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MATH 187A Introduction to Cryptography

HOMEWORK 1

Instructions. You can collaborate with up to two other students on the homework. Prob-lems should be solved together, not divided up between partners. You must write the solu-tions on your own in your own words, though. Homework must be submitted through Gradescope by 11:59pm PST on the due date, and there are no exceptions to this rule.

        You will be able to look at your scanned work before submitting it. Please ensure that your submission is legible (neatly written and not too faint) or your homework may not be graded. By turning in your work, you acknowledge that the work contained in the document is your own and you did not engage in any academic misconduct.

        Students should consult the class notes, lecture slides, instructor, and TAs when they need help with homework. Students should not look for answers to homework problems in other texts or sources, including the internet. You may ask questions about the homework in office hours and on Zulip. However, you should only use Zulip to ask for clarifications on the homework problems. Publicly posting any part of your work on Zulip or anywhere else will be considered cheating, and the author of the post will fail the class immediately!

        Your assignments in this class will be evaluated not only on the correctness of your an-swers, but on your ability to present your ideas clearly and logically. You should always explain how you arrived at your conclusions and justify your answers with mathemat-ically sound reasoning. Whether you use formal proof techniques or write a more informal argument for why something is true, your answers should always be well-supported. Your goal should be to convince the reader that your results and methods are sound.

        All problems have equal weight unless otherwise specified.

Key concepts: Caesar cipher, Vigen`ere cipher, rectangular transposition, Playfair cipher

1. Make a table with all 26 possible Caesar shift decryptions for the ciphertext

PGTND JHXRZ DUODD B

and decide which key was used and what the plaintext said.

Note: It is possible to do your favorite programming language for this problem. The first part of your answer must be given in the table format, as shown below. The plaintext must look like actual English with spaces and punctuation.

2. The ciphertext

EERIH NTSAC CIVEO NANIS GSATP DIIUY TT

was encoded using a rectangular transposition.

(a) What are the possible dimensions of the grid used?

(b) What are the possible lengths of the permutation used as key?

(c) Find the key with which it was encrypted and decrypt the message.

3. The ciphertext

XEIGI TIIMP XEMOX VXEVB IPXBT PIXWQ JFJQC QLOIB WQIMW PSRXE

was encrypted using a Vigen`ere cipher with a 2-letter keyword.

(a) How many 2-letter keywords are there for Vigen`ere?

(b) Decrypt the message and find the keyword used to encrypt it.

4.      (a) Construct the Playfair key using the keyphrase PANDEMIC.

(b) Use it to encrypt

DELTA VARIANT

Your answer should be in 5-grams.

(c) How many possible keys are there for a Playfair cipher? Justify your answer.

5. (Bonus, up to 10%) Decrypt the message

CNGRTLTNSYFGRDTTVNTHGHTHSSNTRLLYNNCRYPTN.