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• Explain the meaning of “Kirchhoff’s Principle” and its relevance to the design of modern ciphers.
• Outline the principles of the cipher block chaining (CBC) mode of operation, and explain the reasons behind its use.
• Compression methods are typically used to prevent the use of data redundancy in cryptanalysis.

Calculate the theoretical maximum compression ratio which can be achieved for the following message (M2):

M2 = 1001111111

• Steve has managed to intercept two of Bob‘s messages to Alice (m1=42813, m2=39667)  with their respective RSA digital signatures  (s1=33121, s2=16879).

Explain with numerical examples two methods that Steve may use to forge Bob’s signature.

It is assumed that the following parameters of the RSA digital signature scheme used are known to Steve

RSA modulus N=49163

The exponent of e=151

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Let 𝐸 be the elliptic curve  =  + 𝑥 + 7 over the field 13 13 We regard 𝐸 as an Abelian group in the usual way.

• Explain the meaning of “group order” in number theory, then find the order of the above group and indicate whether or not this is a cyclic group.
• Find an integer 𝑖 ≥ 0 such that

𝑖(11,6) = (2, 2)     in 𝐸                 and explain your working in details

• Find all pairs of points (P, Q) such that:

P + Q = 0                         and explain your working in detail.

• Alice has received the encrypted message {C1, C2} from Bob,

where:

C1= (2,2)

C2= 5

Explain in detail how to decrypt Alice’s message, assuming the Elgamal encryption algorithm with the above group (𝐸) was used to encrypt it.

You are also given the following information:

The generator point: G= (11,6)

Alice’s secret key: a=2

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