class:
OBRGXIMYAZZAWCATBNMUYYHAZNVGFCXPVVSIJSVLKIFAVGBIECAZSBWGRGRQWUCHMMOCYE
FLGQQNKFSHQMGYALNKCIJQVEKVWXNFOYFYQBESGOYTXMAYTXSISNBPMSGOJBKFWRUTTMLS
BNQMLLRGFNZUAWHZLBRVZGHUVZMCKJEHSLSWGXCNZYEXRIMLPXRIXNUXRNSNRPHFDHBMAY
WKHTKNGNUXRNJUVGMYNYEYNLYYGPGYFSBNQQWUCHMMSLRWTFDYQRNOJUEWNLVUZIDHWXLH
TLKNEXMALBRQGUMMGXCUFXLHTLLLRTROJYFIDHLIGADLUBVXENSCALVCDFFIQCFAHISILU
XXZXNUAMZAWISRNOJYKMQYECGRSBWHAHLUFBBPDPWLJBRYOCYEAYSVYXSISPRKSNZYPHMM
WKHXMWWMGAZNEOFMDHKORMGOKNUHTAZQRAZPWBRTQXGZFMTJAXUTRNWCAPZLUFRODLFYFL
GUKHRODLTYRGRYWHNLRIUCNMDXOCGAKIFAQXKUQMVGZFDBVLSIJSGADLWCFGNCFMGTMWWI
STBIMHGKXBSPVGFVWHRYHNWXSKNGHLBENHYYQPZLXUEXNHDSBGDQZIXGNQKNUXCCKUFMQI
MMRYEYUNFHEUDIAZVUJWNGQYSFVSDNZYFNOLWGRBLJGLGTMWWISKZJAXVMXCFVEBMAAHTB
SNGUPENMWCGBRIFFLHMYOBBBRNZIEHTAZFLTBKMUVGSYVQVMGNZYROHFKISPZLOBBVZHLB
BKNOYBYRTHVYELSUFXGADJJISBSUTFRPZSGZPTQLQCAZHNGHGADMCCYEEODARGDLSFQHDM
FIGKZCKYNLDWGHQEDPQHRBSBWLNKDBAMFNOJDSJTFIFMYHZXWXZHQYLBNGSQAWRHMWWQNK
HMVYPEZLWXUXVCDFAHSQSMGXOLWWVHTMLCZXHHOUVMHHYZBKQYAHSHQWWGRGSMFIEPHFDB
RMTLFBVLZLESOTBEXIEYQYKBFNOJDCRLAOLWEHRMWMGADYFYZRRZJIAMHYJQVMGIMNQXKU
QNUXUUDORHENAGRMGULCFUDCFANEHNLFRTGYSXBYXIMLBIOIFYAMGUKWBNMNWXSHQGGLRM
GUFYVMGYJHHFDLAWNEROHYEBNLANLHQNZYABBYKNPTKWMFNMHIFMJBSBJYTTQXLIPHLGAM
FTQCSN
Assume that encrypting with the key letter A results in no change, B results in an increment by
one place in the alphabet, C results in an increment by two places, and so on.
What is the key? (Show your work.)
2. Here is a Python dictionary of the relative frequency of letters in English text:
{ "A": .08167, "B": .01492, "C": .02782, "D": .04253, "E": .12702, "F": .02228,
"G": .02015, "H": .06094, "I": .06966, "J": .00153, "K": .00772, "L": .04025,
"M": .02406, "N": .06749, "O": .07507, "P": .01929, "Q": .00095, "R": .05987,
"S": .06327, "T": .09056, "U": .02758, "V": .00978, "W": .02360, "X": .00150,
"Y": .01974, "Z": .00074 }
Here is some plaintext:
ethicslawanduniversitypolicieswarningtodefendasystemyouneedtobeabletot
hinklikeanattackerandthatincludesunderstandingtechniquesthatcanbeusedt
ocompromisesecurityhoweverusingthosetechniquesintherealworldmayviolate
thelawortheuniversitysrulesanditmaybeunethicalundersomecircumstancesev
enprobingforweaknessesmayresultinseverepenaltiesuptoandincludingexpuls
ioncivilfinesandjailtimeourpolicyineecsisthatyoumustrespecttheprivacya
ndpropertyrightsofothersatalltimesorelseyouwillfailthecourseactinglawf
ullyandethicallyisyourresponsibilitycarefullyreadthecomputerfraudandab
useactcfaaafederalstatutethatbroadlycriminalizescomputerintrusionthisi
soneofseverallawsthatgovernhackingunderstandwhatthelawprohibitsifindou
btwecanreferyoutoanattorneypleasereviewitsspoliciesonresponsibleuseoft
echnologyresourcesandcaenspolicydocumentsforguidelinesconcerningproper
The population variance of a finite population X of size N and mean µ is given by
Var(X) = 1
N
N
∑
i=1
(xi − µ)
2
.
(a) (10 points) What is the population variance of the relative letter frequencies in English
text?
(b) (10 points) What is the population variance of the relative letter frequencies in the given
plaintext?
(c) (20 points) For each of the following keys — yz, xyz, wxyz, vwxyz, uvwxyz — encrypt
the plaintext with a Vigenère cipher and the given key, then calculate and report the
population variance of the relative letter frequencies in the resulting ciphertext. Describe
and briefly explain the trend in this sequence of variances.
(d) (20 points) Viewing a Vigenère key of length k as a collection of k independent Caesar
ciphers, calculate the mean of the frequency variances of the ciphertext for each one.
(E.g., for key yz, calculate the frequency variance of the even numbered ciphertext
2
characters and the frequency variance of the odd numbered ciphertext characters. Then
take their mean.) Report the result for each key in part (c). Is the mean variance like
those observed in part (b)? Part (c)? Briefly explain.
(e) (10 points) Consider the ciphertext that was produced with key uvwxyz. In part (d), you
calculated the mean of six variances for this key. Revisit that ciphertext, and calculate
the mean of the frequency variances that arise if you had assumed that the key had
length 2, 3, 4, and 5. Does this suggest a variant to the Kasiski attack? (Don’t say no!)
Please provide a Brief explanation.
3. (10 points) Are all the 56 bits of the DES key used an equal number of times in the Ki ?
Specify, for each of the Ki
, which bits are not used. Here, Ki
is the round key for round i.
3