It looks lengthy assignment based on definition and algorithms. Please find the attached document.

Problem 1
1. Substitution Cipher – Substitution cipher is a method in which each unit from the plaintext is substituted with the unit of ciphertext. The units may be single letters, pairs, triples or so on depending upon the agreeing terms.
Message Space {∀c∈A}
Gen It is an algorithm which generates the key to encrypt and decrypt the text.
Enc It is an algorithm which means that if one message is encrypted multiple times, it may yields a different ciphertext every time.
Dec It is an algorithm which means that whichever is the ciphertext, it will yield the correct message from it.
2. Frequency analysis from Figure 1:
JGRMQOYGHMVBJWRWQFPWHGFFDQGFPFZRKBEEBJIZQQOCIBZKLFAFGQVFZFWWEOGWOPFGFHWOLPHLRLOLFDMFGQWBLWBWQOLKFWBYLBLYLFSFLJGRMQBOLWJVFPFWQVHQWFFPQOQVFPQOCFPOGFWFJIGFQVHLHLROQVFGWJVFPFOLFHGQVQVFILEOGQILHQFQGIQVVOSFAFGBWQVHQWIJVWJVFPFWHGFIWIHZZRQGBABHZQOCGFHX
    Letters
    Frequency
    Percentage
    A
    3
    1.22
    B
    12
    4.91
    C
    3
    1.22
    D
    2
    0.81
    E
    4
    1.63
    F
    37
    15.16
    G
    19
    7.78
    H
    14
    5.73
    I
    9
    3.68
    J
    9
    3.68
    K
    3
    1.22
    L
    17
    6.96
    M
    4
    1.63
    N
    0
    0
    O
    16
    6.55
    P
    10
    4.09
    Q
    26
    10.65
    R
    7
    2.86
    S
    2
    0.81
    T
    0
    0
    U
    0
    0
    V
    15
    6.14
    W
    21
    8.61
    X
    1
    0.41
    Y
    3
    1.22
    Z
    7
    2.86
Comparing the above the frequency analysis and the frequency histogram provided in the figure 2, we can assume that E is mapped to F (highest frequency in both), T is mapped to Q (second highest frequency) and so on.
Mapped elements...