Question

1. Consider each of the following encryption scheme and state whether the scheme provides perfect secrecy or not. Justify your answer by giving a detailed proof if your answer is Yes, a counterexample if your answer is No.An encryption scheme whose plaintext space consists of the integers ?={0, 1, ..., 12}and key generation algorithm chooses a uniform key from the key space . Suppose mod 13 and mod 13?={0, 1, ..., 12}????(?)=?+?????(?)=?―?

Answer #1

Enck(m) = m + k Deck(c) = c -k satisfies perfect secrecy

**Proof**: For any m, m0 ,c ∈ G, we have:

Pr [EncK(m) = c]

= Pr [K + m = c]

= Pr [K = c - m]

Since c-m is a constant value for chosen m and c, we are really considering the probabiltiy that a randomly chosen key is equal to their distance. Since all keys are equally likely and chosen from the key space G, this probabiltiy is equal to:

Since the choice of m was arbitrary, we have that Pr [EncK(m) = c] = Pr [EncK(m0 ) = c],

which is one of the definitions of perfect secrecy.

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Consider the following time series data.
Quarter
Year 1
Year 2
Year 3
1
2
4
5
2
4
5
8
3
1
3
4
4
7
9
10
(a)
Choose the correct time series plot.
(i)
(ii)
(iii)
(iv)
- Select your answer -Plot (i)Plot (ii)Plot (iii)Plot (iv)Item
1
What type of pattern exists in the data?
- Select your answer -Positive trend pattern, no
seasonalityHorizontal pattern, no seasonalityNegative trend
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Consider the following time series data.
Quarter
Year 1
Year 2
Year 3
1
2
5
7
2
0
2
6
3
5
8
10
4
5
8
10
(a)
Choose the correct time series plot.
(i)
(ii)
(iii)
(iv)
Plot (iii)- Select your answer -Plot (i)Plot (ii)Plot (iii)Plot
(iv)Item 1
What type of pattern exists in the data?
Positive trend pattern, no seasonality- Select your answer
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Data
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