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Section B: Mathematics and Cryptography

Section B Introduction

Cryptology underpins many protocols in cyber security and, by having an awareness of the fundamental classical and modern techniques in Cryptography and Cryptanalysis, we allow ourselves a broader understanding of how weaknesses can be avoided. The mathematics inherent in these cryptological techniques further enables us to be systematic, clear, and precise about our understanding and presentation of data, numbers, and figures.

What are you required to submit?

Section B: A single Word document saved with the filename

“[First Name][Last Name][Student ID] M&C.docx”.

E.g., “Alex Corner 31415926 M&C.docx”. There is a template Word document provided (CSMC_CW-section-B_answer_sheet.docx) in the Assessment area of the Blackboard site. The document for Section B should not exceed 10 pages.

Part 1: Classical Ciphers

• Decrypt the following ciphertext using a Caesar cipher. You may use Excel to help you.

TDSLWWTYOFPETXPMPLAZPE

(10 marks including 1 mark for identifying the quotation.)

• The following ciphertext has been obtained using a General Substitution cipher. Use an Excel spreadsheet to decrypt it. Explain all the steps of your working.

RSIUBZAWX JAWA MAFAHSUAM LC XARWAZ EDRP LC JSWHM JDW ZJS IDLCHN ZS EWADP RSMAX SWMLCDWN UASUHA MLM CSZ GDFA DRRAXX ZS RSIUBZAWX EARDBXA ZGAN JAWA TAJ LC CBIEAW DCM ZSS AKUACXLFA XSIA UASUHA USXZBHDZAM ZGDZ ZGAWA JSBHM CAFAW EA D CAAM TSW ISWA ZGDC GDHT D MSQAC RSIUBZAWX LC ZGA RSBCZWN DCM DXXBIAM ZGDZ SWMLCDWN UASUHA JSBHM CAFAW GDFA D CAAM TSW RSIUBZAWX XSIA ST ZGA OSFAWCIACZX DZZLZBMA ZSJDWM RWNUZSOWDUGN ZSMDN JAWA TSWIAM LC ZGDZ UAWLSM DCM ILWWSWX ZGA SHM DZZLZBMAX ZSJDWM RSIUBZAWX JGN JSBHM SWMLCDWN UASUHA CAAM ZS GDFA DRRAXX ZS OSSM RWNUZSOWDUGN LC DMMLZLSC ZS ZGA HLILZAM DFDLHDELHLZN ST RSIUBZAWX DCSZGAW UWSEHAI JLZG RWNUZSOWDUGN LC ZGSXA MDNX JDX ZGDZ RWNUZSOWDUGLR PANX GDM ZS EA MLXZWLEBZAM SFAW XARBWA RGDCCAHX XS ZGDZ ESZG UDWZLAX RSBHM XACM ACRWNUZAM ZWDTTLR SFAW LCXARBWA RGDCCAHX OSFAWCIACZX XSHFAM ZGDZ UWSEHAI EN MLXUDZRGLCO PAN RSBWLAWX JLZG XDZRGAHX GDCMRBTTAM ZS ZGALW JWLXZX OSFAWCIACZX RSBHM DTTSWM ZS XACM OBNX HLPA ZGAXA ZS ZGALW AIEDXXLAX SFAWXADX EBZ ZGA OWADZ IDXXAX ST SWMLCDWN UASUHA JSBHM CAFAW GDFA DRRAXX ZS UWDRZLRDH RWNUZSOWDUGN LT PANX GDM ZS EA MLXZWLEBZAM ZGLX JDN CS IDZZAW GSJ RGADU DCM USJAWTBH UAWXSCDH RSIUBZAWX ILOGZ XSIAMDN EARSIA NSB YBXZ RDCZ XACM ZGA PANX AHARZWSCLRDHHN JLZGSBZ ZGA WLXP ST LCZAWRAUZLSC

(40 marks including 3 marks for identifying the text and the connection to the letters KHK.)

