25 Apr 2020 - Dr. Nithin Nagaraj

Lecture Nos. 11, 12, 13 & 14: History of Cryptography, One-Time Pad, Perfect Secrecy, Modern Trends in Cryptography, Break-the-Code Challenge

[Deadline: April 25, 2020]

Instructions: Do not assume anything over and beyond what was defined in the class (unless explicitly asked in the assignment to do so). Show your calculations in entirety. Justify all your answers with appropriate reasoning and arguments. Try to keep your answers brief, but sufficiently long to convey your ideas. If you want a hint to answer any of the questions, please ask me.

  1. Shannon’s maxim. Akbar has designed a very clever cryptographic algorithm which he has disclosed only to Birbal and no one else. Why is this security through obscurity not a good idea? What is Shannon’s maxim?

  2. In the Cryptology $=$ Cricket analogy, what would the umpires represent? According to you, which would be the Rahul Dravid or Don Bradman of all ciphers? Justify your answer.

  3. Ancient Ciphers. Other than the example given in class (the Mleccha dialect which Vidura used with Yudhisthira), give an example of an ancient cipher found in an ancient epic or literature (it could be from any culture - not necessarily Indian, but preferably dating way back in history).

  4. What is the total key space for a Vigenere Cipher (Polyalphabetic) with a $7$ syllabled word as the key?

  5. WWII Enigma. What is the significance of Bletchley Park?

  6. Shannon 1949. (a) From Shannon’s 1949 paper1, identify the specific paragraph where he is indirectly referring to Chaotic Transformations. (b) Pick out the paragraph in Shannon’s 1949 paper which is an answer to Question 1 above.

  7. Perfect Secrecy. Design a binary cryptosystem (different from One-Time Pad or OTP) which satisfies perfect secrecy. Mathematically prove that your system indeed satisfies perfect secrecy. Remember to specify complete details of your cryptosystem.

  8. New Directions in Cryptography. Come up with a different analogy than the mixing-paint analogy for the Merkle-Diffie-Hellman secure key exchange protocol. The analogy need not be mathematical, but it should convey the essential idea of the protocol.

  9. RSA. On what ‘hard’ problem does RSA’s security rests?

  10. Recent trends in Cryptography. Explain the workings of any one of the following: (a) Quantum cryptography, (b) DNA cryptography, (c) Chaos-based cryptography.

  11. Break-the-Code Challenge. The following SMS was sent by a friend. Please help me decipher:

        (1)(2)(3)(4)    (3)(2)(2)    (3)(4)   (1)  (3)(1)(3)(3)(3)(3)    (4)(3)(1)(1)(3)(2)

    (1)(2)(4)(4)(3)(2)    (3)(2)(3)(2)    (3)(3)(2)  (1)(2)(1)    (3)(2)(2)    (3)(3)(2)

        (2)(1)(3)(2)  (1)(3)(1)    (1)(2)(2)(1)    (1)(3)(3).

        8,4,4,7    6,6,3    4,7    2    3,2,4,7,5,9

        7,4,6,7,5,3   7,8,9,9,5,3    6,6,2,3    9,6,8   4,3,8

        6,6,3   9,6,8  4,2,8,3    4,6,8    8,4,3,6    2,5,5.

    Please give me your logic as to how you broke the above cipher.

  1. Shannon’s 1949 Paper on Cryptography ↩