• • Use the Vigenère cipher with keyword ALPHABET to encrypt your surname and first names (12 letters in all), e.g., `John Smith’ becomes plaintext `smithjohnsmi’.
  • The following ciphertext has been obtained using a Vigenère cipher. You are provided with a table of interval values and possible key sizes. Determine an appropriate key size and use an Excel spreadsheet to decrypt the ciphertext. Explain all of your steps and provide evidence such as suitable Excel screenshots.

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

(10 marks for part a) and 40 marks for part b) including 3 for identifying the original plaintext and 3 for its connection to the keyword.)

Part 2: Modern Ciphers

• Upper case ASCII letters A-Z are represented by the denary numbers 65-90; lower case ASCII letters a to z are represented by the denary numbers 97-122. The decimal value is converted to an 8-bit binary string and to encrypt any letter its 8-bit binary representation is combined with an 8-bit secret key using bitwise XOR.

A 3-letter word has been encrypted one letter at a time. The encrypted word is fgq. If the secret key is 00100010, then what was the original plaintext message.

(15 marks)

• Using an Excel spreadsheet encrypt 16 letters (using ASCII) from your surname and first name (e.g., ‘Alex Corner’ would be ‘CornerAlexCorne’) to produce a ciphertext in hexadecimal, by applying the first round of AES (Rijndael) as far as the Shift Row stage. Use the following key :

Explain all of your steps with supporting evidence (e.g., appropriate Excel screenshots) and provide the encrypted value at the end of each stage. I.e., after Add Key, after Byte Sub, and finally after Shift Row. Do not attempt the Mix Columns stage.

(35 marks)

• Use the RSA cipher to decrypt the word TfG. The public key is , . Decrypt a single letter at a time. You may use an Excel spreadsheet but for full marks you must explain each step of your calculation.

(30 marks)

• Alice’s RSA public key [; ] is stored in binary as

[1111010011000111; 00001011].

Eve wants to find Alice’s private key by factorising .

1. What are the prime factors of  and what is Alice’s private key?
   1. What is the maximum number of ASCII letters that can be encrypted in one go and sent to Alice (assuming the message has no padding)? Explain your answer.
   1. Alice decides to change the  value in her public key. Which of the following choices are not allowed? 3, 17, 19, 23, 31, 35, 45, 65. Explain your answer.

(20 marks)

Section B Hints

• When working in an Excel spreadsheet you will find it useful to take screenshots of your working, to show how you have proceeded through encryption/decryption. Only include relevant parts of the screen. E.g., in the Vigenère section you may want to just show a small section of the frequencies when explaining how you found each of the shift values. So (if using Windows) just use the Snipping Tool, shortcut Windows-Shift-S, to capture the relevant part.
• Your work should be readable, meaning that you should explain each step in your working. I’m looking to see your ability to apply the methods we have learnt, along with your ability to explain relevant parts of your working. Some parts may be repetitive and, in these cases, you may want to use phrases such as “Similar to the previous step, we can see from the screenshot that this shift is…”.
• If you are unsure how to present or word something, then ask.
• Word has an in-built equation editor, which you can use to make symbolic expressions more readable. E.g., instead of “x^3 mod n” we can instead have “”. A shortcut to enter equation mode is to press Alt and =. Certain symbols also have shortcuts. E.g.,  is entered by typing \oplus in the equation editor, before pressing space. Ask if you are unsure on how to enter a symbol, or use Detexify to draw and identify the symbol you are looking for.

Section B: Marking Criteria

Each of the questions in Section B has a number of marks displayed below it. For some questions, there are specific criteria to include in your explanation and working. There are a total of 200 marks available for Section B. Your mark out of 200 will translate to a Mark Range, which will then decide a Category, Grade, and %. (See the range of these in Section A: Marking Criteria.)

ANSWERING SHEET

Part 2: Mathematics and Cryptography

Answer Sheet 2324

You may readjust the table sizes, but you should only submit a maximum of 10 pages. Anything more than this will not be reviewed. Save this as

“[First Name][Last Name][Student ID] M&C.docx”.

You may delete this paragraph about filename and table sizes to get more space. The sizes of the table for each question suggest an appropriate upper limit on the amount of work to include.

Section A: Classical Ciphers

Section B: Modern Ciphers

You may want to make use of this symbol: .

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